TSTP Solution File: SWW219+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW219+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:11 EDT 2023
% Result : Theorem 1.28s 1.59s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW219+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 21:41:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.51/0.56 start to proof:theBenchmark
% 1.26/1.52 %-------------------------------------------
% 1.26/1.52 % File :CSE---1.6
% 1.26/1.52 % Problem :theBenchmark
% 1.26/1.52 % Transform :cnf
% 1.26/1.52 % Format :tptp:raw
% 1.26/1.52 % Command :java -jar mcs_scs.jar %d %s
% 1.26/1.52
% 1.26/1.52 % Result :Theorem 0.190000s
% 1.26/1.52 % Output :CNFRefutation 0.190000s
% 1.26/1.52 %-------------------------------------------
% 1.26/1.52 %------------------------------------------------------------------------------
% 1.26/1.52 % File : SWW219+1 : TPTP v8.1.2. Released v5.2.0.
% 1.26/1.52 % Domain : Software Verification
% 1.26/1.52 % Problem : Fundamental Theorem of Algebra 437243, 1000 axioms selected
% 1.26/1.52 % Version : Especial.
% 1.26/1.52 % English :
% 1.26/1.52
% 1.26/1.52 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 1.26/1.53 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 1.26/1.53 % Source : [Bla11]
% 1.26/1.53 % Names : fta_437243.1000.p [Bla11]
% 1.26/1.53
% 1.26/1.53 % Status : Theorem
% 1.26/1.53 % Rating : 0.33 v8.1.0, 0.39 v7.5.0, 0.44 v7.4.0, 0.57 v7.3.0, 0.52 v7.1.0, 0.48 v7.0.0, 0.50 v6.4.0, 0.46 v6.3.0, 0.54 v6.2.0, 0.56 v6.1.0, 0.67 v6.0.0, 0.65 v5.5.0, 0.70 v5.4.0, 0.68 v5.3.0, 0.70 v5.2.0
% 1.26/1.53 % Syntax : Number of formulae : 1267 ( 363 unt; 0 def)
% 1.26/1.53 % Number of atoms : 3080 ( 768 equ)
% 1.26/1.53 % Maximal formula atoms : 13 ( 2 avg)
% 1.26/1.53 % Number of connectives : 1979 ( 166 ~; 56 |; 144 &)
% 1.26/1.53 % ( 240 <=>;1373 =>; 0 <=; 0 <~>)
% 1.26/1.53 % Maximal formula depth : 13 ( 5 avg)
% 1.26/1.53 % Maximal term depth : 7 ( 2 avg)
% 1.26/1.53 % Number of predicates : 78 ( 77 usr; 1 prp; 0-3 aty)
% 1.26/1.53 % Number of functors : 33 ( 33 usr; 8 con; 0-3 aty)
% 1.26/1.53 % Number of variables : 2854 (2802 !; 52 ?)
% 1.26/1.53 % SPC : FOF_THM_RFO_SEQ
% 1.26/1.53
% 1.26/1.53 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 1.26/1.53 % 2011-03-01 11:37:43
% 1.26/1.53 %------------------------------------------------------------------------------
% 1.26/1.53 %----Relevant facts (997)
% 1.26/1.53 fof(fact_ext,axiom,
% 1.26/1.53 ! [V_g_2,V_f_2] :
% 1.26/1.53 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 1.26/1.53 => V_f_2 = V_g_2 ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_rp,axiom,
% 1.26/1.53 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ).
% 1.26/1.53
% 1.26/1.53 fof(fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096,axiom,
% 1.26/1.53 ! [V_x_2,V_z_2] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r)
% 1.26/1.53 => ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_z_2)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)
% 1.26/1.53 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_s1m,axiom,
% 1.26/1.53 ! [V_z] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z),v_r)
% 1.26/1.53 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_z))) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096,axiom,
% 1.26/1.53 ? [B_f] :
% 1.26/1.53 ! [B_x] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B_f,B_x)),v_r)
% 1.26/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(B_f,B_x))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_x))))) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_s,axiom,
% 1.26/1.53 ! [B_y] :
% 1.26/1.53 ( ? [B_x] :
% 1.26/1.53 ( ? [B_z] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.26/1.53 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) )
% 1.26/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
% 1.26/1.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,v_s____) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_th,axiom,
% 1.26/1.53 ! [B_n] :
% 1.26/1.53 ? [B_z] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.26/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096,axiom,
% 1.26/1.53 ! [V_n_2] :
% 1.26/1.53 ? [B_z] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.26/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n_2))))) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096,axiom,
% 1.26/1.53 ! [V_y_2] :
% 1.26/1.53 ( ? [B_z] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.26/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)))),V_y_2) )
% 1.26/1.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_s1,axiom,
% 1.26/1.53 ! [V_y_2] :
% 1.26/1.53 ( ? [B_z] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.26/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),V_y_2) )
% 1.26/1.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096,axiom,
% 1.26/1.53 ( ? [B_z] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.26/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
% 1.26/1.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_mth2,axiom,
% 1.26/1.53 ? [B_z] :
% 1.26/1.53 ! [B_x] :
% 1.26/1.53 ( ? [B_za] :
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_za),v_r)
% 1.26/1.53 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_za)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) )
% 1.26/1.53 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_z) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096,axiom,
% 1.26/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r)
% 1.26/1.53 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_real__of__nat__Suc,axiom,
% 1.26/1.53 ! [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)) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_norm__add__less,axiom,
% 1.26/1.53 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.26/1.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.26/1.53 => 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)) ) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_norm__triangle__ineq,axiom,
% 1.26/1.53 ! [V_y,V_x,T_a] :
% 1.26/1.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.26/1.53 => 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))) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_less__half__sum,axiom,
% 1.26/1.53 ! [V_b,V_a,T_a] :
% 1.26/1.53 ( class_Fields_Olinordered__field(T_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.26/1.53 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_gt__half__sum,axiom,
% 1.26/1.53 ! [V_b,V_a,T_a] :
% 1.26/1.53 ( class_Fields_Olinordered__field(T_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.26/1.53 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_real__of__nat__ge__zero,axiom,
% 1.26/1.53 ! [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)) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_norm__zero,axiom,
% 1.26/1.53 ! [T_a] :
% 1.26/1.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.26/1.53 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_norm__eq__zero,axiom,
% 1.26/1.53 ! [V_x_2,T_a] :
% 1.26/1.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.26/1.53 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.26/1.53 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_divide_Ozero,axiom,
% 1.26/1.53 ! [V_y,T_a] :
% 1.26/1.53 ( class_RealVector_Oreal__normed__field(T_a)
% 1.26/1.53 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_real__zero__not__eq__one,axiom,
% 1.26/1.53 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_norm__le__zero__iff,axiom,
% 1.26/1.53 ! [V_x_2,T_a] :
% 1.26/1.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.26/1.53 => ( 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))
% 1.26/1.53 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_zero__less__norm__iff,axiom,
% 1.26/1.53 ! [V_x_2,T_a] :
% 1.26/1.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.26/1.53 => ( 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))
% 1.26/1.53 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_divide__right__mono__neg,axiom,
% 1.26/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.26/1.53 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)) ) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_divide__right__mono,axiom,
% 1.26/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.26/1.53 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.26/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_divide__le__0__iff,axiom,
% 1.26/1.53 ! [V_b_2,V_a_2,T_a] :
% 1.26/1.53 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.53 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.26/1.53 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.26/1.53 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.53 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_zero__le__divide__iff,axiom,
% 1.26/1.53 ! [V_b_2,V_a_2,T_a] :
% 1.26/1.53 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
% 1.26/1.53 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.26/1.53 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.26/1.53 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.53 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_add__eq__0__iff,axiom,
% 1.26/1.53 ! [V_y_2,V_x_2,T_a] :
% 1.26/1.53 ( class_Groups_Ogroup__add(T_a)
% 1.26/1.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.26/1.53 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 1.26/1.53
% 1.26/1.53 fof(fact_divide__strict__right__mono__neg,axiom,
% 1.26/1.53 ! [V_c,V_a,V_b,T_a] :
% 1.26/1.53 ( class_Fields_Olinordered__field(T_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.26/1.53 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.53 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_divide__strict__right__mono,axiom,
% 1.26/1.54 ! [V_c,V_b,V_a,T_a] :
% 1.26/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.26/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_divide__neg__neg,axiom,
% 1.26/1.54 ! [V_y,V_x,T_a] :
% 1.26/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_divide__neg__pos,axiom,
% 1.26/1.54 ! [V_y,V_x,T_a] :
% 1.26/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.26/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_divide__pos__neg,axiom,
% 1.26/1.54 ! [V_y,V_x,T_a] :
% 1.26/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_divide__pos__pos,axiom,
% 1.26/1.54 ! [V_y,V_x,T_a] :
% 1.26/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.26/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_divide__less__0__iff,axiom,
% 1.26/1.54 ! [V_b_2,V_a_2,T_a] :
% 1.26/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.54 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.26/1.54 & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.26/1.54 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.54 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_zero__less__divide__iff,axiom,
% 1.26/1.54 ! [V_b_2,V_a_2,T_a] :
% 1.26/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.26/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
% 1.26/1.54 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.26/1.54 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.26/1.54 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.26/1.54 & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_real__of__nat__less__iff,axiom,
% 1.26/1.54 ! [V_m_2,V_n_2] :
% 1.26/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
% 1.26/1.54 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_real__of__nat__add,axiom,
% 1.26/1.54 ! [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)) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_norm__ge__zero,axiom,
% 1.26/1.54 ! [V_x,T_a] :
% 1.26/1.54 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.26/1.54 => 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)) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_norm__not__less__zero,axiom,
% 1.26/1.54 ! [V_x,T_a] :
% 1.26/1.54 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.26/1.54 => ~ 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)) ) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_real__of__nat__1,axiom,
% 1.26/1.54 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.26/1.54
% 1.26/1.54 fof(fact_real__0__le__divide__iff,axiom,
% 1.26/1.54 ! [V_y_2,V_x_2] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.28/1.54 <=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.28/1.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) )
% 1.28/1.54 & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.28/1.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_not__real__of__nat__less__zero,axiom,
% 1.28/1.54 ! [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)) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__add__minus__iff,axiom,
% 1.28/1.54 ! [V_a_2,V_x_2] :
% 1.28/1.54 ( 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)
% 1.28/1.54 <=> V_x_2 = V_a_2 ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__add__eq__0__iff,axiom,
% 1.28/1.54 ! [V_y_2,V_x_2] :
% 1.28/1.54 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.28/1.54 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_divide__nonpos__neg,axiom,
% 1.28/1.54 ! [V_y,V_x,T_a] :
% 1.28/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_divide__nonpos__pos,axiom,
% 1.28/1.54 ! [V_y,V_x,T_a] :
% 1.28/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.28/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_frac__le,axiom,
% 1.28/1.54 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.28/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 1.28/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_frac__less,axiom,
% 1.28/1.54 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.28/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 1.28/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_frac__less2,axiom,
% 1.28/1.54 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.28/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
% 1.28/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_divide__nonneg__neg,axiom,
% 1.28/1.54 ! [V_y,V_x,T_a] :
% 1.28/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_divide__nonneg__pos,axiom,
% 1.28/1.54 ! [V_y,V_x,T_a] :
% 1.28/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.28/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_nonzero__norm__divide,axiom,
% 1.28/1.54 ! [V_a,V_b,T_a] :
% 1.28/1.54 ( class_RealVector_Oreal__normed__field(T_a)
% 1.28/1.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.54 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__of__nat__Suc__gt__zero,axiom,
% 1.28/1.54 ! [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))) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__add__le__0__iff,axiom,
% 1.28/1.54 ! [V_y_2,V_x_2] :
% 1.28/1.54 ( 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))
% 1.28/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__0__le__add__iff,axiom,
% 1.28/1.54 ! [V_y_2,V_x_2] :
% 1.28/1.54 ( 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))
% 1.28/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__add__less__0__iff,axiom,
% 1.28/1.54 ! [V_y_2,V_x_2] :
% 1.28/1.54 ( 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))
% 1.28/1.54 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__0__less__add__iff,axiom,
% 1.28/1.54 ! [V_y_2,V_x_2] :
% 1.28/1.54 ( 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))
% 1.28/1.54 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_nat__less__real__le,axiom,
% 1.28/1.54 ! [V_m_2,V_n_2] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 1.28/1.54 <=> 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_m_2)) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_complex__mod__triangle__sub,axiom,
% 1.28/1.54 ! [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))) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__le__antisym,axiom,
% 1.28/1.54 ! [V_w,V_z] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 1.28/1.54 => V_z = V_w ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__le__trans,axiom,
% 1.28/1.54 ! [V_k,V_j,V_i] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 1.28/1.54 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__le__linear,axiom,
% 1.28/1.54 ! [V_w,V_z] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.28/1.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__le__refl,axiom,
% 1.28/1.54 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__of__nat__inject,axiom,
% 1.28/1.54 ! [V_m_2,V_n_2] :
% 1.28/1.54 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
% 1.28/1.54 <=> V_n_2 = V_m_2 ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_divide_Oadd,axiom,
% 1.28/1.54 ! [V_ya,V_y,V_x,T_a] :
% 1.28/1.54 ( class_RealVector_Oreal__normed__field(T_a)
% 1.28/1.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_less__eq__real__def,axiom,
% 1.28/1.54 ! [V_y_2,V_x_2] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.28/1.54 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.28/1.54 | V_x_2 = V_y_2 ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__less__def,axiom,
% 1.28/1.54 ! [V_y_2,V_x_2] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.28/1.54 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.28/1.54 & V_x_2 != V_y_2 ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_minus__divide__divide,axiom,
% 1.28/1.54 ! [V_b,V_a,T_a] :
% 1.28/1.54 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_divide_Ominus,axiom,
% 1.28/1.54 ! [V_y,V_x,T_a] :
% 1.28/1.54 ( class_RealVector_Oreal__normed__field(T_a)
% 1.28/1.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_minus__divide__right,axiom,
% 1.28/1.54 ! [V_b,V_a,T_a] :
% 1.28/1.54 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.54 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_norm__minus__cancel,axiom,
% 1.28/1.54 ! [V_x,T_a] :
% 1.28/1.54 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.54 => 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) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_real__add__left__mono,axiom,
% 1.28/1.54 ! [V_z,V_y,V_x] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.28/1.54 => 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)) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_norm__one,axiom,
% 1.28/1.54 ! [T_a] :
% 1.28/1.54 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.28/1.54 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_norm__divide,axiom,
% 1.28/1.54 ! [V_b,V_a,T_a] :
% 1.28/1.54 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.54 & class_RealVector_Oreal__normed__field(T_a) )
% 1.28/1.54 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_calculation,axiom,
% 1.28/1.54 ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
% 1.28/1.54 => ? [B_z] :
% 1.28/1.54 ! [B_w] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_w),v_r)
% 1.28/1.54 => 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_p),B_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_w))) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_lemma__NBseq__def,axiom,
% 1.28/1.54 ! [V_X_2,T_b] :
% 1.28/1.54 ( class_RealVector_Oreal__normed__vector(T_b)
% 1.28/1.54 => ( ? [B_K] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.54 & ! [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) )
% 1.28/1.54 <=> ? [B_N] :
% 1.28/1.54 ! [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))) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_lemma__NBseq__def2,axiom,
% 1.28/1.54 ! [V_X_2,T_b] :
% 1.28/1.54 ( class_RealVector_Oreal__normed__vector(T_b)
% 1.28/1.54 => ( ? [B_K] :
% 1.28/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.54 & ! [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) )
% 1.28/1.54 <=> ? [B_N] :
% 1.28/1.54 ! [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))) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_zero__less__two,axiom,
% 1.28/1.54 ! [T_a] :
% 1.28/1.54 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.54 => 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))) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_add__nonpos__neg,axiom,
% 1.28/1.54 ! [V_b,V_a,T_a] :
% 1.28/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.54 => 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)) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_add__neg__nonpos,axiom,
% 1.28/1.54 ! [V_b,V_a,T_a] :
% 1.28/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.54 => 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)) ) ) ) ).
% 1.28/1.54
% 1.28/1.54 fof(fact_add__strict__increasing2,axiom,
% 1.28/1.54 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.28/1.55 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__strict__increasing,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.28/1.55 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__nonneg__pos,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__pos__nonneg,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_complex__mod__minus__le__complex__mod,axiom,
% 1.28/1.55 ! [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)) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_nonzero__minus__divide__divide,axiom,
% 1.28/1.55 ! [V_a,V_b,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_real__of__nat__le__iff,axiom,
% 1.28/1.55 ! [V_m_2,V_n_2] :
% 1.28/1.55 ( 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_m_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_real__of__nat__zero__iff,axiom,
% 1.28/1.55 ! [V_n_2] :
% 1.28/1.55 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.28/1.55 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_real__of__nat__zero,axiom,
% 1.28/1.55 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_zero__reorient,axiom,
% 1.28/1.55 ! [V_x_2,T_a] :
% 1.28/1.55 ( class_Groups_Ozero(T_a)
% 1.28/1.55 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 1.28/1.55 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_linorder__neqE__linordered__idom,axiom,
% 1.28/1.55 ! [V_y,V_x,T_a] :
% 1.28/1.55 ( class_Rings_Olinordered__idom(T_a)
% 1.28/1.55 => ( V_x != V_y
% 1.28/1.55 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.55 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oab__semigroup__add(T_a)
% 1.28/1.55 => 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)) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__left__cancel,axiom,
% 1.28/1.55 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
% 1.28/1.55 <=> V_b_2 = V_c_2 ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__right__cancel,axiom,
% 1.28/1.55 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 1.28/1.55 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
% 1.28/1.55 <=> V_b_2 = V_c_2 ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__left__imp__eq,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.28/1.55 => V_b = V_c ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__imp__eq,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.28/1.55 => V_b = V_c ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__right__imp__eq,axiom,
% 1.28/1.55 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.55 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 1.28/1.55 => V_b = V_c ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_one__reorient,axiom,
% 1.28/1.55 ! [V_x_2,T_a] :
% 1.28/1.55 ( class_Groups_Oone(T_a)
% 1.28/1.55 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 1.28/1.55 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__minus,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_equation__minus__iff,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.28/1.55 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__equation__iff,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
% 1.28/1.55 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2 ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__equal__iff__equal,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.28/1.55 <=> V_a_2 = V_b_2 ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 1.28/1.55 ! [V_n_2] :
% 1.28/1.55 ( 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))
% 1.28/1.55 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 1.28/1.55 ! [V_n_2] :
% 1.28/1.55 ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_real__of__nat__one,axiom,
% 1.28/1.55 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) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_nat__le__real__less,axiom,
% 1.28/1.55 ! [V_m_2,V_n_2] :
% 1.28/1.55 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
% 1.28/1.55 <=> 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_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__0__left,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Groups_Omonoid__add(T_a)
% 1.28/1.55 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__0,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.28/1.55 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_double__zero__sym,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 1.28/1.55 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__0__right,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Groups_Omonoid__add(T_a)
% 1.28/1.55 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add_Ocomm__neutral,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.28/1.55 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__le__cancel__right,axiom,
% 1.28/1.55 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__le__cancel__left,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__right__mono,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.55 => 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)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__left__mono,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.55 => 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)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__mono,axiom,
% 1.28/1.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__le__imp__le__right,axiom,
% 1.28/1.55 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__le__imp__le__left,axiom,
% 1.28/1.55 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__less__cancel__right,axiom,
% 1.28/1.55 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__less__cancel__left,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__strict__right__mono,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.55 => 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_c)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__strict__left__mono,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.55 => 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)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__strict__mono,axiom,
% 1.28/1.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__less__imp__less__right,axiom,
% 1.28/1.55 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.28/1.55 => ( 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_c))
% 1.28/1.55 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__less__imp__less__left,axiom,
% 1.28/1.55 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_one__neq__zero,axiom,
% 1.28/1.55 ! [T_a] :
% 1.28/1.55 ( class_Rings_Ozero__neq__one(T_a)
% 1.28/1.55 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_zero__neq__one,axiom,
% 1.28/1.55 ! [T_a] :
% 1.28/1.55 ( class_Rings_Ozero__neq__one(T_a)
% 1.28/1.55 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__zero,axiom,
% 1.28/1.55 ! [T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__0__equal__iff__equal,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
% 1.28/1.55 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_equal__neg__zero,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
% 1.28/1.55 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__equal__0__iff__equal,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__equal__zero,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
% 1.28/1.55 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_le__minus__iff,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__le__iff,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__le__iff__le,axiom,
% 1.28/1.55 ! [V_a_2,V_b_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_le__imp__neg__le,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.55 => 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)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_less__minus__iff,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__less__iff,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__less__iff__less,axiom,
% 1.28/1.55 ! [V_a_2,V_b_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_divide__zero__left,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.55 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_divide__zero,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.28/1.55 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__add__distrib,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oab__group__add(T_a)
% 1.28/1.55 => 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)) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__add,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => 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)) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__minus__cancel,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => 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 ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__add__cancel,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => 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 ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__divide__distrib,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.55 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_divide__1,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.55 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__divide__left,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.55 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__nonneg__nonneg,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__nonneg__eq__0__iff,axiom,
% 1.28/1.55 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 1.28/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__increasing,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.28/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__increasing2,axiom,
% 1.28/1.55 ! [V_a,V_b,V_c,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.28/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__nonpos__nonpos,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__pos__pos,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_pos__add__strict,axiom,
% 1.28/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.28/1.55 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__neg__neg,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__less__le__mono,axiom,
% 1.28/1.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_add__le__less__mono,axiom,
% 1.28/1.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.28/1.55 => 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)) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_not__one__le__zero,axiom,
% 1.28/1.55 ! [T_a] :
% 1.28/1.55 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.55 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_zero__le__one,axiom,
% 1.28/1.55 ! [T_a] :
% 1.28/1.55 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_not__one__less__zero,axiom,
% 1.28/1.55 ! [T_a] :
% 1.28/1.55 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.55 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_zero__less__one,axiom,
% 1.28/1.55 ! [T_a] :
% 1.28/1.55 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__0__le__iff__le,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_le__minus__self__iff,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__le__0__iff__le,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( 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))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__le__self__iff,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__0__less__iff__less,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_less__minus__self__iff,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Rings_Olinordered__idom(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__less__0__iff__less,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_neg__less__nonneg,axiom,
% 1.28/1.55 ! [V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
% 1.28/1.55 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_less__add__one,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.55 => 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))) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_right__minus,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => 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) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 1.28/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.28/1.55 <=> c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_left__minus,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => 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) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_ab__left__minus,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Groups_Oab__group__add(T_a)
% 1.28/1.55 => 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) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_minus__unique,axiom,
% 1.28/1.55 ! [V_b,V_a,T_a] :
% 1.28/1.55 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_divide__self__if,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.28/1.55 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.28/1.55 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_divide__self,axiom,
% 1.28/1.55 ! [V_a,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_right__inverse__eq,axiom,
% 1.28/1.55 ! [V_a_2,V_b_2,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.55 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 => ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 1.28/1.55 <=> V_a_2 = V_b_2 ) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_nonzero__minus__divide__right,axiom,
% 1.28/1.55 ! [V_a,V_b,T_a] :
% 1.28/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.55 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_zero__less__Suc,axiom,
% 1.28/1.55 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 1.28/1.55
% 1.28/1.55 fof(fact_lessI,axiom,
% 1.28/1.55 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 1.28/1.55
% 1.28/1.56 fof(fact_Suc__mono,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__eq__plus1,axiom,
% 1.28/1.56 ! [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)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__eq__plus1__left,axiom,
% 1.28/1.56 ! [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) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__iff__Suc__add,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__add__Suc2,axiom,
% 1.28/1.56 ! [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))) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__add__Suc1,axiom,
% 1.28/1.56 ! [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))) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_even__less__0__iff,axiom,
% 1.28/1.56 ! [V_a_2,T_a] :
% 1.28/1.56 ( class_Rings_Olinordered__idom(T_a)
% 1.28/1.56 => ( 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))
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096,axiom,
% 1.28/1.56 ? [B_s] :
% 1.28/1.56 ! [B_y] :
% 1.28/1.56 ( ? [B_x] :
% 1.28/1.56 ( ? [B_z] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.28/1.56 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) )
% 1.28/1.56 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__zeroE,axiom,
% 1.28/1.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le0,axiom,
% 1.28/1.56 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 1.28/1.56 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__0__eq,axiom,
% 1.28/1.56 ! [V_n_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.28/1.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__antisym,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.28/1.56 => V_m = V_n ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__trans,axiom,
% 1.28/1.56 ! [V_k,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_eq__imp__le,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( V_m = V_n
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__le__linear,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__refl,axiom,
% 1.28/1.56 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__inject,axiom,
% 1.28/1.56 ! [V_y,V_x] :
% 1.28/1.56 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 1.28/1.56 => V_x = V_y ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat_Oinject,axiom,
% 1.28/1.56 ! [V_nat_H_2,V_nat_2] :
% 1.28/1.56 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 1.28/1.56 <=> V_nat_2 = V_nat_H_2 ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__n__not__n,axiom,
% 1.28/1.56 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 1.28/1.56
% 1.28/1.56 fof(fact_n__not__Suc__n,axiom,
% 1.28/1.56 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__neq__Zero,axiom,
% 1.28/1.56 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Zero__neq__Suc,axiom,
% 1.28/1.56 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat_Osimps_I3_J,axiom,
% 1.28/1.56 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__not__Zero,axiom,
% 1.28/1.56 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat_Osimps_I2_J,axiom,
% 1.28/1.56 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Zero__not__Suc,axiom,
% 1.28/1.56 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__leD,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__SucE,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__SucI,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__le__mono,axiom,
% 1.28/1.56 ! [V_m_2,V_n_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__Suc__eq,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_not__less__eq__eq,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__n__not__le__n,axiom,
% 1.28/1.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__less__cases,axiom,
% 1.28/1.56 ! [V_P_2,V_n_2,V_m_2] :
% 1.28/1.56 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 1.28/1.56 => ( ( V_m_2 = V_n_2
% 1.28/1.56 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 1.28/1.56 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 1.28/1.56 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 1.28/1.56 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_gr0I,axiom,
% 1.28/1.56 ! [V_n] :
% 1.28/1.56 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__or__eq__imp__le,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 | V_m = V_n )
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__neq__implies__less,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => ( V_m != V_n
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__imp__le__nat,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__not__refl3,axiom,
% 1.28/1.56 ! [V_t,V_s] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 1.28/1.56 => V_s != V_t ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__not__refl2,axiom,
% 1.28/1.56 ! [V_m,V_n] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.28/1.56 => V_m != V_n ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_gr__implies__not0,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__irrefl__nat,axiom,
% 1.28/1.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__neqE__nat,axiom,
% 1.28/1.56 ! [V_y,V_x] :
% 1.28/1.56 ( V_x != V_y
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__eq__less__or__eq,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 | V_m_2 = V_n_2 ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__less__le,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 & V_m_2 != V_n_2 ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__nat__zero__code,axiom,
% 1.28/1.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__neq__iff,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( V_m_2 != V_n_2
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_neq0__conv,axiom,
% 1.28/1.56 ! [V_n_2] :
% 1.28/1.56 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__not__refl,axiom,
% 1.28/1.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_not__less0,axiom,
% 1.28/1.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__leE,axiom,
% 1.28/1.56 ! [V_n,V_k,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.28/1.56 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__leD1,axiom,
% 1.28/1.56 ! [V_n,V_k,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__leD2,axiom,
% 1.28/1.56 ! [V_n,V_k,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__eq__self__zero,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 1.28/1.56 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__le__mono,axiom,
% 1.28/1.56 ! [V_l,V_k,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.28/1.56 => 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)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__le__mono1,axiom,
% 1.28/1.56 ! [V_k,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => 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)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_trans__le__add2,axiom,
% 1.28/1.56 ! [V_m,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_trans__le__add1,axiom,
% 1.28/1.56 ! [V_m,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__add__left__cancel__le,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__add__right__cancel,axiom,
% 1.28/1.56 ! [V_n_2,V_k_2,V_m_2] :
% 1.28/1.56 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
% 1.28/1.56 <=> V_m_2 = V_n_2 ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__add__left__cancel,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.56 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
% 1.28/1.56 <=> V_m_2 = V_n_2 ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__add__assoc,axiom,
% 1.28/1.56 ! [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)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__is__0,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__add__left__commute,axiom,
% 1.28/1.56 ! [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)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__add__commute,axiom,
% 1.28/1.56 ! [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) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__iff__add,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Nat_Oadd__0__right,axiom,
% 1.28/1.56 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.28/1.56
% 1.28/1.56 fof(fact_plus__nat_Oadd__0,axiom,
% 1.28/1.56 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__add1,axiom,
% 1.28/1.56 ! [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)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__add2,axiom,
% 1.28/1.56 ! [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)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_double__eq__0__iff,axiom,
% 1.28/1.56 ! [V_a_2,T_a] :
% 1.28/1.56 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.28/1.56 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__less__SucD,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__lessD,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__SucE,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => V_m = V_n ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__trans__Suc,axiom,
% 1.28/1.56 ! [V_k,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__lessI,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => ( c_Nat_OSuc(V_m) != V_n
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__SucI,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__antisym,axiom,
% 1.28/1.56 ! [V_m,V_n] :
% 1.28/1.56 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 1.28/1.56 => V_m = V_n ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_not__less__less__Suc__eq,axiom,
% 1.28/1.56 ! [V_m_2,V_n_2] :
% 1.28/1.56 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 1.28/1.56 <=> V_n_2 = V_m_2 ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__less__eq,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__Suc__eq,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 | V_m_2 = V_n_2 ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_not__less__eq,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_gr0__conv__Suc,axiom,
% 1.28/1.56 ! [V_n_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 1.28/1.56 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__Suc0,axiom,
% 1.28/1.56 ! [V_n_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 1.28/1.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__Suc__eq__0__disj,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 1.28/1.56 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 | ? [B_j] :
% 1.28/1.56 ( V_m_2 = c_Nat_OSuc(B_j)
% 1.28/1.56 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__eq__Suc__le,axiom,
% 1.28/1.56 ! [V_m_2,V_n_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__Suc__eq__le,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__le__eq,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__imp__less__Suc,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__leI,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__less__Suc__eq,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 1.28/1.56 <=> V_n_2 = V_m_2 ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_Suc__le__lessD,axiom,
% 1.28/1.56 ! [V_n,V_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__Suc__shift,axiom,
% 1.28/1.56 ! [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)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__Suc,axiom,
% 1.28/1.56 ! [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)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__Suc__right,axiom,
% 1.28/1.56 ! [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)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_one__is__add,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
% 1.28/1.56 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.28/1.56 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.28/1.56 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__is__1,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.28/1.56 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.28/1.56 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.28/1.56 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__lessD1,axiom,
% 1.28/1.56 ! [V_k,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__add__eq__less,axiom,
% 1.28/1.56 ! [V_n,V_m,V_l,V_k] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.28/1.56 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__less__mono,axiom,
% 1.28/1.56 ! [V_l,V_k,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.28/1.56 => 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)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__less__mono1,axiom,
% 1.28/1.56 ! [V_k,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => 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)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_trans__less__add2,axiom,
% 1.28/1.56 ! [V_m,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_trans__less__add1,axiom,
% 1.28/1.56 ! [V_m,V_j,V_i] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__add__left__cancel__less,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__gr__0,axiom,
% 1.28/1.56 ! [V_n_2,V_m_2] :
% 1.28/1.56 ( 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_m_2,V_n_2))
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.28/1.56 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_not__add__less2,axiom,
% 1.28/1.56 ! [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) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_not__add__less1,axiom,
% 1.28/1.56 ! [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) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_One__nat__def,axiom,
% 1.28/1.56 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 1.28/1.56 ! [V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 1.28/1.56 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__refl,axiom,
% 1.28/1.56 ! [V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_mth1,axiom,
% 1.28/1.56 ? [B_x,B_z] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.28/1.56 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_poly__minus,axiom,
% 1.28/1.56 ! [V_x,V_p,T_a] :
% 1.28/1.56 ( class_Rings_Ocomm__ring(T_a)
% 1.28/1.56 => 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)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_poly__1,axiom,
% 1.28/1.56 ! [V_x,T_a] :
% 1.28/1.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.56 => 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) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_poly__add,axiom,
% 1.28/1.56 ! [V_x,V_q,V_p,T_a] :
% 1.28/1.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.28/1.56 => 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)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_poly__0,axiom,
% 1.28/1.56 ! [V_x,T_a] :
% 1.28/1.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.28/1.56 => 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) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_termination__basic__simps_I4_J,axiom,
% 1.28/1.56 ! [V_y,V_z,V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_minus__poly__code_I1_J,axiom,
% 1.28/1.56 ! [T_a] :
% 1.28/1.56 ( class_Groups_Oab__group__add(T_a)
% 1.28/1.56 => 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)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__poly__code_I1_J,axiom,
% 1.28/1.56 ! [V_q,T_a] :
% 1.28/1.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.28/1.56 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__poly__code_I2_J,axiom,
% 1.28/1.56 ! [V_p,T_a] :
% 1.28/1.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.28/1.56 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__fun__def,axiom,
% 1.28/1.56 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.28/1.56 ( class_Orderings_Oord(T_b)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.28/1.56 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__linear,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__eq__iff,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( V_x_2 = V_y_2
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.28/1.56 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__eq__refl,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( V_x = V_y
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__funD,axiom,
% 1.28/1.56 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.28/1.56 ( class_Orderings_Oord(T_b)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__antisym__conv,axiom,
% 1.28/1.56 ! [V_x_2,V_y_2,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_ord__eq__le__trans,axiom,
% 1.28/1.56 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oord(T_a)
% 1.28/1.56 => ( V_a = V_b
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I3_J,axiom,
% 1.28/1.56 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( V_a = V_b
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_ord__le__eq__trans,axiom,
% 1.28/1.56 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oord(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.56 => ( V_b = V_c
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I4_J,axiom,
% 1.28/1.56 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.28/1.56 => ( V_b = V_c
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__antisym,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.28/1.56 => V_x = V_y ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__trans,axiom,
% 1.28/1.56 ! [V_z,V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I5_J,axiom,
% 1.28/1.56 ! [V_x,V_y,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 => V_x = V_y ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I6_J,axiom,
% 1.28/1.56 ! [V_z,V_x,V_y,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__funE,axiom,
% 1.28/1.56 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.28/1.56 ( class_Orderings_Oord(T_b)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__le__cases,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__irrefl,axiom,
% 1.28/1.56 ! [V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__neq__iff,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( V_x_2 != V_y_2
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_not__less__iff__gr__or__eq,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.28/1.56 | V_x_2 = V_y_2 ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__less__linear,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 | V_x = V_y
% 1.28/1.56 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__antisym__conv3,axiom,
% 1.28/1.56 ! [V_x_2,V_y_2,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__neqE,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( V_x != V_y
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__imp__neq,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => V_x != V_y ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__not__sym,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__imp__not__less,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__imp__not__eq,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => V_x != V_y ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__imp__not__eq2,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => V_y != V_x ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__asym_H,axiom,
% 1.28/1.56 ! [V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.56 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I9_J,axiom,
% 1.28/1.56 ! [V_a,V_b,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.28/1.56 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_ord__eq__less__trans,axiom,
% 1.28/1.56 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oord(T_a)
% 1.28/1.56 => ( V_a = V_b
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I1_J,axiom,
% 1.28/1.56 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( V_a = V_b
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_ord__less__eq__trans,axiom,
% 1.28/1.56 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oord(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.56 => ( V_b = V_c
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I2_J,axiom,
% 1.28/1.56 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.28/1.56 => ( V_b = V_c
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__trans,axiom,
% 1.28/1.56 ! [V_z,V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I10_J,axiom,
% 1.28/1.56 ! [V_z,V_x,V_y,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__asym,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__cases,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => ( V_x != V_y
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_poly__zero,axiom,
% 1.28/1.56 ! [V_pa_2,T_a] :
% 1.28/1.56 ( ( class_Int_Oring__char__0(T_a)
% 1.28/1.56 & class_Rings_Oidom(T_a) )
% 1.28/1.56 => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.28/1.56 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_poly__eq__iff,axiom,
% 1.28/1.56 ! [V_q_2,V_pa_2,T_a] :
% 1.28/1.56 ( ( class_Int_Oring__char__0(T_a)
% 1.28/1.56 & class_Rings_Oidom(T_a) )
% 1.28/1.56 => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
% 1.28/1.56 <=> V_pa_2 = V_q_2 ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__not__less,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__not__le,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__le__less__linear,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__le,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.28/1.56 & V_x_2 != V_y_2 ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__le__not__le,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.28/1.56 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__le__less,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 | V_x_2 = V_y_2 ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_leI,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_not__leE,axiom,
% 1.28/1.56 ! [V_x,V_y,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__antisym__conv1,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__neq__le__trans,axiom,
% 1.28/1.56 ! [V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( V_a != V_b
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I12_J,axiom,
% 1.28/1.56 ! [V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( V_a != V_b
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_leD,axiom,
% 1.28/1.56 ! [V_x,V_y,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.28/1.56 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__imp__le,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_linorder__antisym__conv2,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Orderings_Olinorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.28/1.56 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.28/1.56 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__le__imp__less__or__eq,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 | V_x = V_y ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__le__neq__trans,axiom,
% 1.28/1.56 ! [V_b,V_a,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.56 => ( V_a != V_b
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I11_J,axiom,
% 1.28/1.56 ! [V_a,V_b,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.28/1.56 => ( V_a != V_b
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__less__le__trans,axiom,
% 1.28/1.56 ! [V_z,V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I7_J,axiom,
% 1.28/1.56 ! [V_z,V_x,V_y,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__le__less__trans,axiom,
% 1.28/1.56 ! [V_z,V_y,V_x,T_a] :
% 1.28/1.56 ( class_Orderings_Opreorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_xt1_I8_J,axiom,
% 1.28/1.56 ! [V_z,V_x,V_y,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_termination__basic__simps_I1_J,axiom,
% 1.28/1.56 ! [V_z,V_y,V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_termination__basic__simps_I2_J,axiom,
% 1.28/1.56 ! [V_y,V_z,V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 1.28/1.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_termination__basic__simps_I5_J,axiom,
% 1.28/1.56 ! [V_y,V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_termination__basic__simps_I3_J,axiom,
% 1.28/1.56 ! [V_z,V_y,V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_psize__eq__0__iff,axiom,
% 1.28/1.56 ! [V_pa_2,T_a] :
% 1.28/1.56 ( class_Groups_Ozero(T_a)
% 1.28/1.56 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.56 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_order__root,axiom,
% 1.28/1.56 ! [V_a_2,V_pa_2,T_a] :
% 1.28/1.56 ( class_Rings_Oidom(T_a)
% 1.28/1.56 => ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.56 <=> ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.28/1.56 | c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_le__Suc__ex__iff,axiom,
% 1.28/1.56 ! [V_l_2,V_k_2] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 1.28/1.56 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_decseq__def,axiom,
% 1.28/1.56 ! [V_X_2,T_a] :
% 1.28/1.56 ( class_Orderings_Oorder(T_a)
% 1.28/1.56 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 1.28/1.56 <=> ! [B_m,B_n] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_compl__le__compl__iff,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Lattices_Oboolean__algebra(T_a)
% 1.28/1.56 => ( 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))
% 1.28/1.56 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_compl__mono,axiom,
% 1.28/1.56 ! [V_y,V_x,T_a] :
% 1.28/1.56 ( class_Lattices_Oboolean__algebra(T_a)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.28/1.56 => 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)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_less__fun__def,axiom,
% 1.28/1.56 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.28/1.56 ( class_Orderings_Oord(T_b)
% 1.28/1.56 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.28/1.56 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.28/1.56 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_compl__eq__compl__iff,axiom,
% 1.28/1.56 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.56 ( class_Lattices_Oboolean__algebra(T_a)
% 1.28/1.56 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
% 1.28/1.56 <=> V_x_2 = V_y_2 ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_uminus__apply,axiom,
% 1.28/1.56 ! [V_x_2,V_A_2,T_b,T_a] :
% 1.28/1.56 ( class_Groups_Ouminus(T_a)
% 1.28/1.56 => 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)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_double__compl,axiom,
% 1.28/1.56 ! [V_x,T_a] :
% 1.28/1.56 ( class_Lattices_Oboolean__algebra(T_a)
% 1.28/1.56 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_add__0__iff,axiom,
% 1.28/1.56 ! [V_a_2,V_b_2,T_a] :
% 1.28/1.56 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.28/1.56 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
% 1.28/1.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 1.28/1.56 ! [V_a,T_a] :
% 1.28/1.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.56 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 1.28/1.56 ! [V_a,T_a] :
% 1.28/1.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.56 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_natceiling__eq,axiom,
% 1.28/1.56 ! [V_x,V_n] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 1.28/1.56 => ( 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)))
% 1.28/1.56 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_poly__bound__exists,axiom,
% 1.28/1.56 ! [V_p,V_r] :
% 1.28/1.56 ? [B_m] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 1.28/1.56 & ! [B_z] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),V_r)
% 1.28/1.56 => 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_p),B_z)),B_m) ) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_natceiling__real__of__nat,axiom,
% 1.28/1.56 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 1.28/1.56
% 1.28/1.56 fof(fact_natceiling__zero,axiom,
% 1.28/1.56 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_zero__le__natceiling,axiom,
% 1.28/1.56 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_natceiling__mono,axiom,
% 1.28/1.56 ! [V_y,V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_real__natceiling__ge,axiom,
% 1.28/1.56 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_natceiling__one,axiom,
% 1.28/1.56 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_natceiling__neg,axiom,
% 1.28/1.56 ! [V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.28/1.56 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_natceiling__le,axiom,
% 1.28/1.56 ! [V_a,V_x] :
% 1.28/1.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
% 1.28/1.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 1.28/1.56
% 1.28/1.56 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 1.28/1.57 ! [V_c,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 1.28/1.57 ! [V_d,V_c,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 1.28/1.57 ! [V_d,V_c,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 1.28/1.57 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natceiling__le__eq,axiom,
% 1.28/1.57 ! [V_a_2,V_x_2] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
% 1.28/1.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natceiling__le__eq__one,axiom,
% 1.28/1.57 ! [V_x_2] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 1.28/1.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natceiling__add,axiom,
% 1.28/1.57 ! [V_a,V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natceiling__add__one,axiom,
% 1.28/1.57 ! [V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__add__one,axiom,
% 1.28/1.57 ! [V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_ex__least__nat__less,axiom,
% 1.28/1.57 ! [V_n_2,V_P_2] :
% 1.28/1.57 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 1.28/1.57 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 1.28/1.57 => ? [B_k] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)
% 1.28/1.57 & ! [B_i] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
% 1.28/1.57 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 1.28/1.57 & hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_reals__Archimedean6a,axiom,
% 1.28/1.57 ! [V_r] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 1.28/1.57 => ? [B_n] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n),V_r)
% 1.28/1.57 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__eq,axiom,
% 1.28/1.57 ! [V_x,V_n] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 1.28/1.57 => ( 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)))
% 1.28/1.57 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 1.28/1.57 ! [V_n,V_z] :
% 1.28/1.57 ( 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)
% 1.28/1.57 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__real__of__nat,axiom,
% 1.28/1.57 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__zero,axiom,
% 1.28/1.57 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_zero__le__natfloor,axiom,
% 1.28/1.57 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__mono,axiom,
% 1.28/1.57 ! [V_y,V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.28/1.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__one,axiom,
% 1.28/1.57 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__neg,axiom,
% 1.28/1.57 ! [V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.28/1.57 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_real__natfloor__le,axiom,
% 1.28/1.57 ! [V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.28/1.57 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_le__natfloor,axiom,
% 1.28/1.57 ! [V_a,V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
% 1.28/1.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_le__natfloor__eq,axiom,
% 1.28/1.57 ! [V_a_2,V_x_2] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
% 1.28/1.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_le__natfloor__eq__one,axiom,
% 1.28/1.57 ! [V_x_2] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
% 1.28/1.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_real__natfloor__add__one__gt,axiom,
% 1.28/1.57 ! [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))) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_less__natfloor,axiom,
% 1.28/1.57 ! [V_n,V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
% 1.28/1.57 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__add,axiom,
% 1.28/1.57 ! [V_a,V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_natfloor__div__nat,axiom,
% 1.28/1.57 ! [V_y,V_x] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y)
% 1.28/1.57 => c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_Bseq__iff1a,axiom,
% 1.28/1.57 ! [V_X_2,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.57 => ( c_SEQ_OBseq(T_a,V_X_2)
% 1.28/1.57 <=> ? [B_N] :
% 1.28/1.57 ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_Bseq__iff,axiom,
% 1.28/1.57 ! [V_X_2,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.57 => ( c_SEQ_OBseq(T_a,V_X_2)
% 1.28/1.57 <=> ? [B_N] :
% 1.28/1.57 ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_Bseq__def,axiom,
% 1.28/1.57 ! [V_X_2,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.57 => ( c_SEQ_OBseq(T_a,V_X_2)
% 1.28/1.57 <=> ? [B_K] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.57 & ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_incseq__def,axiom,
% 1.28/1.57 ! [V_X_2,T_a] :
% 1.28/1.57 ( class_Orderings_Oorder(T_a)
% 1.28/1.57 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 1.28/1.57 <=> ! [B_m,B_n] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 1.28/1.57 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_real__of__nat__div4,axiom,
% 1.28/1.57 ! [V_x,V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x))) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__less__dividend,axiom,
% 1.28/1.57 ! [V_m,V_n] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.28/1.57 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__le__mono2,axiom,
% 1.28/1.57 ! [V_k,V_n,V_m] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__add__self2,axiom,
% 1.28/1.57 ! [V_a,V_b,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__add__self1,axiom,
% 1.28/1.57 ! [V_a,V_b,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__less,axiom,
% 1.28/1.57 ! [V_n,V_m] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_poly__div__minus__left,axiom,
% 1.28/1.57 ! [V_y,V_x,T_a] :
% 1.28/1.57 ( class_Fields_Ofield(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_poly__div__minus__right,axiom,
% 1.28/1.57 ! [V_y,V_x,T_a] :
% 1.28/1.57 ( class_Fields_Ofield(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__0,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__by__0,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__by__1,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__le__mono,axiom,
% 1.28/1.57 ! [V_k,V_n,V_m] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__le__dividend,axiom,
% 1.28/1.57 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__self,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__1,axiom,
% 1.28/1.57 ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 1.28/1.57
% 1.28/1.57 fof(fact_Bseq__iff3,axiom,
% 1.28/1.57 ! [V_X_2,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.57 => ( c_SEQ_OBseq(T_a,V_X_2)
% 1.28/1.57 <=> ? [B_k] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)
% 1.28/1.57 & ? [B_N] :
% 1.28/1.57 ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_Bseq__iff2,axiom,
% 1.28/1.57 ! [V_X_2,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.57 => ( c_SEQ_OBseq(T_a,V_X_2)
% 1.28/1.57 <=> ? [B_k] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)
% 1.28/1.57 & ? [B_x] :
% 1.28/1.57 ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_BseqI,axiom,
% 1.28/1.57 ! [V_X_2,V_K_2,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)
% 1.28/1.57 => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
% 1.28/1.57 => c_SEQ_OBseq(T_a,V_X_2) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_BseqD,axiom,
% 1.28/1.57 ! [V_X_2,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.57 => ( c_SEQ_OBseq(T_a,V_X_2)
% 1.28/1.57 => ? [B_K] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.57 & ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_real__of__nat__div__aux,axiom,
% 1.28/1.57 ! [V_x,V_d] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_d)
% 1.28/1.57 => c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_d)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x,V_d)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_d)),c_RealDef_Oreal(tc_Nat_Onat,V_d))) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_BseqI2_H,axiom,
% 1.28/1.57 ! [V_K_2,V_X_2,V_N_2,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.57 => ( ! [B_n] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2,B_n)
% 1.28/1.57 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2) )
% 1.28/1.57 => c_SEQ_OBseq(T_a,V_X_2) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_split__div_H,axiom,
% 1.28/1.57 ! [V_n_2,V_m_2,V_P_2] :
% 1.28/1.57 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
% 1.28/1.57 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.57 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.28/1.57 | ? [B_q] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q),V_m_2)
% 1.28/1.57 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q)))
% 1.28/1.57 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_split__div__lemma,axiom,
% 1.28/1.57 ! [V_m_2,V_q_2,V_n_2] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 1.28/1.57 => ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2),V_m_2)
% 1.28/1.57 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2))) )
% 1.28/1.57 <=> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__mult2__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult2__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__mult1__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__div__equality2,axiom,
% 1.28/1.57 ! [V_a,V_b,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__div__equality,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__mod__equality2,axiom,
% 1.28/1.57 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_div__mod__equality,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_norm__mult__less,axiom,
% 1.28/1.57 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 1.28/1.57 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 1.28/1.57 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 1.28/1.57 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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))) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 1.28/1.57 ! [V_rx,V_ly,V_lx,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 1.28/1.57 ! [V_rx,V_ly,V_lx,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 1.28/1.57 ! [V_ry,V_rx,V_lx,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 1.28/1.57 ! [V_ry,V_rx,V_lx,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 1.28/1.57 ! [V_z,V_y,V_x,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_crossproduct__noteq,axiom,
% 1.28/1.57 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 1.28/1.57 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.28/1.57 => ( ( V_a_2 != V_b_2
% 1.28/1.57 & V_c_2 != V_d_2 )
% 1.28/1.57 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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_c_2)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 1.28/1.57 ! [V_b,V_m,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_crossproduct__eq,axiom,
% 1.28/1.57 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 1.28/1.57 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.28/1.57 => ( 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_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 1.28/1.57 <=> ( V_w_2 = V_x_2
% 1.28/1.57 | V_y_2 = V_z_2 ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_minus__mult__right,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oring(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_minus__mult__left,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oring(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_minus__mult__commute,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oring(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_minus__mult__minus,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oring(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_square__eq__iff,axiom,
% 1.28/1.57 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.57 ( class_Rings_Oidom(T_a)
% 1.28/1.57 => ( 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)
% 1.28/1.57 <=> ( V_a_2 = V_b_2
% 1.28/1.57 | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult_Ominus__right,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__right_Ominus,axiom,
% 1.28/1.57 ! [V_x,V_xa,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult_Ominus__left,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__left_Ominus,axiom,
% 1.28/1.57 ! [V_y,V_x,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__cancel2,axiom,
% 1.28/1.57 ! [V_n_2,V_k_2,V_m_2] :
% 1.28/1.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
% 1.28/1.57 <=> ( V_m_2 = V_n_2
% 1.28/1.57 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__cancel1,axiom,
% 1.28/1.57 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 1.28/1.57 <=> ( V_m_2 = V_n_2
% 1.28/1.57 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__is__0,axiom,
% 1.28/1.57 ! [V_n_2,V_m_2] :
% 1.28/1.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.57 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.57 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__0__right,axiom,
% 1.28/1.57 ! [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) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__0,axiom,
% 1.28/1.57 ! [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) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_times__divide__eq__right,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_times__divide__times__eq,axiom,
% 1.28/1.57 ! [V_w,V_z,V_y,V_x,T_a] :
% 1.28/1.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_poly__mult,axiom,
% 1.28/1.57 ! [V_x,V_q,V_p,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Groups_Oab__semigroup__mult(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_norm__mult,axiom,
% 1.28/1.57 ! [V_y,V_x,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_nat__mult__assoc,axiom,
% 1.28/1.57 ! [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)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_nat__mult__commute,axiom,
% 1.28/1.57 ! [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) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__1__left,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Groups_Omonoid__mult(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__1,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__1__right,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Groups_Omonoid__mult(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult_Ocomm__neutral,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__class_Odistrib,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_combine__common__factor,axiom,
% 1.28/1.57 ! [V_c,V_b,V_e,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Osemiring(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult_Oadd__right,axiom,
% 1.28/1.57 ! [V_b_H,V_b,V_a,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__right_Oadd,axiom,
% 1.28/1.57 ! [V_y,V_x,V_xa,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult_Oadd__left,axiom,
% 1.28/1.57 ! [V_b,V_a_H,V_a,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__left_Oadd,axiom,
% 1.28/1.57 ! [V_ya,V_y,V_x,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_divisors__zero,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ono__zero__divisors(T_a)
% 1.28/1.57 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_no__zero__divisors,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ono__zero__divisors(T_a)
% 1.28/1.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__eq__0__iff,axiom,
% 1.28/1.57 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.57 ( class_Rings_Oring__no__zero__divisors(T_a)
% 1.28/1.57 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__zero__right,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Rings_Omult__zero(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__zero__left,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Rings_Omult__zero(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__right_Ozero,axiom,
% 1.28/1.57 ! [V_x,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult_Ozero__right,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__left_Ozero,axiom,
% 1.28/1.57 ! [V_y,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult_Ozero__left,axiom,
% 1.28/1.57 ! [V_b,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_norm__mult__ineq,axiom,
% 1.28/1.57 ! [V_y,V_x,T_a] :
% 1.28/1.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.57 => 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))) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__left__idem,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__idem,axiom,
% 1.28/1.57 ! [V_x,T_a] :
% 1.28/1.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_times_Oidem,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_nat__mult__1,axiom,
% 1.28/1.57 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 1.28/1.57
% 1.28/1.57 fof(fact_nat__1__eq__mult__iff,axiom,
% 1.28/1.57 ! [V_n_2,V_m_2] :
% 1.28/1.57 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 1.28/1.57 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.28/1.57 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_nat__mult__1__right,axiom,
% 1.28/1.57 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 1.28/1.57
% 1.28/1.57 fof(fact_nat__mult__eq__1__iff,axiom,
% 1.28/1.57 ! [V_n_2,V_m_2] :
% 1.28/1.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.28/1.57 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.28/1.57 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_le__square,axiom,
% 1.28/1.57 ! [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)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_le__cube,axiom,
% 1.28/1.57 ! [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))) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__le__mono1,axiom,
% 1.28/1.57 ! [V_k,V_j,V_i] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__le__mono2,axiom,
% 1.28/1.57 ! [V_k,V_j,V_i] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__le__mono,axiom,
% 1.28/1.57 ! [V_l,V_k,V_j,V_i] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.28/1.57 => 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)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_add__mult__distrib2,axiom,
% 1.28/1.57 ! [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)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_add__mult__distrib,axiom,
% 1.28/1.57 ! [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)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_Suc__mult__cancel1,axiom,
% 1.28/1.57 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
% 1.28/1.57 <=> V_m_2 = V_n_2 ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__less__eq__dividend,axiom,
% 1.28/1.57 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_m) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 1.28/1.57 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__cong,axiom,
% 1.28/1.57 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 1.28/1.57 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_zmod__simps_I4_J,axiom,
% 1.28/1.57 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__mult2,axiom,
% 1.28/1.57 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__mult1,axiom,
% 1.28/1.57 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__left__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__right__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__distrib,axiom,
% 1.28/1.57 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mod__trivial,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__distrib2,axiom,
% 1.28/1.57 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__self2,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__self1,axiom,
% 1.28/1.57 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__self3,axiom,
% 1.28/1.57 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__add__self2,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__add__self1,axiom,
% 1.28/1.57 ! [V_a,V_b,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__add__right__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__add__left__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__add__eq,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_zmod__simps_I2_J,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_zmod__simps_I1_J,axiom,
% 1.28/1.57 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__add__cong,axiom,
% 1.28/1.57 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 1.28/1.57 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_H,V_b_H),V_c) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__self4,axiom,
% 1.28/1.57 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__0,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__by__0,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__self,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__self1__is__0,axiom,
% 1.28/1.57 ! [V_a,V_b,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__mult__self2__is__0,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__eq__0__iff,axiom,
% 1.28/1.57 ! [V_d_2,V_m_2] :
% 1.28/1.57 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.57 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__minus__cong,axiom,
% 1.28/1.57 ! [V_a_H,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Oring__div(T_a)
% 1.28/1.57 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_H),V_b) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__minus__eq,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Oring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__less,axiom,
% 1.28/1.57 ! [V_n,V_m] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__lemma,axiom,
% 1.28/1.57 ! [V_q,V_b,V_r,V_c] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_c)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_r,V_b)
% 1.28/1.57 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c)),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_split__mod,axiom,
% 1.28/1.57 ! [V_k_2,V_n_2,V_P_2] :
% 1.28/1.57 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 1.28/1.57 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.57 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 1.28/1.57 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.57 => ! [B_i,B_j] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)
% 1.28/1.57 => ( V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
% 1.28/1.57 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_Suc__times__mod__eq,axiom,
% 1.28/1.57 ! [V_m,V_k] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_k)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__by__1,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__div__trivial,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.57 => c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__1,axiom,
% 1.28/1.57 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__Suc,axiom,
% 1.28/1.57 ! [V_n,V_m] :
% 1.28/1.57 ( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 1.28/1.57 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.28/1.57 & ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 1.28/1.57 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mod__less__divisor,axiom,
% 1.28/1.57 ! [V_m,V_n] :
% 1.28/1.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.57 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_zero__le__square,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring(T_a)
% 1.28/1.57 => 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_zero__le__mult__iff,axiom,
% 1.28/1.57 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( 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))
% 1.28/1.57 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.28/1.57 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.28/1.57 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__le__0__iff,axiom,
% 1.28/1.57 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( 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))
% 1.28/1.57 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.28/1.57 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.28/1.57 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__nonneg__nonneg,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__nonneg__nonpos,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__nonneg__nonpos2,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__nonpos__nonneg,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__nonpos__nonpos,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__ring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__right__mono,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__left__mono,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__mult__left__mono,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__comm__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__right__mono__neg,axiom,
% 1.28/1.57 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__ring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__left__mono__neg,axiom,
% 1.28/1.57 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__ring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__mono_H,axiom,
% 1.28/1.57 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.57 => 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)) ) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__mono,axiom,
% 1.28/1.57 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__semiring(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.57 => 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)) ) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_split__mult__pos__le,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__ring(T_a)
% 1.28/1.57 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 1.28/1.57 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.28/1.57 => 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)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_split__mult__neg__le,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.28/1.57 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.28/1.57 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 1.28/1.57 => 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)) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_not__square__less__zero,axiom,
% 1.28/1.57 ! [V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring(T_a)
% 1.28/1.57 => ~ 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)) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__less__cancel__right__disj,axiom,
% 1.28/1.57 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
% 1.28/1.57 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.57 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 1.28/1.57 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__less__cancel__left__disj,axiom,
% 1.28/1.57 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 1.28/1.57 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.57 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 1.28/1.57 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__less__cancel__left__pos,axiom,
% 1.28/1.57 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 1.28/1.57 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__pos__pos,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__pos__neg,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__pos__neg2,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_zero__less__mult__pos,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.57 => ( 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))
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_zero__less__mult__pos2,axiom,
% 1.28/1.57 ! [V_a,V_b,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.57 => ( 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))
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.57 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__less__cancel__left__neg,axiom,
% 1.28/1.57 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 1.28/1.57 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__neg__pos,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__neg__neg,axiom,
% 1.28/1.57 ! [V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__strict__right__mono,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__strict__left__mono,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__mult__strict__left__mono,axiom,
% 1.28/1.57 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__strict__right__mono__neg,axiom,
% 1.28/1.57 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__strict__left__mono__neg,axiom,
% 1.28/1.57 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_sum__squares__eq__zero__iff,axiom,
% 1.28/1.57 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.57 => ( 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)
% 1.28/1.57 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_add__scale__eq__noteq,axiom,
% 1.28/1.57 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 1.28/1.57 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.28/1.57 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => ( ( V_a = V_b
% 1.28/1.57 & V_c != V_d )
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_less__1__mult,axiom,
% 1.28/1.57 ! [V_n,V_m,T_a] :
% 1.28/1.57 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 1.28/1.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 1.28/1.57 => 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)) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 1.28/1.57 ! [V_m,V_a,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 1.28/1.57 ! [V_a,V_m,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 1.28/1.57 ! [V_m,T_a] :
% 1.28/1.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.57 => 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) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_eq__divide__eq,axiom,
% 1.28/1.57 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 1.28/1.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.57 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
% 1.28/1.57 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 )
% 1.28/1.57 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_divide__eq__eq,axiom,
% 1.28/1.57 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 1.28/1.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.57 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
% 1.28/1.57 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) )
% 1.28/1.57 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__divide__mult__cancel__right,axiom,
% 1.28/1.57 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_mult__divide__mult__cancel__left,axiom,
% 1.28/1.57 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.57 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.28/1.57
% 1.28/1.57 fof(fact_frac__eq__eq,axiom,
% 1.28/1.57 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
% 1.28/1.57 ( class_Fields_Ofield(T_a)
% 1.28/1.57 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.57 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => ( c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2)
% 1.28/1.58 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nonzero__eq__divide__eq,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.58 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
% 1.28/1.58 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nonzero__divide__eq__eq,axiom,
% 1.28/1.58 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.58 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
% 1.28/1.58 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide__eq__imp,axiom,
% 1.28/1.58 ! [V_a,V_b,V_c,T_a] :
% 1.28/1.58 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.58 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 1.28/1.58 => c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_eq__divide__imp,axiom,
% 1.28/1.58 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.58 ( class_Rings_Odivision__ring(T_a)
% 1.28/1.58 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 1.28/1.58 => V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__add1__eq,axiom,
% 1.28/1.58 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_square__eq__1__iff,axiom,
% 1.28/1.58 ! [V_x_2,T_a] :
% 1.28/1.58 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.28/1.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.28/1.58 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 1.28/1.58 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 1.28/1.58 ! [V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__ring__1(T_a)
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__mult1__if,axiom,
% 1.28/1.58 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.58 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.58 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.28/1.58 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__self2__is__id,axiom,
% 1.28/1.58 ! [V_a,V_b,T_a] :
% 1.28/1.58 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__self1__is__id,axiom,
% 1.28/1.58 ! [V_a,V_b,T_a] :
% 1.28/1.58 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__mult2,axiom,
% 1.28/1.58 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.58 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.58 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__mult1,axiom,
% 1.28/1.58 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.58 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.58 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__eq__1__iff,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2] :
% 1.28/1.58 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.28/1.58 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.28/1.58 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__less__mono2,axiom,
% 1.28/1.58 ! [V_k,V_j,V_i] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__less__mono1,axiom,
% 1.28/1.58 ! [V_k,V_j,V_i] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__less__cancel2,axiom,
% 1.28/1.58 ! [V_n_2,V_k_2,V_m_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
% 1.28/1.58 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.28/1.58 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__less__cancel1,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 1.28/1.58 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.28/1.58 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__0__less__mult__iff,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
% 1.28/1.58 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.28/1.58 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_Suc__mult__less__cancel1,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.58 ( 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_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__Suc__right,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__Suc,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_Suc__mult__le__cancel1,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.58 ( 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_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__eq__self__implies__10,axiom,
% 1.28/1.58 ! [V_n,V_m] :
% 1.28/1.58 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 1.28/1.58 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.28/1.58 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mod__le__divisor,axiom,
% 1.28/1.58 ! [V_m,V_n] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__left__le__imp__le,axiom,
% 1.28/1.58 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__right__le__imp__le,axiom,
% 1.28/1.58 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__less__imp__less__left,axiom,
% 1.28/1.58 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__left__less__imp__less,axiom,
% 1.28/1.58 ! [V_b,V_a,V_c,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring(T_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__less__imp__less__right,axiom,
% 1.28/1.58 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__right__less__imp__less,axiom,
% 1.28/1.58 ! [V_b,V_c,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring(T_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__le__less__imp__less,axiom,
% 1.28/1.58 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => 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)) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__less__le__imp__less,axiom,
% 1.28/1.58 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => 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)) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__strict__mono_H,axiom,
% 1.28/1.58 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => 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)) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__strict__mono,axiom,
% 1.28/1.58 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => 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)) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__le__cancel__left__neg,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__le__cancel__left__pos,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_sum__squares__le__zero__iff,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.58 => ( 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_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))
% 1.28/1.58 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_sum__squares__ge__zero,axiom,
% 1.28/1.58 ! [V_y,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__ring(T_a)
% 1.28/1.58 => 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))) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_sum__squares__gt__zero__iff,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.28/1.58 => ( 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)))
% 1.28/1.58 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_not__sum__squares__lt__zero,axiom,
% 1.28/1.58 ! [V_y,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__ring(T_a)
% 1.28/1.58 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__left__le__one__le,axiom,
% 1.28/1.58 ! [V_y,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__idom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__right__le__one__le,axiom,
% 1.28/1.58 ! [V_y,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__idom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide__strict__left__mono__neg,axiom,
% 1.28/1.58 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => ( 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))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide__strict__left__mono,axiom,
% 1.28/1.58 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_neg__divide__less__eq,axiom,
% 1.28/1.58 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_neg__less__divide__eq,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__imp__less__div__pos,axiom,
% 1.28/1.58 ! [V_x,V_z,V_y,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__imp__div__pos__less,axiom,
% 1.28/1.58 ! [V_z,V_x,V_y,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_pos__divide__less__eq,axiom,
% 1.28/1.58 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_pos__less__divide__eq,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide__less__eq,axiom,
% 1.28/1.58 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 1.28/1.58 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_less__divide__eq,axiom,
% 1.28/1.58 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 1.28/1.58 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_add__frac__eq,axiom,
% 1.28/1.58 ! [V_w,V_x,V_z,V_y,T_a] :
% 1.28/1.58 ( class_Fields_Ofield(T_a)
% 1.28/1.58 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide__add__eq__iff,axiom,
% 1.28/1.58 ! [V_y,V_x,V_z,T_a] :
% 1.28/1.58 ( class_Fields_Ofield(T_a)
% 1.28/1.58 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_add__frac__num,axiom,
% 1.28/1.58 ! [V_z,V_x,V_y,T_a] :
% 1.28/1.58 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.58 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_add__divide__eq__iff,axiom,
% 1.28/1.58 ! [V_y,V_x,V_z,T_a] :
% 1.28/1.58 ( class_Fields_Ofield(T_a)
% 1.28/1.58 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_add__num__frac,axiom,
% 1.28/1.58 ! [V_x,V_z,V_y,T_a] :
% 1.28/1.58 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.58 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__self2,axiom,
% 1.28/1.58 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.58 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__self1,axiom,
% 1.28/1.58 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.58 ( class_Divides_Osemiring__div(T_a)
% 1.28/1.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_one__less__mult,axiom,
% 1.28/1.58 ! [V_m,V_n] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_n__less__n__mult__m,axiom,
% 1.28/1.58 ! [V_m,V_n] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_n__less__m__mult__n,axiom,
% 1.28/1.58 ! [V_m,V_n] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_one__le__mult__iff,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2] :
% 1.28/1.58 ( 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_m_2),V_n_2))
% 1.28/1.58 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
% 1.28/1.58 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__le__cancel2,axiom,
% 1.28/1.58 ! [V_n_2,V_k_2,V_m_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
% 1.28/1.58 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__le__cancel1,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 1.28/1.58 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__self1__is__m,axiom,
% 1.28/1.58 ! [V_m,V_n] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__mult__self__is__m,axiom,
% 1.28/1.58 ! [V_m,V_n] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_div__Suc,axiom,
% 1.28/1.58 ! [V_c,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(V_a),V_c) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)),V_c)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_convex__bound__le,axiom,
% 1.28/1.58 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__1(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.28/1.58 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.28/1.58 => 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_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide__left__mono__neg,axiom,
% 1.28/1.58 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => ( 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))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide__left__mono,axiom,
% 1.28/1.58 ! [V_c,V_a,V_b,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_neg__divide__le__eq,axiom,
% 1.28/1.58 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_neg__le__divide__eq,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__imp__le__div__pos,axiom,
% 1.28/1.58 ! [V_x,V_z,V_y,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__imp__div__pos__le,axiom,
% 1.28/1.58 ! [V_z,V_x,V_y,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_pos__divide__le__eq,axiom,
% 1.28/1.58 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_pos__le__divide__eq,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide__le__eq,axiom,
% 1.28/1.58 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 1.28/1.58 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_le__divide__eq,axiom,
% 1.28/1.58 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 1.28/1.58 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.28/1.58 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_split__div,axiom,
% 1.28/1.58 ! [V_k_2,V_n_2,V_P_2] :
% 1.28/1.58 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
% 1.28/1.58 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.28/1.58 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 => ! [B_i,B_j] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)
% 1.28/1.58 => ( V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
% 1.28/1.58 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_convex__bound__lt,axiom,
% 1.28/1.58 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.28/1.58 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__mult__div__cancel1,axiom,
% 1.28/1.58 ! [V_n,V_m,V_k] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__mult__le__cancel1,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__mult__div__cancel__disj,axiom,
% 1.28/1.58 ! [V_n,V_m,V_k] :
% 1.28/1.58 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.28/1.58 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__mult__less__cancel1,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_poly__mod__mult__right,axiom,
% 1.28/1.58 ! [V_z,V_y,V_x,T_a] :
% 1.28/1.58 ( class_Fields_Ofield(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_poly__mod__minus__right,axiom,
% 1.28/1.58 ! [V_y,V_x,T_a] :
% 1.28/1.58 ( class_Fields_Ofield(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_poly__mod__minus__left,axiom,
% 1.28/1.58 ! [V_y,V_x,T_a] :
% 1.28/1.58 ( class_Fields_Ofield(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__assoc,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__commute,axiom,
% 1.28/1.58 ! [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) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__poly__0__left,axiom,
% 1.28/1.58 ! [V_q,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__poly__0__right,axiom,
% 1.28/1.58 ! [V_p,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__add__mult__distrib,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__1,axiom,
% 1.28/1.58 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__left__cancel,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2] :
% 1.28/1.58 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.28/1.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)
% 1.28/1.58 <=> V_a_2 = V_b_2 ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__right__cancel,axiom,
% 1.28/1.58 ! [V_b_2,V_a_2,V_c_2] :
% 1.28/1.58 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.28/1.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)
% 1.28/1.58 <=> V_a_2 = V_b_2 ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__poly__add__left,axiom,
% 1.28/1.58 ! [V_r,V_q,V_p,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_poly__div__mult__right,axiom,
% 1.28/1.58 ! [V_z,V_y,V_x,T_a] :
% 1.28/1.58 ( class_Fields_Ofield(T_a)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__less__mono2,axiom,
% 1.28/1.58 ! [V_y,V_x,V_z] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__order,axiom,
% 1.28/1.58 ! [V_y,V_x] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__less__iff1,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2,V_z_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__two__squares__add__zero__iff,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2] :
% 1.28/1.58 ( 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)
% 1.28/1.58 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.28/1.58 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__minus__mult__self__le,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__of__nat__mult,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__le__cancel__iff1,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2,V_z_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__mult__le__cancel__iff2,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2,V_z_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_norm__ratiotest__lemma,axiom,
% 1.28/1.58 ! [V_y,V_x,V_c,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.28/1.58 => ( 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)))
% 1.28/1.58 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_le__mult__natfloor,axiom,
% 1.28/1.58 ! [V_b,V_a] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
% 1.28/1.58 => 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))) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.58 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 1.28/1.58 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 | V_m_2 = V_n_2 ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_left__add__mult__distrib,axiom,
% 1.28/1.58 ! [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) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__mult__eq__cancel1,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.28/1.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 1.28/1.58 <=> V_m_2 = V_n_2 ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_not__real__square__gt__zero,axiom,
% 1.28/1.58 ! [V_x_2] :
% 1.28/1.58 ( ~ 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))
% 1.28/1.58 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide_Opos__bounded,axiom,
% 1.28/1.58 ! [V_y,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__field(T_a)
% 1.28/1.58 => ? [B_K] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.58 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult_Opos__bounded,axiom,
% 1.28/1.58 ! [T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.58 => ? [B_K] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.58 & ! [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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__divide__square__eq,axiom,
% 1.28/1.58 ! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__left_Opos__bounded,axiom,
% 1.28/1.58 ! [V_y,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.58 => ? [B_K] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.58 & ! [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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__right_Opos__bounded,axiom,
% 1.28/1.58 ! [V_x,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.58 => ? [B_K] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.58 & ! [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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divide_Ononneg__bounded,axiom,
% 1.28/1.58 ! [V_y,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__field(T_a)
% 1.28/1.58 => ? [B_K] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.58 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult_Ononneg__bounded,axiom,
% 1.28/1.58 ! [T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.58 => ? [B_K] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.58 & ! [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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__left_Ononneg__bounded,axiom,
% 1.28/1.58 ! [V_y,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.58 => ? [B_K] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.58 & ! [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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_mult__right_Ononneg__bounded,axiom,
% 1.28/1.58 ! [V_x,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.58 => ? [B_K] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.28/1.58 & ! [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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 1.28/1.58 ! [V_n,V_x] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_field__le__mult__one__interval,axiom,
% 1.28/1.58 ! [V_y,V_x,T_a] :
% 1.28/1.58 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.28/1.58 => ( ! [B_z] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x),V_y) ) )
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 1.28/1.58 ! [V_q,V_y,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 1.28/1.58 ! [V_q,V_p,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 1.28/1.58 ! [V_q,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 1.28/1.58 ! [V_q,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 1.28/1.58 ! [V_q,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 1.28/1.58 ! [V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 1.28/1.58 ! [V_q,V_p,V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 1.28/1.58 ! [V_x,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_poly__power,axiom,
% 1.28/1.58 ! [V_x,V_n,V_p,T_a] :
% 1.28/1.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_norm__power,axiom,
% 1.28/1.58 ! [V_n,V_x,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_norm__power__ineq,axiom,
% 1.28/1.58 ! [V_n,V_x,T_a] :
% 1.28/1.58 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_realpow__two__disj,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2,T_a] :
% 1.28/1.58 ( class_Rings_Oidom(T_a)
% 1.28/1.58 => ( 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))))
% 1.28/1.58 <=> ( V_x_2 = V_y_2
% 1.28/1.58 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_realpow__Suc__le__self,axiom,
% 1.28/1.58 ! [V_n,V_r,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
% 1.28/1.58 => 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) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__strict__mono,axiom,
% 1.28/1.58 ! [V_n,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.58 => 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)) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_one__less__power,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.58 => 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),V_n)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zpower__zadd__distrib,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zpower__zpower,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__one__le__power,axiom,
% 1.28/1.58 ! [V_n,V_i] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zero__less__power__nat__eq,axiom,
% 1.28/1.58 ! [V_n_2,V_x_2] :
% 1.28/1.58 ( 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))
% 1.28/1.58 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__real__of__nat,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_real__of__nat__power,axiom,
% 1.28/1.58 ! [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) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__zero__less__power__iff,axiom,
% 1.28/1.58 ! [V_n_2,V_x_2] :
% 1.28/1.58 ( 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))
% 1.28/1.58 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 1.28/1.58 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__power__less__imp__less,axiom,
% 1.28/1.58 ! [V_n,V_m,V_i] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__Suc__0,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 1.28/1.58 ! [V_m_2,V_x_2] :
% 1.28/1.58 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.28/1.58 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_natfloor__power,axiom,
% 1.28/1.58 ! [V_n,V_x] :
% 1.28/1.58 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_field__power__not__zero,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.28/1.58 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__mult__distrib,axiom,
% 1.28/1.58 ! [V_n,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__commutes,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Groups_Omonoid__mult(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__one,axiom,
% 1.28/1.58 ! [V_n,T_a] :
% 1.28/1.58 ( class_Groups_Omonoid__mult(T_a)
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__divide,axiom,
% 1.28/1.58 ! [V_n,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__mult,axiom,
% 1.28/1.58 ! [V_n,V_m,V_a,T_a] :
% 1.28/1.58 ( class_Groups_Omonoid__mult(T_a)
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__one__right,axiom,
% 1.28/1.58 ! [V_a,T_a] :
% 1.28/1.58 ( class_Groups_Omonoid__mult(T_a)
% 1.28/1.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zero__le__power,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__mono,axiom,
% 1.28/1.58 ! [V_n,V_b,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => 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)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zero__less__power,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_one__le__power,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__eq__0__iff,axiom,
% 1.28/1.58 ! [V_n_2,V_a_2,T_a] :
% 1.28/1.58 ( ( class_Power_Opower(T_a)
% 1.28/1.58 & class_Rings_Omult__zero(T_a)
% 1.28/1.58 & class_Rings_Ono__zero__divisors(T_a)
% 1.28/1.58 & class_Rings_Ozero__neq__one(T_a) )
% 1.28/1.58 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__inject__exp,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
% 1.28/1.58 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
% 1.28/1.58 <=> V_m_2 = V_n_2 ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__0__Suc,axiom,
% 1.28/1.58 ! [V_n,T_a] :
% 1.28/1.58 ( ( class_Power_Opower(T_a)
% 1.28/1.58 & class_Rings_Osemiring__0(T_a) )
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_nonzero__power__divide,axiom,
% 1.28/1.58 ! [V_n,V_a,V_b,T_a] :
% 1.28/1.58 ( class_Fields_Ofield(T_a)
% 1.28/1.58 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__Suc2,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Groups_Omonoid__mult(T_a)
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__Suc,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Power_Opower(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__0,axiom,
% 1.28/1.58 ! [V_a,T_a] :
% 1.28/1.58 ( class_Power_Opower(T_a)
% 1.28/1.58 => 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) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__add,axiom,
% 1.28/1.58 ! [V_n,V_m,V_a,T_a] :
% 1.28/1.58 ( class_Groups_Omonoid__mult(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__one__over,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.28/1.58 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)),V_n) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__less__imp__less__base,axiom,
% 1.28/1.58 ! [V_b,V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.58 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__inject__base,axiom,
% 1.28/1.58 ! [V_b,V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.58 => V_a = V_b ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__le__imp__le__base,axiom,
% 1.28/1.58 ! [V_b,V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( 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)))
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__gt1__lemma,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => 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))) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__less__power__Suc,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => 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))) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__0__left,axiom,
% 1.28/1.58 ! [V_n,T_a] :
% 1.28/1.58 ( ( class_Power_Opower(T_a)
% 1.28/1.58 & class_Rings_Osemiring__0(T_a) )
% 1.28/1.58 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 => 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) )
% 1.28/1.58 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 => 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) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__gt1,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => 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))) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__minus,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Oring__1(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__strict__increasing,axiom,
% 1.28/1.58 ! [V_a,V_N,V_n,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => 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)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__less__imp__less__exp,axiom,
% 1.28/1.58 ! [V_n,V_m,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__strict__increasing__iff,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 1.28/1.58 => ( 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))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__increasing,axiom,
% 1.28/1.58 ! [V_a,V_N,V_n,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => 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)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__Suc__less,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.28/1.58 => 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)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__Suc__less__one,axiom,
% 1.28/1.58 ! [V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.28/1.58 => 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)) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__strict__decreasing,axiom,
% 1.28/1.58 ! [V_a,V_N,V_n,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.28/1.58 => 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)) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__eq__imp__eq__base,axiom,
% 1.28/1.58 ! [V_b,V_n,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( 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)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.58 => V_a = V_b ) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__decreasing,axiom,
% 1.28/1.58 ! [V_a,V_N,V_n,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.28/1.58 => 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)) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__increasing__iff,axiom,
% 1.28/1.58 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 1.28/1.58 => ( 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))
% 1.28/1.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__le__imp__le__exp,axiom,
% 1.28/1.58 ! [V_n,V_m,V_a,T_a] :
% 1.28/1.58 ( class_Rings_Olinordered__semidom(T_a)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.28/1.58 => ( 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))
% 1.28/1.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_reduce__poly__simple,axiom,
% 1.28/1.58 ! [V_n,V_b] :
% 1.28/1.58 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 1.28/1.58 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.58 => ? [B_z] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_power__power__power,axiom,
% 1.28/1.58 ! [T_a] :
% 1.28/1.58 ( class_Power_Opower(T_a)
% 1.28/1.58 => 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)) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zpower__zmod,axiom,
% 1.28/1.58 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zdiv__zmult2__eq,axiom,
% 1.28/1.58 ! [V_b,V_a,V_c] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_divmod__int__rel__div__eq,axiom,
% 1.28/1.58 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 1.28/1.58 ( V_a_1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y),V_r_1)
% 1.28/1.58 => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1)
% 1.28/1.58 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1) ) )
% 1.28/1.58 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1)
% 1.28/1.58 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
% 1.28/1.58 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.58 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_split__zdiv,axiom,
% 1.28/1.58 ! [V_k_2,V_n_2,V_P_2] :
% 1.28/1.58 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
% 1.28/1.58 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.58 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 1.28/1.58 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.28/1.58 => ! [B_i] :
% 1.28/1.58 ( ? [B_j] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)
% 1.28/1.58 & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
% 1.28/1.58 & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) )
% 1.28/1.58 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 1.28/1.58 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.58 => ! [B_i] :
% 1.28/1.58 ( ? [B_j] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 1.28/1.58 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.58 & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) )
% 1.28/1.58 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zmult__zminus,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zmult__zless__mono2,axiom,
% 1.28/1.58 ! [V_k,V_j,V_i] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.28/1.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 1.28/1.58 => 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)) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_pos__zmult__eq__1__iff,axiom,
% 1.28/1.58 ! [V_n_2,V_m_2] :
% 1.28/1.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)
% 1.28/1.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.28/1.58 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.28/1.58 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zmult__1,axiom,
% 1.28/1.58 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zmult__1__right,axiom,
% 1.28/1.58 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zadd__zmult__distrib2,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zadd__zmult__distrib,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zmult__assoc,axiom,
% 1.28/1.58 ! [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)) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zmult__commute,axiom,
% 1.28/1.58 ! [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) ).
% 1.28/1.58
% 1.28/1.58 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 1.28/1.59 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.28/1.59 ( 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)
% 1.28/1.59 => ( 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))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_unique__quotient__lemma__neg,axiom,
% 1.28/1.59 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.28/1.59 ( 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))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__mono2__lemma,axiom,
% 1.28/1.59 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.28/1.59 ( 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)
% 1.28/1.59 => ( 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))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_unique__quotient__lemma,axiom,
% 1.28/1.59 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.28/1.59 ( 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))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_q__neg__lemma,axiom,
% 1.28/1.59 ! [V_r_H,V_q_H,V_b_H] :
% 1.28/1.59 ( 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))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_q__pos__lemma,axiom,
% 1.28/1.59 ! [V_r_H,V_q_H,V_b_H] :
% 1.28/1.59 ( 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))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_self__quotient__aux1,axiom,
% 1.28/1.59 ! [V_q,V_r,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.28/1.59 => ( 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))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_self__quotient__aux2,axiom,
% 1.28/1.59 ! [V_q,V_r,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.28/1.59 => ( 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))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_split__zmod,axiom,
% 1.28/1.59 ! [V_k_2,V_n_2,V_P_2] :
% 1.28/1.59 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 1.28/1.59 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 1.28/1.59 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.28/1.59 => ! [B_i,B_j] :
% 1.28/1.59 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)
% 1.28/1.59 & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
% 1.28/1.59 & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) )
% 1.28/1.59 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 1.28/1.59 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ! [B_i,B_j] :
% 1.28/1.59 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 1.28/1.59 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) )
% 1.28/1.59 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmult2__lemma__aux3,axiom,
% 1.28/1.59 ! [V_q,V_b,V_r,V_c] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.28/1.59 => 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),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmult2__lemma__aux4,axiom,
% 1.28/1.59 ! [V_q,V_b,V_r,V_c] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.28/1.59 => 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),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmult2__lemma__aux1,axiom,
% 1.28/1.59 ! [V_q,V_r,V_b,V_c] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmult2__lemma__aux2,axiom,
% 1.28/1.59 ! [V_q,V_r,V_b,V_c] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => 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),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_divmod__int__rel__mod__eq,axiom,
% 1.28/1.59 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 1.28/1.59 ( V_a_1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1),V_y)
% 1.28/1.59 => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.28/1.59 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_b_1) ) )
% 1.28/1.59 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_y)
% 1.28/1.59 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
% 1.28/1.59 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__eq__0__iff,axiom,
% 1.28/1.59 ! [V_d_2,V_m_2] :
% 1.28/1.59 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zmult1__eq,axiom,
% 1.28/1.59 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__simps_I3_J,axiom,
% 1.28/1.59 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_split__pos__lemma,axiom,
% 1.28/1.59 ! [V_n_2,V_P_2,V_k_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.28/1.59 => ( hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 1.28/1.59 <=> ! [B_i,B_j] :
% 1.28/1.59 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)
% 1.28/1.59 & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
% 1.28/1.59 & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) )
% 1.28/1.59 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_split__neg__lemma,axiom,
% 1.28/1.59 ! [V_n_2,V_P_2,V_k_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 1.28/1.59 <=> ! [B_i,B_j] :
% 1.28/1.59 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 1.28/1.59 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) )
% 1.28/1.59 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zmult2__eq,axiom,
% 1.28/1.59 ! [V_b,V_a,V_c] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__zmod__equality2,axiom,
% 1.28/1.59 ! [V_k,V_b,V_a] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_k) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__zmod__equality,axiom,
% 1.28/1.59 ! [V_k,V_a,V_b] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_k) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__zmult1__eq,axiom,
% 1.28/1.59 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zdiv__equality,axiom,
% 1.28/1.59 ! [V_b,V_a] : V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_power_Opower_Opower__0,axiom,
% 1.28/1.59 ! [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 ).
% 1.28/1.59
% 1.28/1.59 fof(fact_power_Opower_Opower__Suc,axiom,
% 1.28/1.59 ! [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)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_DeMoivre2,axiom,
% 1.28/1.59 ! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_realpow__pos__nth,axiom,
% 1.28/1.59 ! [V_a,V_n] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.28/1.59 => ? [B_r] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)
% 1.28/1.59 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__self,axiom,
% 1.28/1.59 ! [V_a] :
% 1.28/1.59 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_int__div__less__self,axiom,
% 1.28/1.59 ! [V_k,V_x] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
% 1.28/1.59 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_int__one__le__iff__zero__less,axiom,
% 1.28/1.59 ! [V_z_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zle__add1__eq__le,axiom,
% 1.28/1.59 ! [V_z_2,V_w_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_add1__zle__eq,axiom,
% 1.28/1.59 ! [V_z_2,V_w_2] :
% 1.28/1.59 ( 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_z_2)
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__imp__0__less,axiom,
% 1.28/1.59 ! [V_z] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 1.28/1.59 => 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zless__imp__add1__zle,axiom,
% 1.28/1.59 ! [V_z,V_w] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 1.28/1.59 => 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) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_odd__less__0,axiom,
% 1.28/1.59 ! [V_z_2] :
% 1.28/1.59 ( 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_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zless__add1__eq,axiom,
% 1.28/1.59 ! [V_z_2,V_w_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.28/1.59 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
% 1.28/1.59 | V_w_2 = V_z_2 ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_int__0__less__1,axiom,
% 1.28/1.59 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_int__0__neq__1,axiom,
% 1.28/1.59 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_odd__nonzero,axiom,
% 1.28/1.59 ! [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) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__zadd1__eq,axiom,
% 1.28/1.59 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zdiv__trivial,axiom,
% 1.28/1.59 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_DIVISION__BY__ZERO,axiom,
% 1.28/1.59 ! [V_a] :
% 1.28/1.59 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__le__nonneg__dividend,axiom,
% 1.28/1.59 ! [V_k,V_m] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k),V_m) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.28/1.59 ! [V_y,V_x] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__self,axiom,
% 1.28/1.59 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zero,axiom,
% 1.28/1.59 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zminus2__not__zero,axiom,
% 1.28/1.59 ! [V_l,V_k] :
% 1.28/1.59 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zminus1__not__zero,axiom,
% 1.28/1.59 ! [V_l,V_k] :
% 1.28/1.59 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_pos__mod__bound,axiom,
% 1.28/1.59 ! [V_a,V_b] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_neg__mod__bound,axiom,
% 1.28/1.59 ! [V_a,V_b] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zminus2,axiom,
% 1.28/1.59 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zmod__zminus__zminus,axiom,
% 1.28/1.59 ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zminus__zmod,axiom,
% 1.28/1.59 ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_x),V_m) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__neg__neg__trivial,axiom,
% 1.28/1.59 ! [V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_neg__mod__conj,axiom,
% 1.28/1.59 ! [V_a,V_b] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_neg__mod__sign,axiom,
% 1.28/1.59 ! [V_a,V_b] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__pos__neg__trivial,axiom,
% 1.28/1.59 ! [V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__pos__pos__trivial,axiom,
% 1.28/1.59 ! [V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_pos__mod__conj,axiom,
% 1.28/1.59 ! [V_a,V_b] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))
% 1.28/1.59 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_pos__mod__sign,axiom,
% 1.28/1.59 ! [V_a,V_b] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__left__mono,axiom,
% 1.28/1.59 ! [V_k,V_j,V_i] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.28/1.59 => 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zle__refl,axiom,
% 1.28/1.59 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zle__linear,axiom,
% 1.28/1.59 ! [V_w,V_z] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.28/1.59 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zle__trans,axiom,
% 1.28/1.59 ! [V_k,V_j,V_i] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zle__antisym,axiom,
% 1.28/1.59 ! [V_w,V_z] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 1.28/1.59 => V_z = V_w ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__assoc,axiom,
% 1.28/1.59 ! [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)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__left__commute,axiom,
% 1.28/1.59 ! [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)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__commute,axiom,
% 1.28/1.59 ! [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) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__0__right,axiom,
% 1.28/1.59 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__0,axiom,
% 1.28/1.59 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zminus__0,axiom,
% 1.28/1.59 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zminus__zadd__distrib,axiom,
% 1.28/1.59 ! [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)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__zminus__inverse2,axiom,
% 1.28/1.59 ! [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) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__strict__right__mono,axiom,
% 1.28/1.59 ! [V_k,V_j,V_i] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.28/1.59 => 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zminus__zminus,axiom,
% 1.28/1.59 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zless__linear,axiom,
% 1.28/1.59 ! [V_y,V_x] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 1.28/1.59 | V_x = V_y
% 1.28/1.59 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zless__le,axiom,
% 1.28/1.59 ! [V_w_2,V_z_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
% 1.28/1.59 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2)
% 1.28/1.59 & V_z_2 != V_w_2 ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zadd__zless__mono,axiom,
% 1.28/1.59 ! [V_z,V_z_H,V_w,V_w_H] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 1.28/1.59 => 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)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__eq__0__iff,axiom,
% 1.28/1.59 ! [V_k_2,V_i_2] :
% 1.28/1.59 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.28/1.59 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)
% 1.28/1.59 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) )
% 1.28/1.59 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 1.28/1.59 ! [V_a_2,V_b_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 1.28/1.59 ! [V_i_2,V_k_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 1.28/1.59 ! [V_b_2,V_a_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
% 1.28/1.59 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_a_2)
% 1.28/1.59 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__mono2,axiom,
% 1.28/1.59 ! [V_b,V_b_H,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_div__nonneg__neg__le0,axiom,
% 1.28/1.59 ! [V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_div__pos__pos__trivial,axiom,
% 1.28/1.59 ! [V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 1.28/1.59 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 1.28/1.59 ! [V_a_2,V_b_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_div__nonpos__pos__le0,axiom,
% 1.28/1.59 ! [V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__mono2__neg,axiom,
% 1.28/1.59 ! [V_b,V_b_H,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_div__neg__neg__trivial,axiom,
% 1.28/1.59 ! [V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 1.28/1.59 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__mono1,axiom,
% 1.28/1.59 ! [V_b,V_a_H,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__mono1__neg,axiom,
% 1.28/1.59 ! [V_b,V_a_H,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__zminus__zminus,axiom,
% 1.28/1.59 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__zminus2,axiom,
% 1.28/1.59 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_div__neg__pos__less0,axiom,
% 1.28/1.59 ! [V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.28/1.59 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 1.28/1.59 ! [V_a_2,V_b_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 1.28/1.59 ! [V_a_2,V_b_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zdiv__zero,axiom,
% 1.28/1.59 ! [V_b] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 1.28/1.59 ! [V_y,V_x] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_rcis__zero__mod,axiom,
% 1.28/1.59 ! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_rcis__mult,axiom,
% 1.28/1.59 ! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 1.28/1.59 ! [V_n,V_x] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.28/1.59 => 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.28/1.59 ! [V_y,V_x] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.28/1.59 => 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)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 1.28/1.59 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)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 1.28/1.59 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)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 1.28/1.59 ! [V_y,V_x] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.28/1.59 => 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)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_z3mod__def,axiom,
% 1.28/1.59 ! [V_k,V_l] :
% 1.28/1.59 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l)
% 1.28/1.59 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 1.28/1.59 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l)
% 1.28/1.59 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_z3div__def,axiom,
% 1.28/1.59 ! [V_k,V_l] :
% 1.28/1.59 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l)
% 1.28/1.59 => c_SMT_Oz3div(V_k,V_l) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l) )
% 1.28/1.59 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l)
% 1.28/1.59 => c_SMT_Oz3div(V_k,V_l) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_int__power__div__base,axiom,
% 1.28/1.59 ! [V_k,V_m] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 1.28/1.59 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_realpow__pos__nth__unique,axiom,
% 1.28/1.59 ! [V_a,V_n] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.28/1.59 => ? [B_x] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x)
% 1.28/1.59 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
% 1.28/1.59 & ! [B_y] :
% 1.28/1.59 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)
% 1.28/1.59 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a )
% 1.28/1.59 => B_y = B_x ) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_eq__add__iff2,axiom,
% 1.28/1.59 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.28/1.59 ( class_Rings_Oring(T_a)
% 1.28/1.59 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_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)
% 1.28/1.59 <=> V_c_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) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_eq__add__iff1,axiom,
% 1.28/1.59 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.28/1.59 ( class_Rings_Oring(T_a)
% 1.28/1.59 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_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)
% 1.28/1.59 <=> 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_c_2) = V_d_2 ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mult_Oprod__diff__prod,axiom,
% 1.28/1.59 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.28/1.59 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.28/1.59 => 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))) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mult__diff__mult,axiom,
% 1.28/1.59 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.28/1.59 ( class_Rings_Oring(T_a)
% 1.28/1.59 => 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__Suc__1,axiom,
% 1.28/1.59 ! [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 ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 1.28/1.59 ! [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) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__diff__cong,axiom,
% 1.28/1.59 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 1.28/1.59 ( class_Divides_Oring__div(T_a)
% 1.28/1.59 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 1.28/1.59 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_H,V_b_H),V_c) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__diff__eq,axiom,
% 1.28/1.59 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.59 ( class_Divides_Oring__div(T_a)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__diff__left__eq,axiom,
% 1.28/1.59 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.59 ( class_Divides_Oring__div(T_a)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__diff__right__eq,axiom,
% 1.28/1.59 ! [V_c,V_b,V_a,T_a] :
% 1.28/1.59 ( class_Divides_Oring__div(T_a)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__geq,axiom,
% 1.28/1.59 ! [V_n,V_m] :
% 1.28/1.59 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_mod__if,axiom,
% 1.28/1.59 ! [V_n,V_m] :
% 1.28/1.59 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 1.28/1.59 & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__mod__geq,axiom,
% 1.28/1.59 ! [V_m,V_n] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.28/1.59 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_norm__triangle__ineq2,axiom,
% 1.28/1.59 ! [V_b,V_a,T_a] :
% 1.28/1.59 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.28/1.59 => 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))) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__0__right,axiom,
% 1.28/1.59 ! [V_a,T_a] :
% 1.28/1.59 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.59 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__self,axiom,
% 1.28/1.59 ! [V_a,T_a] :
% 1.28/1.59 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.59 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_eq__iff__diff__eq__0,axiom,
% 1.28/1.59 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.59 ( class_Groups_Oab__group__add(T_a)
% 1.28/1.59 => ( V_a_2 = V_b_2
% 1.28/1.59 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_right__minus__eq,axiom,
% 1.28/1.59 ! [V_b_2,V_a_2,T_a] :
% 1.28/1.59 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.59 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.28/1.59 <=> V_a_2 = V_b_2 ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__eq__diff__less__eq,axiom,
% 1.28/1.59 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 1.28/1.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.59 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_add__diff__cancel,axiom,
% 1.28/1.59 ! [V_b,V_a,T_a] :
% 1.28/1.59 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.59 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__add__cancel,axiom,
% 1.28/1.59 ! [V_b,V_a,T_a] :
% 1.28/1.59 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.59 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__0__eq__0,axiom,
% 1.28/1.59 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_minus__nat_Odiff__0,axiom,
% 1.28/1.59 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__self__eq__0,axiom,
% 1.28/1.59 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diffs0__imp__equal,axiom,
% 1.28/1.59 ! [V_n,V_m] :
% 1.28/1.59 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.59 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.59 => V_m = V_n ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__diff__iff,axiom,
% 1.28/1.59 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Nat_Odiff__diff__eq,axiom,
% 1.28/1.59 ! [V_n,V_m,V_k] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.28/1.59 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_eq__diff__iff,axiom,
% 1.28/1.59 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 1.28/1.59 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
% 1.28/1.59 <=> V_m_2 = V_n_2 ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__diff__cancel,axiom,
% 1.28/1.59 ! [V_n,V_i] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 1.28/1.59 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__le__mono,axiom,
% 1.28/1.59 ! [V_l,V_n,V_m] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__le__mono2,axiom,
% 1.28/1.59 ! [V_l,V_n,V_m] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.59 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__le__self,axiom,
% 1.28/1.59 ! [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) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__cancel2,axiom,
% 1.28/1.59 ! [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) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__cancel,axiom,
% 1.28/1.59 ! [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) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__diff__left,axiom,
% 1.28/1.59 ! [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)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__add__inverse,axiom,
% 1.28/1.59 ! [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 ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__add__inverse2,axiom,
% 1.28/1.59 ! [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 ).
% 1.28/1.59
% 1.28/1.59 fof(fact_less__imp__diff__less,axiom,
% 1.28/1.59 ! [V_n,V_k,V_j] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.28/1.59 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__less__mono2,axiom,
% 1.28/1.59 ! [V_l,V_n,V_m] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 1.28/1.59 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_minus__diff__eq,axiom,
% 1.28/1.59 ! [V_b,V_a,T_a] :
% 1.28/1.59 ( class_Groups_Oab__group__add(T_a)
% 1.28/1.59 => 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) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__eq__diff__less,axiom,
% 1.28/1.59 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 1.28/1.59 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.28/1.59 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__add__assoc2,axiom,
% 1.28/1.59 ! [V_i,V_j,V_k] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.28/1.59 => 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) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_add__diff__assoc2,axiom,
% 1.28/1.59 ! [V_i,V_j,V_k] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.28/1.59 => 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) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__add__assoc,axiom,
% 1.28/1.59 ! [V_i,V_j,V_k] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.28/1.59 => 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__imp__diff__is__add,axiom,
% 1.28/1.59 ! [V_k_2,V_j_2,V_i_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.28/1.59 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 1.28/1.59 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__add__diff__inverse2,axiom,
% 1.28/1.59 ! [V_m,V_n] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.28/1.59 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__diff__conv2,axiom,
% 1.28/1.59 ! [V_i_2,V_j_2,V_k_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
% 1.28/1.59 => ( 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))
% 1.28/1.59 <=> 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) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_add__diff__assoc,axiom,
% 1.28/1.59 ! [V_i,V_j,V_k] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.28/1.59 => 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) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__add__diff__inverse,axiom,
% 1.28/1.59 ! [V_m,V_n] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.28/1.59 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__add__diff,axiom,
% 1.28/1.59 ! [V_m,V_n,V_k] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.28/1.59 => 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_le__diff__conv,axiom,
% 1.28/1.59 ! [V_i_2,V_k_2,V_j_2] :
% 1.28/1.59 ( 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)
% 1.28/1.59 <=> 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__diff__right,axiom,
% 1.28/1.59 ! [V_i,V_j,V_k] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.28/1.59 => 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) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_less__diff__iff,axiom,
% 1.28/1.59 ! [V_n_2,V_m_2,V_k_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__less__mono,axiom,
% 1.28/1.59 ! [V_c,V_b,V_a] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 1.28/1.59 => 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)) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_add__diff__inverse,axiom,
% 1.28/1.59 ! [V_n,V_m] :
% 1.28/1.59 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.28/1.59 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_less__diff__conv,axiom,
% 1.28/1.59 ! [V_k_2,V_j_2,V_i_2] :
% 1.28/1.59 ( 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))
% 1.28/1.59 <=> 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) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_Suc__diff__le,axiom,
% 1.28/1.59 ! [V_m,V_n] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.28/1.59 => 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)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__is__0__eq,axiom,
% 1.28/1.59 ! [V_n_2,V_m_2] :
% 1.28/1.59 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__is__0__eq_H,axiom,
% 1.28/1.59 ! [V_n,V_m] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.28/1.59 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__add__0,axiom,
% 1.28/1.59 ! [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) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__less__Suc,axiom,
% 1.28/1.59 ! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__less,axiom,
% 1.28/1.59 ! [V_m,V_n] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.28/1.59 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.28/1.59 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_zero__less__diff,axiom,
% 1.28/1.59 ! [V_m_2,V_n_2] :
% 1.28/1.59 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))
% 1.28/1.59 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.28/1.59
% 1.28/1.59 fof(fact_diff__minus__eq__add,axiom,
% 1.28/1.59 ! [V_b,V_a,T_a] :
% 1.28/1.59 ( class_Groups_Ogroup__add(T_a)
% 1.28/1.59 => 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) ) ).
% 1.28/1.59
% 1.28/1.59 %----Arity declarations (268)
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.28/1.59 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 1.28/1.59 ! [T_2,T_1] :
% 1.28/1.59 ( class_Lattices_Oboolean__algebra(T_1)
% 1.28/1.59 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_fun__Orderings_Opreorder,axiom,
% 1.28/1.59 ! [T_2,T_1] :
% 1.28/1.59 ( class_Orderings_Opreorder(T_1)
% 1.28/1.59 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_fun__Orderings_Oorder,axiom,
% 1.28/1.59 ! [T_2,T_1] :
% 1.28/1.59 ( class_Orderings_Oorder(T_1)
% 1.28/1.59 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_fun__Orderings_Oord,axiom,
% 1.28/1.59 ! [T_2,T_1] :
% 1.28/1.59 ( class_Orderings_Oord(T_1)
% 1.28/1.59 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_fun__Groups_Ouminus,axiom,
% 1.28/1.59 ! [T_2,T_1] :
% 1.28/1.59 ( class_Groups_Ouminus(T_1)
% 1.28/1.59 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.28/1.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.28/1.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 1.28/1.59 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 1.28/1.59 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 1.28/1.59 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 1.28/1.59 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 1.28/1.59 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 1.28/1.59 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 1.28/1.59 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 1.28/1.59 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 1.28/1.59 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 1.28/1.59 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 1.28/1.59 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 1.28/1.59 class_Orderings_Opreorder(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 1.28/1.59 class_Orderings_Olinorder(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 1.28/1.59 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 1.28/1.59 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 1.28/1.59 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 1.28/1.59 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 1.28/1.59 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 1.28/1.59 class_Divides_Oring__div(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 1.28/1.59 class_Rings_Omult__zero(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 1.28/1.59 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 1.28/1.59 class_Orderings_Oorder(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 1.28/1.59 class_Int_Oring__char__0(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 1.28/1.59 class_Rings_Osemiring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 1.28/1.59 class_Orderings_Oord(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 1.28/1.59 class_Groups_Ouminus(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 1.28/1.59 class_Rings_Oring__1(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Power_Opower,axiom,
% 1.28/1.59 class_Power_Opower(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 1.28/1.59 class_Groups_Ozero(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oring,axiom,
% 1.28/1.59 class_Rings_Oring(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 1.28/1.59 class_Rings_Oidom(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Int__Oint__Groups_Oone,axiom,
% 1.28/1.59 class_Groups_Oone(tc_Int_Oint) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.28/1.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.28/1.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 1.28/1.59 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 1.28/1.59 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 1.28/1.59 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 1.28/1.59 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 1.28/1.59 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 1.28/1.59 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 1.28/1.59 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 1.28/1.59 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 1.28/1.59 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 1.28/1.59 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 1.28/1.59 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 1.28/1.59 class_Orderings_Oorder(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 1.28/1.59 class_Rings_Osemiring(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 1.28/1.59 class_Orderings_Oord(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Power_Opower,axiom,
% 1.28/1.59 class_Power_Opower(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 1.28/1.59 class_Groups_Ozero(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 1.28/1.59 class_Groups_Oone(tc_Nat_Onat) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 1.28/1.59 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 1.28/1.59 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 1.28/1.59 class_Orderings_Oorder(tc_HOL_Obool) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 1.28/1.59 class_Orderings_Oord(tc_HOL_Obool) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 1.28/1.59 class_Groups_Ouminus(tc_HOL_Obool) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.28/1.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.28/1.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 1.28/1.59 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 1.28/1.59 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 1.28/1.59 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 1.28/1.59 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 1.28/1.59 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 1.28/1.59 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 1.28/1.59 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 1.28/1.59 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 1.28/1.59 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 1.28/1.59 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 1.28/1.59 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 1.28/1.59 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 1.28/1.59 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 1.28/1.59 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 1.28/1.59 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 1.28/1.59 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 1.28/1.59 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 1.28/1.59 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 1.28/1.59 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 1.28/1.59 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 1.28/1.59 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 1.28/1.59 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 1.28/1.59 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 1.28/1.59 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 1.28/1.59 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 1.28/1.59 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 1.28/1.59 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 1.28/1.59 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 1.28/1.59 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 1.28/1.59 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 1.28/1.59 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
% 1.28/1.59 class_Groups_Ouminus(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 1.28/1.59 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 1.28/1.59 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 1.28/1.59 class_Power_Opower(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 1.28/1.59 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 1.28/1.59 class_Rings_Oring(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 1.28/1.59 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 1.28/1.59 class_Groups_Oone(tc_RealDef_Oreal) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.28/1.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 1.28/1.59 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
% 1.28/1.59 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 1.28/1.59 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 1.28/1.59 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 1.28/1.59 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 1.28/1.59 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 1.28/1.59 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 1.28/1.59 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 1.28/1.59 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 1.28/1.59 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 1.28/1.59 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 1.28/1.59 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 1.28/1.59 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 1.28/1.59 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 1.28/1.59 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 1.28/1.59 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 1.28/1.59 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 1.28/1.59 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 1.28/1.59 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 1.28/1.59 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 1.28/1.59 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
% 1.28/1.59 class_Groups_Ouminus(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 1.28/1.59 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 1.28/1.59 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 1.28/1.59 class_Power_Opower(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 1.28/1.59 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 1.28/1.59 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 1.28/1.59 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 1.28/1.59 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Oidom(T_1)
% 1.28/1.59 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.28/1.59 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Oidom(T_1)
% 1.28/1.59 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Oidom(T_1)
% 1.28/1.59 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.28/1.59 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.28/1.59 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.28/1.59 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.28/1.59 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Oidom(T_1)
% 1.28/1.59 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.28/1.59 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.28/1.59 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.28/1.59 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Fields_Ofield(T_1)
% 1.28/1.59 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.28/1.59 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Oab__group__add(T_1)
% 1.28/1.59 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.28/1.59 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.28/1.59 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__ring__1(T_1)
% 1.28/1.59 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.28/1.59 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.28/1.59 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Oab__group__add(T_1)
% 1.28/1.59 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Divides_Oring__div,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Fields_Ofield(T_1)
% 1.28/1.59 => class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.28/1.59 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__ring(T_1)
% 1.28/1.59 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.28/1.59 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Olinordered__idom(T_1)
% 1.28/1.59 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Oab__group__add(T_1)
% 1.28/1.59 => class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__ring__1(T_1)
% 1.28/1.59 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.28/1.59 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Groups_Ozero(T_1)
% 1.28/1.59 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__ring(T_1)
% 1.28/1.59 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Oidom(T_1)
% 1.28/1.59 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 1.28/1.59 ! [T_1] :
% 1.28/1.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.28/1.59 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 1.28/1.59
% 1.28/1.59 %----Conjectures (2)
% 1.28/1.59 fof(conj_0,hypothesis,
% 1.28/1.59 ! [B_g] :
% 1.28/1.59 ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B_g,B_n)),v_r)
% 1.28/1.59 => ( ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(B_g,B_n))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))))
% 1.28/1.59 => v_thesis____ ) ) ).
% 1.28/1.59
% 1.28/1.59 fof(conj_1,conjecture,
% 1.28/1.59 v_thesis____ ).
% 1.28/1.59
% 1.28/1.59 %------------------------------------------------------------------------------
% 1.28/1.59 %-------------------------------------------
% 1.28/1.59 % Proof found
% 1.28/1.59 % SZS status Theorem for theBenchmark
% 1.28/1.59 % SZS output start Proof
% 1.28/1.59 %ClaNum:2114(EqnAxiom:317)
% 1.28/1.59 %VarNum:11168(SingletonVarNum:3709)
% 1.28/1.59 %MaxLitNum:7
% 1.28/1.59 %MaxfuncDepth:6
% 1.28/1.59 %SharedTerms:290
% 1.28/1.59 %goalClause: 672
% 1.28/1.59 %singleGoalClaCount:1
% 1.28/1.59 [318]P1(a1)
% 1.28/1.59 [319]P1(a2)
% 1.28/1.59 [320]P2(a1)
% 1.28/1.59 [321]P12(a1)
% 1.28/1.59 [322]P12(a2)
% 1.28/1.59 [323]P13(a1)
% 1.28/1.59 [324]P14(a1)
% 1.28/1.59 [325]P14(a2)
% 1.28/1.59 [326]P14(a110)
% 1.28/1.59 [327]P3(a1)
% 1.28/1.59 [328]P3(a2)
% 1.28/1.59 [329]P23(a1)
% 1.28/1.59 [330]P23(a2)
% 1.28/1.59 [331]P45(a1)
% 1.28/1.59 [332]P45(a112)
% 1.28/1.59 [333]P45(a110)
% 1.28/1.59 [334]P24(a1)
% 1.28/1.59 [335]P24(a112)
% 1.28/1.59 [336]P24(a110)
% 1.28/1.59 [337]P46(a1)
% 1.28/1.59 [338]P46(a2)
% 1.28/1.59 [339]P33(a1)
% 1.28/1.59 [340]P33(a2)
% 1.28/1.59 [341]P33(a112)
% 1.28/1.59 [342]P33(a110)
% 1.28/1.59 [343]P52(a1)
% 1.28/1.59 [344]P52(a110)
% 1.28/1.59 [345]P15(a1)
% 1.28/1.59 [346]P15(a2)
% 1.28/1.59 [347]P15(a112)
% 1.28/1.59 [348]P15(a110)
% 1.28/1.59 [349]P17(a1)
% 1.28/1.59 [350]P17(a2)
% 1.28/1.59 [351]P17(a112)
% 1.28/1.59 [352]P17(a110)
% 1.28/1.59 [353]P18(a1)
% 1.28/1.59 [354]P18(a2)
% 1.28/1.59 [355]P18(a112)
% 1.28/1.59 [356]P18(a110)
% 1.28/1.59 [357]P25(a1)
% 1.28/1.59 [358]P25(a2)
% 1.28/1.59 [359]P25(a112)
% 1.28/1.59 [360]P25(a110)
% 1.28/1.59 [361]P26(a1)
% 1.28/1.59 [362]P26(a2)
% 1.28/1.59 [363]P26(a112)
% 1.28/1.59 [364]P26(a110)
% 1.28/1.59 [365]P21(a1)
% 1.28/1.59 [366]P21(a2)
% 1.28/1.59 [367]P21(a112)
% 1.28/1.59 [368]P21(a110)
% 1.28/1.59 [369]P27(a1)
% 1.28/1.59 [370]P27(a110)
% 1.28/1.59 [371]P29(a1)
% 1.28/1.59 [372]P29(a112)
% 1.28/1.59 [373]P29(a110)
% 1.28/1.59 [374]P30(a1)
% 1.28/1.59 [375]P30(a112)
% 1.28/1.59 [376]P30(a110)
% 1.28/1.59 [377]P32(a1)
% 1.28/1.59 [378]P32(a112)
% 1.28/1.59 [379]P32(a110)
% 1.28/1.59 [380]P58(a1)
% 1.28/1.59 [381]P58(a2)
% 1.28/1.59 [382]P58(a112)
% 1.28/1.59 [383]P58(a110)
% 1.28/1.59 [384]P31(a1)
% 1.28/1.59 [385]P31(a110)
% 1.28/1.59 [386]P53(a1)
% 1.28/1.59 [387]P53(a2)
% 1.28/1.59 [388]P16(a1)
% 1.28/1.59 [389]P16(a2)
% 1.28/1.59 [390]P16(a110)
% 1.28/1.59 [391]P35(a1)
% 1.28/1.59 [392]P35(a112)
% 1.28/1.59 [393]P35(a110)
% 1.28/1.59 [394]P35(a111)
% 1.28/1.59 [395]P47(a1)
% 1.28/1.59 [396]P47(a2)
% 1.28/1.59 [397]P47(a110)
% 1.28/1.59 [398]P48(a1)
% 1.28/1.59 [399]P48(a2)
% 1.28/1.59 [400]P48(a112)
% 1.28/1.59 [401]P48(a110)
% 1.28/1.59 [402]P49(a1)
% 1.28/1.59 [403]P49(a2)
% 1.28/1.59 [404]P49(a112)
% 1.28/1.59 [405]P49(a110)
% 1.28/1.59 [406]P36(a1)
% 1.28/1.59 [407]P36(a112)
% 1.28/1.59 [408]P36(a110)
% 1.28/1.59 [409]P36(a111)
% 1.28/1.59 [410]P37(a1)
% 1.28/1.59 [411]P37(a112)
% 1.28/1.59 [412]P37(a110)
% 1.28/1.59 [413]P41(a1)
% 1.28/1.59 [414]P41(a112)
% 1.28/1.59 [415]P41(a110)
% 1.28/1.59 [416]P41(a111)
% 1.28/1.59 [417]P38(a1)
% 1.28/1.59 [418]P38(a2)
% 1.28/1.59 [419]P38(a110)
% 1.28/1.59 [420]P54(a1)
% 1.28/1.59 [421]P54(a2)
% 1.28/1.59 [422]P54(a110)
% 1.28/1.59 [423]P39(a111)
% 1.28/1.59 [424]P34(a1)
% 1.28/1.59 [425]P34(a2)
% 1.28/1.59 [426]P34(a110)
% 1.28/1.59 [427]P34(a111)
% 1.28/1.59 [428]P75(a1)
% 1.28/1.59 [429]P75(a2)
% 1.28/1.59 [430]P75(a112)
% 1.28/1.59 [431]P75(a110)
% 1.28/1.59 [432]P4(a112)
% 1.28/1.59 [433]P4(a110)
% 1.28/1.59 [434]P11(a1)
% 1.28/1.59 [435]P11(a2)
% 1.28/1.59 [436]P42(a1)
% 1.28/1.59 [437]P42(a2)
% 1.28/1.59 [438]P59(a1)
% 1.28/1.59 [439]P59(a2)
% 1.28/1.59 [440]P59(a110)
% 1.28/1.60 [441]P19(a1)
% 1.28/1.60 [442]P19(a2)
% 1.28/1.60 [443]P19(a112)
% 1.28/1.60 [444]P19(a110)
% 1.28/1.60 [445]P44(a1)
% 1.28/1.60 [446]P44(a2)
% 1.28/1.60 [447]P28(a1)
% 1.28/1.60 [448]P28(a2)
% 1.28/1.60 [449]P28(a112)
% 1.28/1.60 [450]P28(a110)
% 1.28/1.60 [451]P22(a1)
% 1.28/1.60 [452]P22(a2)
% 1.28/1.60 [453]P22(a112)
% 1.28/1.60 [454]P22(a110)
% 1.28/1.60 [455]P50(a1)
% 1.28/1.60 [456]P50(a2)
% 1.28/1.60 [457]P50(a112)
% 1.28/1.60 [458]P50(a110)
% 1.28/1.60 [459]P70(a1)
% 1.28/1.60 [460]P70(a2)
% 1.28/1.60 [461]P70(a112)
% 1.28/1.60 [462]P70(a110)
% 1.28/1.60 [463]P60(a1)
% 1.28/1.60 [464]P60(a2)
% 1.28/1.60 [465]P60(a112)
% 1.28/1.60 [466]P60(a110)
% 1.28/1.60 [467]P71(a1)
% 1.28/1.60 [468]P71(a2)
% 1.28/1.60 [469]P71(a110)
% 1.28/1.60 [470]P61(a1)
% 1.28/1.60 [471]P61(a2)
% 1.28/1.60 [472]P61(a112)
% 1.28/1.60 [473]P61(a110)
% 1.28/1.60 [474]P5(a110)
% 1.28/1.60 [475]P56(a1)
% 1.28/1.60 [476]P56(a110)
% 1.28/1.60 [477]P57(a1)
% 1.28/1.60 [478]P57(a110)
% 1.28/1.60 [479]P66(a1)
% 1.28/1.60 [480]P66(a112)
% 1.28/1.60 [481]P66(a110)
% 1.28/1.60 [482]P67(a1)
% 1.28/1.60 [483]P67(a110)
% 1.28/1.60 [484]P69(a1)
% 1.28/1.60 [485]P69(a112)
% 1.28/1.60 [486]P69(a110)
% 1.28/1.60 [487]P68(a1)
% 1.28/1.60 [488]P68(a112)
% 1.28/1.60 [489]P68(a110)
% 1.28/1.60 [490]P62(a1)
% 1.28/1.60 [491]P62(a112)
% 1.28/1.60 [492]P62(a110)
% 1.28/1.60 [493]P55(a1)
% 1.28/1.60 [494]P55(a112)
% 1.28/1.60 [495]P55(a110)
% 1.28/1.60 [496]P72(a1)
% 1.28/1.60 [497]P72(a2)
% 1.28/1.60 [498]P72(a110)
% 1.28/1.60 [499]P51(a1)
% 1.28/1.60 [500]P51(a2)
% 1.28/1.60 [501]P51(a110)
% 1.28/1.60 [502]P63(a1)
% 1.28/1.60 [503]P63(a112)
% 1.28/1.60 [504]P63(a110)
% 1.28/1.60 [505]P64(a1)
% 1.28/1.60 [506]P64(a110)
% 1.28/1.60 [507]P65(a1)
% 1.28/1.60 [508]P65(a110)
% 1.28/1.60 [509]P43(a1)
% 1.28/1.60 [510]P43(a2)
% 1.28/1.60 [511]P43(a112)
% 1.28/1.60 [512]P43(a110)
% 1.28/1.60 [513]P74(a1)
% 1.28/1.60 [514]P74(a2)
% 1.28/1.60 [515]P74(a112)
% 1.28/1.60 [516]P74(a110)
% 1.28/1.60 [517]P73(a1)
% 1.28/1.60 [518]P73(a2)
% 1.28/1.60 [519]P73(a110)
% 1.28/1.60 [520]P20(a1)
% 1.28/1.60 [521]P20(a2)
% 1.28/1.60 [522]P20(a112)
% 1.28/1.60 [523]P20(a110)
% 1.28/1.60 [672]~P76(a500)
% 1.28/1.60 [544]P6(a1,f3(a1),a114)
% 1.28/1.60 [561]P6(a110,f3(a110),f4(a110))
% 1.28/1.60 [562]P7(a110,f3(a110),f4(a110))
% 1.28/1.60 [566]P6(a1,f22(a2,a21),a114)
% 1.28/1.60 [673]~E(f4(a1),f3(a1))
% 1.28/1.60 [674]~E(f4(a110),f3(a110))
% 1.28/1.60 [524]E(f13(f3(a1)),f3(a112))
% 1.28/1.60 [525]E(f13(f4(a1)),f4(a112))
% 1.28/1.60 [526]E(f18(f3(a1)),f3(a112))
% 1.28/1.60 [527]E(f18(f4(a1)),f4(a112))
% 1.28/1.60 [528]E(f10(a110,f3(a110)),f3(a110))
% 1.28/1.60 [529]E(f19(a112,f3(a112)),f3(a1))
% 1.28/1.60 [530]E(f19(a112,f4(a112)),f4(a1))
% 1.28/1.60 [569]P6(a1,f22(a2,f3(a2)),a114)
% 1.28/1.60 [571]E(f22(a2,f20(f14(a2,a115),a21)),f10(a1,a23))
% 1.28/1.60 [582]E(f19(a112,f12(a112,f3(a112),f4(a112))),f4(a1))
% 1.28/1.60 [645]E(f10(a1,f10(a1,f22(a2,f20(f14(a2,a115),f3(a2))))),f22(a2,f20(f14(a2,a115),f3(a2))))
% 1.28/1.60 [538]P6(a1,x5381,x5381)
% 1.28/1.60 [539]P6(a112,x5391,x5391)
% 1.28/1.60 [540]P6(a110,x5401,x5401)
% 1.28/1.60 [676]~P7(a112,x6761,x6761)
% 1.28/1.60 [546]E(f6(a110,x5461,x5461),f3(a110))
% 1.28/1.60 [547]E(f8(a112,x5471,x5471),f3(a112))
% 1.28/1.60 [549]P6(a112,f3(a112),x5491)
% 1.28/1.60 [568]P6(a1,f3(a1),f19(a112,x5681))
% 1.28/1.60 [679]~P7(a112,x6791,f3(a112))
% 1.28/1.60 [688]~P7(a1,f19(a112,x6881),f3(a1))
% 1.28/1.60 [531]E(f5(f3(a1),x5311),f3(a2))
% 1.28/1.60 [532]E(f13(f19(a112,x5321)),x5321)
% 1.28/1.60 [533]E(f18(f19(a112,x5331)),x5331)
% 1.28/1.60 [534]E(f10(a110,f10(a110,x5341)),x5341)
% 1.28/1.60 [535]E(f20(f20(f11(a112),x5351),f4(a112)),x5351)
% 1.28/1.60 [536]E(f20(f20(f11(a110),x5361),f4(a110)),x5361)
% 1.28/1.60 [537]E(f20(f20(f11(a112),x5371),f3(a112)),f3(a112))
% 1.28/1.60 [550]E(f12(a112,x5501,f3(a112)),x5501)
% 1.28/1.60 [551]E(f12(a110,x5511,f3(a110)),x5511)
% 1.28/1.60 [552]E(f6(a110,x5521,f3(a110)),x5521)
% 1.28/1.60 [553]E(f8(a112,x5531,f3(a112)),x5531)
% 1.28/1.60 [554]E(f12(a112,f3(a112),x5541),x5541)
% 1.28/1.60 [555]E(f12(a110,f3(a110),x5551),x5551)
% 1.28/1.60 [556]E(f7(a110,x5561,f3(a110)),f3(a110))
% 1.28/1.60 [557]E(f7(a110,f3(a110),x5571),f3(a110))
% 1.28/1.60 [558]E(f6(a110,f3(a110),x5581),f3(a110))
% 1.28/1.60 [559]E(f8(a112,f3(a112),x5591),f3(a112))
% 1.28/1.60 [567]E(f12(a110,f10(a110,x5671),x5671),f3(a110))
% 1.28/1.60 [572]P6(a1,f22(a2,f51(x5721)),a114)
% 1.28/1.60 [573]P6(a1,f22(a2,f80(x5731)),a114)
% 1.28/1.60 [574]P6(a1,x5741,f19(a112,f13(x5741)))
% 1.28/1.60 [581]P6(a1,f22(a2,f20(a46,x5811)),a114)
% 1.28/1.60 [584]P6(a1,f10(a1,f22(a2,x5841)),f22(a2,x5841))
% 1.28/1.60 [596]P7(a112,x5961,f12(a112,x5961,f4(a112)))
% 1.28/1.60 [597]P7(a112,f3(a112),f12(a112,x5971,f4(a112)))
% 1.28/1.60 [609]P7(a1,x6091,f12(a1,f19(a112,f18(x6091)),f4(a1)))
% 1.28/1.60 [681]~E(f12(a112,x6811,f4(a112)),x6811)
% 1.28/1.60 [687]~E(f12(a112,x6871,f4(a112)),f3(a112))
% 1.28/1.60 [691]~P6(a112,f12(a112,x6911,f4(a112)),x6911)
% 1.28/1.60 [541]E(f20(f20(f11(a1),f4(a1)),x5411),x5411)
% 1.28/1.60 [542]E(f20(f20(f11(a112),f4(a112)),x5421),x5421)
% 1.28/1.60 [543]E(f20(f20(f11(a110),f4(a110)),x5431),x5431)
% 1.28/1.60 [545]E(f20(f20(f11(a112),f3(a112)),x5451),f3(a112))
% 1.28/1.60 [583]P6(a112,x5831,f20(f20(f11(a112),x5831),x5831))
% 1.28/1.60 [599]E(f7(a112,x5991,f12(a112,f3(a112),f4(a112))),x5991)
% 1.28/1.60 [600]E(f6(a112,x6001,f12(a112,f3(a112),f4(a112))),f3(a112))
% 1.28/1.60 [604]E(f12(a1,f19(a112,x6041),f4(a1)),f19(a112,f12(a112,x6041,f4(a112))))
% 1.28/1.60 [614]P7(a1,f3(a1),f19(a112,f12(a112,x6141,f4(a112))))
% 1.28/1.60 [692]~E(f12(a110,f12(a110,f4(a110),x6921),x6921),f3(a110))
% 1.28/1.60 [626]P6(a112,x6261,f20(f20(f11(a112),x6261),f20(f20(f11(a112),x6261),x6261)))
% 1.28/1.60 [630]E(f20(f20(f16(a112),f12(a112,f3(a112),f4(a112))),x6301),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [666]P7(a1,f22(a2,f20(f14(a2,a115),f51(x6661))),f12(a1,f10(a1,a117),f24(a1,f4(a1),f19(a112,f12(a112,x6661,f4(a112))))))
% 1.28/1.60 [667]P7(a1,f22(a2,f20(f14(a2,a115),f80(x6671))),f12(a1,f10(a1,a117),f24(a1,f4(a1),f19(a112,f12(a112,x6671,f4(a112))))))
% 1.28/1.60 [668]P7(a1,f22(a2,f20(f14(a2,a115),f20(a46,x6681))),f12(a1,f10(a1,a117),f24(a1,f4(a1),f19(a112,f12(a112,x6681,f4(a112))))))
% 1.28/1.60 [570]P7(a1,f3(a1),f45(x5701,x5702))
% 1.28/1.60 [578]E(f12(a112,x5781,x5782),f12(a112,x5782,x5781))
% 1.28/1.60 [579]E(f12(a110,x5791,x5792),f12(a110,x5792,x5791))
% 1.28/1.60 [587]P6(a112,x5871,f12(a112,x5872,x5871))
% 1.28/1.60 [588]P6(a112,x5881,f12(a112,x5881,x5882))
% 1.28/1.60 [589]P6(a112,f7(a112,x5891,x5892),x5891)
% 1.28/1.60 [590]P6(a112,f6(a112,x5901,x5902),x5901)
% 1.28/1.60 [591]P6(a112,f8(a112,x5911,x5912),x5911)
% 1.28/1.60 [689]~P7(a112,f12(a112,x6891,x6892),x6892)
% 1.28/1.60 [690]~P7(a112,f12(a112,x6901,x6902),x6901)
% 1.28/1.60 [585]E(f7(a110,f10(a110,x5851),x5852),f7(a110,x5851,f10(a110,x5852)))
% 1.28/1.60 [586]E(f7(a110,f10(a110,x5861),f10(a110,x5862)),f7(a110,x5861,x5862))
% 1.28/1.60 [592]E(f8(a112,f12(a112,x5921,x5922),x5922),x5921)
% 1.28/1.60 [593]E(f8(a112,f12(a112,x5931,x5932),x5931),x5932)
% 1.28/1.60 [594]E(f8(a112,x5941,f12(a112,x5941,x5942)),f3(a112))
% 1.28/1.60 [595]E(f7(a110,f6(a110,x5951,x5952),x5952),f3(a110))
% 1.28/1.60 [605]E(f12(a110,f10(a110,x6051),f10(a110,x6052)),f10(a110,f12(a110,x6051,x6052)))
% 1.28/1.60 [606]E(f12(a1,f19(a112,x6061),f19(a112,x6062)),f19(a112,f12(a112,x6061,x6062)))
% 1.28/1.60 [607]E(f6(a110,f10(a110,x6071),f10(a110,x6072)),f10(a110,f6(a110,x6071,x6072)))
% 1.28/1.60 [612]P7(a112,f8(a112,x6121,x6122),f12(a112,x6121,f4(a112)))
% 1.28/1.60 [637]P7(a112,x6371,f12(a112,f12(a112,x6372,x6371),f4(a112)))
% 1.28/1.60 [638]P7(a112,x6381,f12(a112,f12(a112,x6381,x6382),f4(a112)))
% 1.28/1.60 [646]E(f12(a110,f20(f20(f11(a110),x6461),f7(a110,x6462,x6461)),f6(a110,x6462,x6461)),x6462)
% 1.28/1.60 [648]P6(a1,f19(a112,f7(a112,x6481,x6482)),f24(a1,f19(a112,x6481),f19(a112,x6482)))
% 1.28/1.60 [656]P6(a1,f22(a2,x6561),f12(a1,f22(a2,f12(a2,x6561,x6562)),f22(a2,x6562)))
% 1.28/1.60 [575]E(f20(f20(f11(a1),x5751),x5752),f20(f20(f11(a1),x5752),x5751))
% 1.28/1.60 [576]E(f20(f20(f11(a112),x5761),x5762),f20(f20(f11(a112),x5762),x5761))
% 1.28/1.60 [577]E(f20(f20(f11(a110),x5771),x5772),f20(f20(f11(a110),x5772),x5771))
% 1.28/1.60 [610]E(f10(a110,f6(a110,f10(a110,x6101),x6102)),f6(a110,x6101,f10(a110,x6102)))
% 1.28/1.60 [625]E(f12(a112,f12(a112,x6251,f4(a112)),x6252),f12(a112,f12(a112,x6251,x6252),f4(a112)))
% 1.28/1.60 [627]E(f8(a112,f8(a112,x6271,f4(a112)),x6272),f8(a112,x6271,f12(a112,x6272,f4(a112))))
% 1.28/1.60 [628]E(f12(a112,f12(a112,x6281,f4(a112)),x6282),f12(a112,x6281,f12(a112,x6282,f4(a112))))
% 1.28/1.60 [632]E(f6(a110,f10(a110,f6(a110,x6321,x6322)),x6322),f6(a110,f10(a110,x6321),x6322))
% 1.28/1.60 [655]E(f6(a112,f12(a112,f6(a112,x6551,x6552),f4(a112)),x6552),f6(a112,f12(a112,x6551,f4(a112)),x6552))
% 1.28/1.60 [602]E(f20(f20(f11(a110),f10(a110,x6021)),x6022),f10(a110,f20(f20(f11(a110),x6021),x6022)))
% 1.28/1.60 [603]E(f20(f20(f16(a1),f19(a112,x6031)),x6032),f19(a112,f20(f20(f16(a112),x6031),x6032)))
% 1.28/1.60 [608]E(f20(f20(f11(a1),f19(a112,x6081)),f19(a112,x6082)),f19(a112,f20(f20(f11(a112),x6081),x6082)))
% 1.28/1.60 [613]E(f24(a1,f20(f20(f11(a1),x6131),x6132),f20(f20(f11(a1),x6131),x6131)),f24(a1,x6132,x6131))
% 1.28/1.60 [615]E(f20(f20(f11(a112),x6151),f12(a112,x6152,f4(a112))),f12(a112,x6151,f20(f20(f11(a112),x6151),x6152)))
% 1.28/1.60 [631]P6(a1,f10(a1,f20(f20(f11(a1),x6311),x6311)),f20(f20(f11(a1),x6312),x6312))
% 1.28/1.60 [644]E(f20(f20(f11(a112),f12(a112,x6441,f4(a112))),x6442),f12(a112,x6442,f20(f20(f11(a112),x6441),x6442)))
% 1.28/1.60 [671]E(f12(a112,f12(a112,f7(a112,x6711,x6712),f7(a112,f12(a112,f3(a112),f4(a112)),x6712)),f7(a112,f12(a112,f6(a112,x6711,x6712),f6(a112,f12(a112,f3(a112),f4(a112)),x6712)),x6712)),f7(a112,f12(a112,x6711,f4(a112)),x6712))
% 1.28/1.60 [617]E(f12(a112,x6171,f12(a112,x6172,x6173)),f12(a112,x6172,f12(a112,x6171,x6173)))
% 1.28/1.60 [618]E(f12(a110,x6181,f12(a110,x6182,x6183)),f12(a110,x6182,f12(a110,x6181,x6183)))
% 1.28/1.60 [619]E(f12(a112,f12(a112,x6191,x6192),x6193),f12(a112,x6191,f12(a112,x6192,x6193)))
% 1.28/1.60 [620]E(f12(a110,f12(a110,x6201,x6202),x6203),f12(a110,x6201,f12(a110,x6202,x6203)))
% 1.28/1.60 [621]E(f8(a112,f8(a112,x6211,x6212),x6213),f8(a112,x6211,f12(a112,x6212,x6213)))
% 1.28/1.60 [622]E(f8(a112,f12(a112,x6221,x6222),f12(a112,x6223,x6222)),f8(a112,x6221,x6223))
% 1.28/1.60 [623]E(f8(a112,f12(a112,x6231,x6232),f12(a112,x6231,x6233)),f8(a112,x6232,x6233))
% 1.28/1.60 [658]E(f6(a112,f12(a112,f12(a112,f20(f20(f11(a112),x6581),x6582),x6583),f4(a112)),x6582),f6(a112,f12(a112,x6583,f4(a112)),x6582))
% 1.28/1.60 [661]E(f12(a110,f12(a110,f20(f20(f11(a110),x6611),f7(a110,x6612,x6611)),f6(a110,x6612,x6611)),x6613),f12(a110,x6612,x6613))
% 1.28/1.60 [665]E(f12(a110,f12(a110,f20(f20(f11(a110),f7(a110,x6651,x6652)),x6652),f6(a110,x6651,x6652)),x6653),f12(a110,x6651,x6653))
% 1.28/1.60 [616]E(f7(a112,x6161,f20(f20(f11(a112),x6162),x6163)),f7(a112,f7(a112,x6161,x6162),x6163))
% 1.28/1.60 [639]E(f12(a112,f20(f20(f11(a112),x6391),x6392),f20(f20(f11(a112),x6391),x6393)),f20(f20(f11(a112),x6391),f12(a112,x6392,x6393)))
% 1.28/1.60 [640]E(f6(a112,f20(f20(f11(a112),x6401),x6402),f20(f20(f11(a112),x6401),x6403)),f20(f20(f11(a112),x6401),f6(a112,x6402,x6403)))
% 1.28/1.60 [641]E(f12(a110,f20(f20(f11(a110),x6411),x6412),f20(f20(f11(a110),x6411),x6413)),f20(f20(f11(a110),x6411),f12(a110,x6412,x6413)))
% 1.28/1.60 [642]E(f5(f20(f20(f16(a1),x6421),x6422),f20(f20(f11(a1),f19(a112,x6422)),x6423)),f20(f20(f16(a2),f5(x6421,x6423)),x6422))
% 1.28/1.60 [647]E(f20(f20(f11(a110),f20(f20(f16(a110),x6471),x6472)),f20(f20(f16(a110),x6471),x6473)),f20(f20(f16(a110),x6471),f12(a112,x6472,x6473)))
% 1.28/1.60 [649]E(f12(a1,f20(f20(f11(a1),x6491),x6492),f20(f20(f11(a1),x6493),x6492)),f20(f20(f11(a1),f12(a1,x6491,x6493)),x6492))
% 1.28/1.60 [650]E(f12(a112,f20(f20(f11(a112),x6501),x6502),f20(f20(f11(a112),x6503),x6502)),f20(f20(f11(a112),f12(a112,x6501,x6503)),x6502))
% 1.28/1.60 [651]E(f6(a112,f20(f20(f11(a112),x6511),x6512),f20(f20(f11(a112),x6513),x6512)),f20(f20(f11(a112),f6(a112,x6511,x6513)),x6512))
% 1.28/1.60 [652]E(f12(a110,f20(f20(f11(a110),x6521),x6522),f20(f20(f11(a110),x6523),x6522)),f20(f20(f11(a110),f12(a110,x6521,x6523)),x6522))
% 1.28/1.60 [654]E(f6(a110,f20(f20(f11(a110),x6541),f6(a110,x6542,x6543)),x6543),f6(a110,f20(f20(f11(a110),x6541),x6542),x6543))
% 1.28/1.60 [657]E(f6(a110,f20(f20(f16(a110),f6(a110,x6571,x6572)),x6573),x6572),f6(a110,f20(f20(f16(a110),x6571),x6573),x6572))
% 1.28/1.60 [662]E(f12(a112,f20(f20(f11(a112),x6621),f6(a112,f7(a112,x6622,x6621),x6623)),f6(a112,x6622,x6621)),f6(a112,x6622,f20(f20(f11(a112),x6621),x6623)))
% 1.28/1.60 [663]E(f12(a112,f20(f20(f11(a112),x6631),f7(a112,x6632,x6633)),f7(a112,f20(f20(f11(a112),x6631),f6(a112,x6632,x6633)),x6633)),f7(a112,f20(f20(f11(a112),x6631),x6632),x6633))
% 1.28/1.60 [664]E(f12(a110,f20(f20(f11(a110),x6641),f7(a110,x6642,x6643)),f7(a110,f20(f20(f11(a110),x6641),f6(a110,x6642,x6643)),x6643)),f7(a110,f20(f20(f11(a110),x6641),x6642),x6643))
% 1.28/1.60 [669]E(f12(a112,f12(a112,f7(a112,x6691,x6692),f7(a112,x6693,x6692)),f7(a112,f12(a112,f6(a112,x6691,x6692),f6(a112,x6693,x6692)),x6692)),f7(a112,f12(a112,x6691,x6693),x6692))
% 1.28/1.60 [670]E(f12(a110,f12(a110,f7(a110,x6701,x6702),f7(a110,x6703,x6702)),f7(a110,f12(a110,f6(a110,x6701,x6702),f6(a110,x6703,x6702)),x6702)),f7(a110,f12(a110,x6701,x6703),x6702))
% 1.28/1.60 [633]E(f20(f20(f11(a1),f20(f20(f11(a1),x6331),x6332)),x6333),f20(f20(f11(a1),x6331),f20(f20(f11(a1),x6332),x6333)))
% 1.28/1.60 [634]E(f20(f20(f11(a112),f20(f20(f11(a112),x6341),x6342)),x6343),f20(f20(f11(a112),x6341),f20(f20(f11(a112),x6342),x6343)))
% 1.28/1.60 [635]E(f20(f20(f11(a110),f20(f20(f11(a110),x6351),x6352)),x6353),f20(f20(f11(a110),x6351),f20(f20(f11(a110),x6352),x6353)))
% 1.28/1.60 [636]E(f20(f20(f16(a110),f20(f20(f16(a110),x6361),x6362)),x6363),f20(f20(f16(a110),x6361),f20(f20(f11(a112),x6362),x6363)))
% 1.28/1.60 [643]E(f6(a112,f12(a112,f20(f20(f11(a112),x6431),x6432),x6433),x6432),f6(a112,x6433,x6432))
% 1.28/1.60 [611]E(f20(f20(f17(x6111,x6112,x6113),x6114),f3(a112)),x6112)
% 1.28/1.60 [629]E(f5(f20(f20(f11(a1),x6291),x6292),f12(a1,x6293,x6294)),f20(f20(f11(a2),f5(x6291,x6293)),f5(x6292,x6294)))
% 1.28/1.60 [660]E(f12(a112,f20(f20(f11(a112),x6601),x6602),f12(a112,f20(f20(f11(a112),x6603),x6602),x6604)),f12(a112,f20(f20(f11(a112),f12(a112,x6601,x6603)),x6602),x6604))
% 1.28/1.60 [659]E(f20(f20(f17(x6591,x6592,x6593),x6594),f12(a112,x6595,f4(a112))),f20(f20(x6593,x6594),f20(f20(f17(x6591,x6592,x6593),x6594),x6595)))
% 1.28/1.60 [1201]~P7(a1,f10(a1,a117),f10(a1,a117))+P6(a1,f22(a2,a109),a114)
% 1.28/1.60 [1554]~P7(a1,f10(a1,a117),f10(a1,a117))+P7(a1,f22(a2,f20(f14(a2,a115),a109)),f10(a1,a117))
% 1.28/1.60 [693]~P16(x6931)+P14(f113(x6931))
% 1.28/1.60 [694]~P52(x6941)+P45(f113(x6941))
% 1.28/1.60 [695]~P52(x6951)+P24(f113(x6951))
% 1.28/1.60 [696]~P33(x6961)+P33(f113(x6961))
% 1.28/1.60 [697]~P52(x6971)+P52(f113(x6971))
% 1.28/1.60 [698]~P21(x6981)+P15(f113(x6981))
% 1.28/1.60 [699]~P20(x6991)+P17(f113(x6991))
% 1.28/1.60 [700]~P20(x7001)+P18(f113(x7001))
% 1.28/1.60 [701]~P48(x7011)+P25(f113(x7011))
% 1.28/1.60 [702]~P21(x7021)+P26(f113(x7021))
% 1.28/1.60 [703]~P21(x7031)+P21(f113(x7031))
% 1.28/1.60 [704]~P52(x7041)+P27(f113(x7041))
% 1.28/1.60 [705]~P52(x7051)+P29(f113(x7051))
% 1.28/1.60 [706]~P52(x7061)+P30(f113(x7061))
% 1.28/1.60 [707]~P52(x7071)+P32(f113(x7071))
% 1.28/1.60 [708]~P48(x7081)+P58(f113(x7081))
% 1.28/1.60 [709]~P52(x7091)+P31(f113(x7091))
% 1.28/1.60 [710]~P16(x7101)+P16(f113(x7101))
% 1.28/1.60 [711]~P52(x7111)+P35(f113(x7111))
% 1.28/1.60 [712]~P47(x7121)+P47(f113(x7121))
% 1.28/1.60 [713]~P48(x7131)+P48(f113(x7131))
% 1.28/1.60 [714]~P49(x7141)+P49(f113(x7141))
% 1.28/1.60 [715]~P52(x7151)+P36(f113(x7151))
% 1.28/1.60 [716]~P52(x7161)+P37(f113(x7161))
% 1.28/1.60 [717]~P52(x7171)+P41(f113(x7171))
% 1.28/1.60 [718]~P52(x7181)+P38(f113(x7181))
% 1.28/1.60 [719]~P54(x7191)+P54(f113(x7191))
% 1.28/1.60 [720]~P16(x7201)+P34(f113(x7201))
% 1.28/1.60 [721]~P54(x7211)+P75(f113(x7211))
% 1.28/1.60 [722]~P11(x7221)+P4(f113(x7221))
% 1.28/1.60 [723]~P47(x7231)+P59(f113(x7231))
% 1.28/1.60 [724]~P49(x7241)+P19(f113(x7241))
% 1.28/1.60 [725]~P48(x7251)+P28(f113(x7251))
% 1.28/1.60 [726]~P48(x7261)+P22(f113(x7261))
% 1.28/1.60 [727]~P49(x7271)+P50(f113(x7271))
% 1.28/1.60 [728]~P49(x7281)+P70(f113(x7281))
% 1.28/1.60 [729]~P54(x7291)+P60(f113(x7291))
% 1.28/1.60 [730]~P54(x7301)+P71(f113(x7301))
% 1.28/1.60 [731]~P49(x7311)+P61(f113(x7311))
% 1.28/1.60 [732]~P11(x7321)+P5(f113(x7321))
% 1.28/1.60 [733]~P52(x7331)+P56(f113(x7331))
% 1.28/1.60 [734]~P52(x7341)+P57(f113(x7341))
% 1.28/1.60 [735]~P52(x7351)+P66(f113(x7351))
% 1.28/1.60 [736]~P52(x7361)+P67(f113(x7361))
% 1.28/1.60 [737]~P52(x7371)+P69(f113(x7371))
% 1.28/1.60 [738]~P52(x7381)+P68(f113(x7381))
% 1.28/1.60 [739]~P52(x7391)+P62(f113(x7391))
% 1.28/1.60 [740]~P52(x7401)+P55(f113(x7401))
% 1.28/1.60 [741]~P54(x7411)+P72(f113(x7411))
% 1.28/1.60 [742]~P51(x7421)+P51(f113(x7421))
% 1.28/1.60 [743]~P52(x7431)+P63(f113(x7431))
% 1.28/1.60 [744]~P52(x7441)+P64(f113(x7441))
% 1.28/1.60 [745]~P52(x7451)+P65(f113(x7451))
% 1.28/1.60 [746]~P48(x7461)+P43(f113(x7461))
% 1.28/1.60 [747]~P49(x7471)+P74(f113(x7471))
% 1.28/1.60 [748]~P51(x7481)+P73(f113(x7481))
% 1.28/1.60 [749]~P20(x7491)+P20(f113(x7491))
% 1.28/1.60 [751]~P58(x7511)+~E(f4(x7511),f3(x7511))
% 1.28/1.60 [752]~E(x7521,f3(a112))+E(f19(a112,x7521),f3(a1))
% 1.28/1.60 [753]E(x7531,f3(a112))+~E(f19(a112,x7531),f3(a1))
% 1.28/1.60 [790]E(x7901,f3(a110))+E(f7(a110,x7901,x7901),f4(a110))
% 1.28/1.60 [792]E(x7921,f3(a112))+P7(a112,f3(a112),x7921)
% 1.28/1.60 [829]~P42(x8291)+P6(a1,f3(a1),f81(x8291))
% 1.28/1.60 [830]~P42(x8301)+P7(a1,f3(a1),f82(x8301))
% 1.28/1.60 [852]~P45(x8521)+P6(x8521,f3(x8521),f4(x8521))
% 1.28/1.60 [853]~P45(x8531)+P7(x8531,f3(x8531),f4(x8531))
% 1.28/1.60 [874]~E(x8741,f3(a112))+P6(a1,f19(a112,x8741),f3(a1))
% 1.28/1.60 [904]E(x9041,f3(a112))+~P6(a112,x9041,f3(a112))
% 1.28/1.60 [908]E(f13(x9081),f3(a112))+~P6(a1,x9081,f3(a1))
% 1.28/1.60 [909]E(f18(x9091),f3(a112))+~P6(a1,x9091,f3(a1))
% 1.28/1.60 [951]~P45(x9511)+~P6(x9511,f4(x9511),f3(x9511))
% 1.28/1.60 [952]~P45(x9521)+~P7(x9521,f4(x9521),f3(x9521))
% 1.28/1.60 [980]E(x9801,f3(a112))+~P6(a1,f19(a112,x9801),f3(a1))
% 1.28/1.60 [1010]~P7(a1,x10101,a117)+P7(a1,x10101,f54(x10101))
% 1.28/1.60 [1011]~P7(a1,x10111,a39)+P7(a1,x10111,f38(x10111))
% 1.28/1.60 [1015]~P7(a110,f3(a110),x10151)+P6(a110,f4(a110),x10151)
% 1.28/1.60 [1016]~P6(a110,f4(a110),x10161)+P7(a110,f3(a110),x10161)
% 1.28/1.60 [1042]~P6(a1,x10421,f4(a1))+P6(a112,f13(x10421),f4(a112))
% 1.28/1.60 [1043]~P6(a1,f4(a1),x10431)+P6(a112,f4(a112),f18(x10431))
% 1.28/1.60 [1057]~P6(a112,f13(x10571),f4(a112))+P6(a1,x10571,f4(a1))
% 1.28/1.60 [1058]~P6(a112,f4(a112),f18(x10581))+P6(a1,f4(a1),x10581)
% 1.28/1.60 [1073]~P7(a112,f3(a112),x10731)+P7(a1,f3(a1),f19(a112,x10731))
% 1.28/1.60 [1121]P7(a112,f3(a112),x11211)+~P7(a1,f3(a1),f19(a112,x11211))
% 1.28/1.60 [754]~P1(x7541)+E(f22(x7541,f3(x7541)),f3(a1))
% 1.28/1.60 [755]~P23(x7551)+E(f22(x7551,f4(x7551)),f4(a1))
% 1.28/1.60 [758]~P14(x7581)+E(f10(x7581,f3(x7581)),f3(x7581))
% 1.28/1.60 [864]~P43(x8641)+E(f17(x8641,f4(x8641),f11(x8641)),f16(x8641))
% 1.28/1.60 [1044]~P7(a112,f3(a112),x10441)+E(f12(a112,f41(x10441),f4(a112)),x10441)
% 1.28/1.60 [1077]~P7(a1,x10771,a117)+P6(a1,f22(a2,f69(x10771)),a114)
% 1.28/1.60 [1078]~P7(a1,x10781,a39)+P6(a1,f22(a2,f43(x10781)),a114)
% 1.28/1.60 [1097]~P6(a1,f3(a1),x10971)+P6(a1,f19(a112,f18(x10971)),x10971)
% 1.28/1.60 [1098]~P6(a1,f3(a1),x10981)+P6(a1,f19(a112,f56(x10981)),x10981)
% 1.28/1.60 [1156]~P45(x11561)+P7(x11561,f3(x11561),f12(x11561,f4(x11561),f4(x11561)))
% 1.28/1.60 [1168]~P7(a1,f10(a1,a117),x11681)+P6(a1,f22(a2,f91(x11681)),a114)
% 1.28/1.60 [1169]~P7(a1,f10(a1,a117),x11691)+P6(a1,f22(a2,f102(x11691)),a114)
% 1.28/1.60 [1307]~P6(a110,f3(a110),x13071)+P7(a110,f3(a110),f12(a110,f4(a110),x13071))
% 1.28/1.60 [1326]E(x13261,f3(a112))+~P7(a112,x13261,f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [785]~P16(x7851)+E(f10(f113(x7851),f3(f113(x7851))),f3(f113(x7851)))
% 1.28/1.60 [1027]E(x10271,f3(a1))+P7(a1,f3(a1),f20(f20(f11(a1),x10271),x10271))
% 1.28/1.60 [1146]~P7(a1,x11461,a117)+E(f22(a2,f20(f14(a2,a115),f69(x11461))),f10(a1,f54(x11461)))
% 1.28/1.60 [1147]~P7(a1,x11471,a39)+E(f22(a2,f20(f14(a2,a115),f43(x11471))),f10(a1,f38(x11471)))
% 1.28/1.60 [1250]~E(x12501,f3(a1))+~P7(a1,f3(a1),f20(f20(f11(a1),x12501),x12501))
% 1.28/1.60 [1317]~P6(a1,f3(a1),x13171)+E(f13(f12(a1,x13171,f4(a1))),f12(a112,f13(x13171),f4(a112)))
% 1.28/1.60 [1318]~P6(a1,f3(a1),x13181)+E(f18(f12(a1,x13181,f4(a1))),f12(a112,f18(x13181),f4(a112)))
% 1.28/1.60 [1482]~P6(a1,f22(a2,x14821),a114)+P6(a1,f10(a1,a117),f22(a2,f20(f14(a2,a115),x14821)))
% 1.28/1.60 [1483]~P7(a1,f10(a1,a117),x14831)+P7(a1,f22(a2,f20(f14(a2,a115),f102(x14831))),x14831)
% 1.28/1.60 [1634]~P6(a1,f3(a1),x16341)+P7(a1,x16341,f19(a112,f12(a112,f56(x16341),f4(a112))))
% 1.28/1.60 [1734]~P7(a110,x17341,f3(a110))+P7(a110,f12(a110,f12(a110,f4(a110),x17341),x17341),f3(a110))
% 1.28/1.60 [1952]P7(a110,x19521,f3(a110))+~P7(a110,f12(a110,f12(a110,f4(a110),x19521),x19521),f3(a110))
% 1.28/1.60 [2042]~P7(a1,f10(a1,a117),x20421)+P7(a1,f10(a1,f10(a1,f22(a2,f20(f14(a2,a115),f91(x20421))))),x20421)
% 1.28/1.60 [786]~E(x7861,x7862)+P6(a1,x7861,x7862)
% 1.28/1.60 [789]~E(x7891,x7892)+P6(a112,x7891,x7892)
% 1.28/1.60 [800]~P35(x8001)+P6(x8001,x8002,x8002)
% 1.28/1.60 [878]~E(x8781,x8782)+~P7(a1,x8781,x8782)
% 1.28/1.60 [883]~E(x8831,x8832)+~P7(a112,x8831,x8832)
% 1.28/1.60 [884]~E(x8841,x8842)+~P7(a110,x8841,x8842)
% 1.28/1.60 [905]~P7(x9051,x9052,x9052)+~P35(x9051)
% 1.28/1.60 [934]P6(a1,x9342,x9341)+P6(a1,x9341,x9342)
% 1.28/1.60 [935]P6(a112,x9352,x9351)+P6(a112,x9351,x9352)
% 1.28/1.60 [936]P6(a110,x9362,x9361)+P6(a110,x9361,x9362)
% 1.28/1.60 [988]~P7(a1,x9881,x9882)+P6(a1,x9881,x9882)
% 1.28/1.60 [993]~P7(a112,x9931,x9932)+P6(a112,x9931,x9932)
% 1.28/1.60 [994]~P7(a110,x9941,x9942)+P6(a110,x9941,x9942)
% 1.28/1.60 [764]~P35(x7642)+P35(f116(x7641,x7642))
% 1.28/1.60 [765]~P36(x7652)+P36(f116(x7651,x7652))
% 1.28/1.60 [766]~P41(x7662)+P41(f116(x7661,x7662))
% 1.28/1.60 [767]~P39(x7672)+P39(f116(x7671,x7672))
% 1.28/1.60 [768]~P34(x7682)+P34(f116(x7681,x7682))
% 1.28/1.60 [772]E(x7721,x7722)+~E(f19(a112,x7721),f19(a112,x7722))
% 1.28/1.60 [799]~E(x7992,f3(a110))+E(f7(a110,x7991,x7992),f3(a110))
% 1.28/1.60 [808]~P4(x8081)+E(f6(x8081,x8082,x8082),f3(x8081))
% 1.28/1.60 [809]~P14(x8091)+E(f8(x8091,x8092,x8092),f3(x8091))
% 1.28/1.60 [863]~E(x8632,f10(a1,x8631))+E(f12(a1,x8631,x8632),f3(a1))
% 1.28/1.60 [887]~E(f12(a112,x8872,x8871),x8872)+E(x8871,f3(a112))
% 1.28/1.60 [889]~P1(x8891)+P6(a1,f3(a1),f22(x8891,x8892))
% 1.28/1.60 [890]~P12(x8902)+P6(a1,f3(a1),f83(x8901,x8902))
% 1.28/1.60 [891]~P42(x8912)+P6(a1,f3(a1),f86(x8911,x8912))
% 1.28/1.60 [892]~P42(x8922)+P6(a1,f3(a1),f87(x8921,x8922))
% 1.28/1.60 [893]~P12(x8932)+P7(a1,f3(a1),f52(x8931,x8932))
% 1.28/1.60 [894]~P42(x8942)+P7(a1,f3(a1),f84(x8941,x8942))
% 1.28/1.60 [895]~P42(x8952)+P7(a1,f3(a1),f85(x8951,x8952))
% 1.28/1.60 [898]~P7(a112,x8982,x8981)+~E(x8981,f3(a112))
% 1.28/1.60 [899]E(x8991,f3(a112))+~E(f12(a112,x8992,x8991),f3(a112))
% 1.28/1.60 [900]E(x9001,f3(a112))+~E(f12(a112,x9001,x9002),f3(a112))
% 1.28/1.60 [925]E(x9251,f10(a1,x9252))+~E(f12(a1,x9252,x9251),f3(a1))
% 1.28/1.60 [986]~P1(x9861)+~P7(a1,f22(x9861,x9862),f3(a1))
% 1.28/1.60 [996]~P7(a112,x9961,x9962)+E(f6(a112,x9961,x9962),x9961)
% 1.28/1.60 [1000]~P7(a112,x10001,x10002)+E(f7(a112,x10001,x10002),f3(a112))
% 1.28/1.60 [1002]~P6(a112,x10021,x10022)+E(f8(a112,x10021,x10022),f3(a112))
% 1.28/1.60 [1009]P6(a112,x10091,x10092)+~E(f8(a112,x10091,x10092),f3(a112))
% 1.28/1.60 [1023]~P6(a1,x10231,x10232)+P6(a112,f13(x10231),f13(x10232))
% 1.28/1.60 [1024]~P6(a1,x10241,x10242)+P6(a112,f18(x10241),f18(x10242))
% 1.28/1.60 [1061]E(f6(a110,x10611,x10612),f26(x10611,x10612))+~P6(a110,f3(a110),x10612)
% 1.28/1.60 [1062]E(f7(a110,x10621,x10622),f27(x10621,x10622))+~P6(a110,f3(a110),x10622)
% 1.28/1.60 [1103]P6(a112,x11031,f18(x11032))+~P6(a1,f19(a112,x11031),x11032)
% 1.28/1.60 [1104]P6(a112,f13(x11041),x11042)+~P6(a1,x11041,f19(a112,x11042))
% 1.28/1.60 [1127]~P6(a112,x11271,x11272)+P6(a1,f19(a112,x11271),f19(a112,x11272))
% 1.28/1.60 [1128]~P7(a112,x11281,x11282)+P7(a1,f19(a112,x11281),f19(a112,x11282))
% 1.28/1.60 [1179]P6(a112,x11791,x11792)+~P6(a1,f19(a112,x11791),f19(a112,x11792))
% 1.28/1.60 [1180]P7(a112,x11801,x11802)+~P7(a1,f19(a112,x11801),f19(a112,x11802))
% 1.28/1.60 [1273]~P7(a112,x12732,x12731)+P7(a112,f3(a112),f8(a112,x12731,x12732))
% 1.28/1.60 [1278]P7(a110,x12781,f6(a110,x12782,x12781))+~P7(a110,x12781,f3(a110))
% 1.28/1.60 [1279]P6(a112,f6(a112,x12791,x12792),x12792)+~P7(a112,f3(a112),x12792)
% 1.28/1.60 [1280]P6(a110,f6(a110,x12801,x12802),x12801)+~P6(a110,f3(a110),x12801)
% 1.28/1.60 [1281]P7(a112,f6(a112,x12811,x12812),x12812)+~P7(a112,f3(a112),x12812)
% 1.28/1.60 [1283]P7(a110,f6(a110,x12831,x12832),x12832)+~P7(a110,f3(a110),x12832)
% 1.28/1.60 [1300]~P7(a110,f3(a110),x13002)+P6(a110,f3(a110),f6(a110,x13001,x13002))
% 1.28/1.60 [1304]~P7(a110,x13042,f3(a110))+P6(a110,f6(a110,x13041,x13042),f3(a110))
% 1.28/1.60 [1344]~P6(a1,f10(a1,x13441),x13442)+P6(a1,f3(a1),f12(a1,x13441,x13442))
% 1.28/1.60 [1345]~P7(a1,f10(a1,x13451),x13452)+P7(a1,f3(a1),f12(a1,x13451,x13452))
% 1.28/1.60 [1346]~P6(a1,x13462,f10(a1,x13461))+P6(a1,f12(a1,x13461,x13462),f3(a1))
% 1.28/1.60 [1347]~P7(a1,x13472,f10(a1,x13471))+P7(a1,f12(a1,x13471,x13472),f3(a1))
% 1.28/1.60 [1378]P7(a112,x13781,x13782)+~P7(a112,f3(a112),f8(a112,x13782,x13781))
% 1.28/1.60 [1425]P6(a1,x14251,f10(a1,x14252))+~P6(a1,f12(a1,x14252,x14251),f3(a1))
% 1.28/1.60 [1426]P7(a1,x14261,f10(a1,x14262))+~P7(a1,f12(a1,x14262,x14261),f3(a1))
% 1.28/1.60 [1427]P6(a1,f10(a1,x14271),x14272)+~P6(a1,f3(a1),f12(a1,x14271,x14272))
% 1.28/1.60 [1428]P7(a1,f10(a1,x14281),x14282)+~P7(a1,f3(a1),f12(a1,x14281,x14282))
% 1.28/1.60 [779]~P14(x7791)+E(f10(x7791,f10(x7791,x7792)),x7792)
% 1.28/1.60 [780]~P39(x7801)+E(f10(x7801,f10(x7801,x7802)),x7802)
% 1.28/1.60 [798]~P1(x7981)+E(f22(x7981,f10(x7981,x7982)),f22(x7981,x7982))
% 1.28/1.60 [802]~P48(x8021)+E(f20(f20(f16(x8021),x8022),f4(a112)),x8022)
% 1.28/1.60 [803]~P28(x8031)+E(f20(f20(f16(x8031),x8032),f4(a112)),x8032)
% 1.28/1.60 [810]~P48(x8101)+E(f20(f20(f11(x8101),x8102),f4(x8101)),x8102)
% 1.28/1.60 [811]~P28(x8111)+E(f20(f20(f11(x8111),x8112),f4(x8111)),x8112)
% 1.28/1.60 [812]~P22(x8121)+E(f20(f20(f11(x8121),x8122),f4(x8121)),x8122)
% 1.28/1.60 [813]~P48(x8131)+E(f20(f20(f16(x8131),x8132),f3(a112)),f4(x8131))
% 1.28/1.60 [814]~P43(x8141)+E(f20(f20(f16(x8141),x8142),f3(a112)),f4(x8141))
% 1.28/1.60 [816]~P46(x8161)+E(f24(x8161,x8162,f4(x8161)),x8162)
% 1.28/1.60 [817]~P26(x8171)+E(f12(x8171,x8172,f3(x8171)),x8172)
% 1.28/1.60 [818]~P21(x8181)+E(f12(x8181,x8182,f3(x8181)),x8182)
% 1.28/1.60 [819]~P48(x8191)+E(f12(x8191,x8192,f3(x8191)),x8192)
% 1.28/1.60 [820]~P4(x8201)+E(f7(x8201,x8202,f4(x8201)),x8202)
% 1.28/1.60 [821]~P4(x8211)+E(f6(x8211,x8212,f3(x8211)),x8212)
% 1.28/1.60 [822]~P14(x8221)+E(f8(x8221,x8222,f3(x8221)),x8222)
% 1.28/1.60 [823]~P26(x8231)+E(f12(x8231,f3(x8231),x8232),x8232)
% 1.28/1.60 [824]~P21(x8241)+E(f12(x8241,f3(x8241),x8242),x8242)
% 1.28/1.60 [825]~P48(x8251)+E(f12(x8251,f3(x8251),x8252),x8252)
% 1.28/1.60 [831]~P48(x8311)+E(f20(f20(f11(x8311),x8312),f3(x8311)),f3(x8311))
% 1.28/1.60 [833]~P42(x8331)+E(f20(f20(f11(x8331),x8332),f3(x8331)),f3(x8331))
% 1.28/1.60 [834]~P61(x8341)+E(f20(f20(f11(x8341),x8342),f3(x8341)),f3(x8341))
% 1.28/1.60 [839]~P53(x8391)+E(f24(x8391,x8392,f3(x8391)),f3(x8391))
% 1.28/1.60 [840]~P4(x8401)+E(f7(x8401,x8402,f3(x8401)),f3(x8401))
% 1.28/1.60 [841]~P4(x8411)+E(f6(x8411,x8412,f4(x8411)),f3(x8411))
% 1.28/1.60 [842]~P12(x8421)+E(f24(x8421,f3(x8421),x8422),f3(x8421))
% 1.28/1.60 [843]~P46(x8431)+E(f24(x8431,f3(x8431),x8432),f3(x8431))
% 1.28/1.60 [844]~P4(x8441)+E(f7(x8441,f3(x8441),x8442),f3(x8441))
% 1.28/1.60 [845]~P4(x8451)+E(f6(x8451,f3(x8451),x8452),f3(x8451))
% 1.28/1.60 [872]~E(x8721,x8722)+E(f12(a1,x8721,f10(a1,x8722)),f3(a1))
% 1.28/1.60 [901]~P14(x9011)+E(f12(x9011,x9012,f10(x9011,x9012)),f3(x9011))
% 1.28/1.60 [902]~P14(x9021)+E(f12(x9021,f10(x9021,x9022),x9022),f3(x9021))
% 1.28/1.60 [903]~P16(x9031)+E(f12(x9031,f10(x9031,x9032),x9032),f3(x9031))
% 1.28/1.60 [976]E(x9761,x9762)+~E(f12(a1,x9761,f10(a1,x9762)),f3(a1))
% 1.28/1.60 [979]E(x9791,x9792)+~E(f20(x9791,f25(x9792,x9791)),f20(x9792,f25(x9792,x9791)))
% 1.28/1.60 [1017]P7(a112,f3(a112),x10171)+~E(x10171,f12(a112,x10172,f4(a112)))
% 1.28/1.60 [1018]P6(a110,f3(a110),x10182)+E(f6(a110,x10181,f10(a110,x10182)),f26(x10181,x10182))
% 1.28/1.60 [1063]~E(f6(a112,x10632,x10631),f3(a112))+E(f20(f20(f11(a112),x10631),f73(x10631,x10632)),x10632)
% 1.28/1.60 [1064]~E(f6(a110,x10642,x10641),f3(a110))+E(f20(f20(f11(a110),x10641),f88(x10641,x10642)),x10642)
% 1.28/1.60 [1066]~P6(a112,x10661,x10662)+E(f12(a112,x10661,f42(x10662,x10661)),x10662)
% 1.28/1.60 [1067]~P6(a112,x10671,x10672)+E(f12(a112,x10671,f49(x10672,x10671)),x10672)
% 1.28/1.60 [1068]~E(f6(a110,x10681,x10682),f3(a110))+E(f6(a110,x10681,f10(a110,x10682)),f3(a110))
% 1.28/1.60 [1069]~E(f6(a110,x10691,x10692),f3(a110))+E(f6(a110,f10(a110,x10691),x10692),f3(a110))
% 1.28/1.60 [1071]~E(x10711,x10712)+P7(a112,x10711,f12(a112,x10712,f4(a112)))
% 1.28/1.60 [1072]~E(x10721,x10722)+P7(a110,x10721,f12(a110,x10722,f4(a110)))
% 1.28/1.60 [1081]~E(x10811,f3(a112))+P7(a112,x10811,f12(a112,x10812,f4(a112)))
% 1.28/1.60 [1120]~P45(x11201)+P7(x11201,x11202,f12(x11201,x11202,f4(x11201)))
% 1.28/1.60 [1181]P7(a112,x11812,x11811)+E(f12(a112,x11811,f8(a112,x11812,x11811)),x11812)
% 1.28/1.60 [1199]P7(a112,x11991,x11992)+P7(a112,x11992,f12(a112,x11991,f4(a112)))
% 1.28/1.60 [1200]P6(a112,x12001,x12002)+P6(a112,f12(a112,x12002,f4(a112)),x12001)
% 1.28/1.60 [1270]~P6(a112,x12701,x12702)+E(f12(a112,x12701,f8(a112,x12702,x12701)),x12702)
% 1.28/1.60 [1271]~P6(a112,x12712,x12711)+E(f8(a112,x12711,f8(a112,x12711,x12712)),x12712)
% 1.28/1.60 [1272]~P6(a112,x12722,x12721)+E(f12(a112,f8(a112,x12721,x12722),x12722),x12721)
% 1.28/1.60 [1287]~P6(a112,x12871,x12872)+P7(a112,x12871,f12(a112,x12872,f4(a112)))
% 1.28/1.60 [1290]~P6(a110,x12901,x12902)+P7(a110,x12901,f12(a110,x12902,f4(a110)))
% 1.28/1.60 [1291]~P7(a110,x12911,x12912)+P7(a110,x12911,f12(a110,x12912,f4(a110)))
% 1.28/1.60 [1294]~P7(a112,x12941,x12942)+P6(a112,f12(a112,x12941,f4(a112)),x12942)
% 1.28/1.60 [1296]~P7(a110,x12961,x12962)+P6(a110,f12(a110,x12961,f4(a110)),x12962)
% 1.28/1.60 [1315]P7(a112,x13151,x13152)+E(f6(a112,f8(a112,x13151,x13152),x13152),f6(a112,x13151,x13152))
% 1.28/1.60 [1358]~P6(a112,x13582,x13581)+E(f6(a112,f8(a112,x13581,x13582),x13582),f6(a112,x13581,x13582))
% 1.28/1.60 [1364]~P7(a112,x13641,x13642)+E(f12(a112,f12(a112,x13641,f40(x13642,x13641)),f4(a112)),x13642)
% 1.28/1.60 [1380]P6(a112,x13801,x13802)+~P7(a112,x13801,f12(a112,x13802,f4(a112)))
% 1.28/1.60 [1381]P6(a110,x13811,x13812)+~P7(a110,x13811,f12(a110,x13812,f4(a110)))
% 1.28/1.60 [1385]P7(a112,x13851,x13852)+~P6(a112,f12(a112,x13851,f4(a112)),x13852)
% 1.28/1.60 [1387]P7(a110,x13871,x13872)+~P6(a110,f12(a110,x13871,f4(a110)),x13872)
% 1.28/1.60 [1394]~P6(a112,x13941,x13942)+P7(a1,f19(a112,x13941),f12(a1,f19(a112,x13942),f4(a1)))
% 1.28/1.60 [1395]~P7(a112,x13951,x13952)+P6(a1,f12(a1,f19(a112,x13951),f4(a1)),f19(a112,x13952))
% 1.28/1.60 [1466]~P7(a112,x14661,x14662)+~P7(a112,x14662,f12(a112,x14661,f4(a112)))
% 1.28/1.60 [1467]~P6(a112,x14671,x14672)+~P6(a112,f12(a112,x14672,f4(a112)),x14671)
% 1.28/1.60 [1489]P7(a1,x14891,f19(a112,x14892))+~P6(a112,f12(a112,f18(x14891),f4(a112)),x14892)
% 1.28/1.60 [1637]P6(a112,x16371,x16372)+~P7(a1,f19(a112,x16371),f12(a1,f19(a112,x16372),f4(a1)))
% 1.28/1.60 [1638]P7(a112,x16381,x16382)+~P6(a1,f12(a1,f19(a112,x16381),f4(a1)),f19(a112,x16382))
% 1.28/1.60 [1737]P6(a112,x17371,x17372)+~P6(a112,f12(a112,x17371,f4(a112)),f12(a112,x17372,f4(a112)))
% 1.28/1.60 [1739]P7(a112,x17391,x17392)+~P7(a112,f12(a112,x17391,f4(a112)),f12(a112,x17392,f4(a112)))
% 1.28/1.60 [783]~E(x7832,f3(a112))+E(f20(f20(f11(a112),x7831),x7832),f3(a112))
% 1.28/1.60 [784]~E(x7841,f3(a112))+E(f20(f20(f11(a112),x7841),x7842),f3(a112))
% 1.28/1.60 [794]~P40(x7941)+E(f20(f20(f11(x7941),x7942),x7942),x7942)
% 1.28/1.60 [849]~P48(x8491)+E(f20(f20(f11(x8491),f4(x8491)),x8492),x8492)
% 1.28/1.60 [850]~P28(x8501)+E(f20(f20(f11(x8501),f4(x8501)),x8502),x8502)
% 1.28/1.60 [851]~P22(x8511)+E(f20(f20(f11(x8511),f4(x8511)),x8512),x8512)
% 1.28/1.60 [858]~P48(x8581)+E(f20(f20(f11(x8581),f3(x8581)),x8582),f3(x8581))
% 1.28/1.60 [860]~P42(x8601)+E(f20(f20(f11(x8601),f3(x8601)),x8602),f3(x8601))
% 1.28/1.60 [861]~P61(x8611)+E(f20(f20(f11(x8611),f3(x8611)),x8612),f3(x8611))
% 1.28/1.60 [862]~P28(x8621)+E(f20(f20(f16(x8621),f4(x8621)),x8622),f4(x8621))
% 1.28/1.60 [869]E(x8691,f4(a112))+~E(f20(f20(f11(a112),x8692),x8691),f4(a112))
% 1.28/1.60 [870]E(x8701,f4(a112))+~E(f20(f20(f11(a112),x8701),x8702),f4(a112))
% 1.28/1.60 [876]~P21(x8761)+E(f12(f113(x8761),x8762,f3(f113(x8761))),x8762)
% 1.28/1.60 [877]~P21(x8771)+E(f12(f113(x8771),f3(f113(x8771)),x8772),x8772)
% 1.28/1.60 [944]~E(x9442,f3(a112))+E(f20(f20(f16(a112),x9441),x9442),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [950]~P49(x9501)+E(f20(f20(f11(f113(x9501)),x9502),f3(f113(x9501))),f3(f113(x9501)))
% 1.28/1.60 [1052]~E(x10522,f3(a112))+P7(a112,f3(a112),f20(f20(f16(a112),x10521),x10522))
% 1.28/1.60 [1089]~P56(x10891)+P6(x10891,f3(x10891),f20(f20(f11(x10891),x10892),x10892))
% 1.28/1.60 [1157]~E(x11571,f12(a112,f3(a112),f4(a112)))+E(f20(f20(f16(a112),x11571),x11572),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1216]E(x12161,f12(a112,f3(a112),f4(a112)))+~E(f20(f20(f11(a112),x12162),x12161),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1217]E(x12171,f12(a112,f3(a112),f4(a112)))+~E(f20(f20(f11(a112),x12171),x12172),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1233]P6(a110,f3(a110),x12332)+E(f10(a110,f7(a110,x12331,f10(a110,x12332))),f27(x12331,x12332))
% 1.28/1.60 [1246]~P6(a110,f3(a110),x12461)+P6(a110,f3(a110),f20(f20(f16(a110),x12461),x12462))
% 1.28/1.60 [1248]~P7(a112,f3(a112),x12481)+P7(a112,f3(a112),f20(f20(f16(a112),x12481),x12482))
% 1.28/1.60 [1316]~P56(x13161)+~P7(x13161,f20(f20(f11(x13161),x13162),x13162),f3(x13161))
% 1.28/1.60 [1348]P7(a112,f3(a112),x13481)+~P7(a112,f3(a112),f20(f20(f11(a112),x13482),x13481))
% 1.28/1.60 [1349]P7(a112,f3(a112),x13491)+~P7(a112,f3(a112),f20(f20(f11(a112),x13491),x13492))
% 1.28/1.60 [1372]~P6(a1,f3(a1),x13721)+E(f13(f12(a1,x13721,f19(a112,x13722))),f12(a112,f13(x13721),x13722))
% 1.28/1.60 [1373]~P6(a1,f3(a1),x13731)+E(f18(f12(a1,x13731,f19(a112,x13732))),f12(a112,f18(x13731),x13732))
% 1.28/1.60 [1643]~E(f12(a112,f6(a112,x16431,x16432),f4(a112)),x16432)+E(f6(a112,f12(a112,x16431,f4(a112)),x16432),f3(a112))
% 1.28/1.60 [1676]~P7(a112,f4(a112),x16761)+E(f6(a112,f12(a112,f20(f20(f11(a112),x16761),x16762),f4(a112)),x16761),f4(a112))
% 1.28/1.60 [1740]E(f12(a112,f6(a112,x17401,x17402),f4(a112)),x17402)+E(f12(a112,f6(a112,x17401,x17402),f4(a112)),f6(a112,f12(a112,x17401,f4(a112)),x17402))
% 1.28/1.60 [1813]~P6(a112,f12(a112,f3(a112),f4(a112)),x18131)+P6(a112,f12(a112,f3(a112),f4(a112)),f20(f20(f16(a112),x18131),x18132))
% 1.28/1.60 [1899]P6(a112,f12(a112,f3(a112),f4(a112)),x18991)+~P6(a112,f12(a112,f3(a112),f4(a112)),f20(f20(f11(a112),x18992),x18991))
% 1.28/1.60 [1900]P6(a112,f12(a112,f3(a112),f4(a112)),x19001)+~P6(a112,f12(a112,f3(a112),f4(a112)),f20(f20(f11(a112),x19001),x19002))
% 1.28/1.60 [2065]~P7(a112,f3(a112),x20652)+E(f12(a1,f19(a112,f7(a112,x20651,x20652)),f24(a1,f19(a112,f6(a112,x20651,x20652)),f19(a112,x20652))),f24(a1,f19(a112,x20651),f19(a112,x20652)))
% 1.28/1.60 [885]~P49(x8851)+E(f20(f14(x8851,f3(f113(x8851))),x8852),f3(x8851))
% 1.28/1.60 [886]~P48(x8861)+E(f20(f14(x8861,f4(f113(x8861))),x8862),f4(x8861))
% 1.28/1.60 [984]~P49(x9841)+E(f20(f20(f11(f113(x9841)),f3(f113(x9841))),x9842),f3(f113(x9841)))
% 1.28/1.60 [1026]~P51(x10261)+E(f20(f20(f11(x10261),f10(x10261,f4(x10261))),x10262),f10(x10261,x10262))
% 1.28/1.60 [1130]~E(f19(a112,f18(x11301)),x11301)+E(f18(f20(f20(f16(a1),x11301),x11302)),f20(f20(f16(a112),f18(x11301)),x11302))
% 1.28/1.60 [1234]~P7(a112,f3(a112),x12342)+E(f7(a112,f20(f20(f11(a112),x12341),x12342),x12342),x12341)
% 1.28/1.60 [1235]~P7(a112,f3(a112),x12351)+E(f7(a112,f20(f20(f11(a112),x12351),x12352),x12351),x12352)
% 1.28/1.60 [1555]E(x15551,f3(a1))+~E(f12(a1,f20(f20(f11(a1),x15552),x15552),f20(f20(f11(a1),x15551),x15551)),f3(a1))
% 1.28/1.60 [1556]E(x15561,f3(a1))+~E(f12(a1,f20(f20(f11(a1),x15561),x15561),f20(f20(f11(a1),x15562),x15562)),f3(a1))
% 1.28/1.60 [1558]~P48(x15581)+E(f12(x15581,x15582,x15582),f20(f20(f11(x15581),f12(x15581,f4(x15581),f4(x15581))),x15582))
% 1.28/1.60 [2072]~P6(a1,f3(a1),x20722)+P6(a1,f12(a1,f20(f20(f11(a1),f19(a112,x20721)),x20722),f4(a1)),f20(f20(f16(a1),f12(a1,x20722,f4(a1))),x20721))
% 1.28/1.60 [956]~P48(x9561)+E(f12(x9561,x9562,x9563),f12(x9561,x9563,x9562))
% 1.28/1.60 [998]P6(a112,x9981,x9982)+~E(x9982,f12(a112,x9981,x9983))
% 1.28/1.60 [1079]E(x10791,x10792)+~E(f12(a112,x10793,x10791),f12(a112,x10793,x10792))
% 1.28/1.60 [1080]E(x10801,x10802)+~E(f12(a112,x10801,x10803),f12(a112,x10802,x10803))
% 1.28/1.60 [1258]~P6(a112,x12581,x12583)+P6(a112,x12581,f12(a112,x12582,x12583))
% 1.28/1.60 [1260]~P6(a112,x12601,x12602)+P6(a112,x12601,f12(a112,x12602,x12603))
% 1.28/1.60 [1262]~P7(a112,x12621,x12623)+P7(a112,x12621,f12(a112,x12622,x12623))
% 1.28/1.60 [1264]~P7(a112,x12641,x12642)+P7(a112,x12641,f12(a112,x12642,x12643))
% 1.28/1.60 [1265]~P7(a112,x12651,x12653)+P7(a112,f8(a112,x12651,x12652),x12653)
% 1.28/1.60 [1369]P6(a112,x13691,x13692)+~P6(a112,f12(a112,x13693,x13691),x13692)
% 1.28/1.60 [1370]P6(a112,x13701,x13702)+~P6(a112,f12(a112,x13701,x13703),x13702)
% 1.28/1.60 [1371]P7(a112,x13711,x13712)+~P7(a112,f12(a112,x13711,x13713),x13712)
% 1.28/1.60 [1472]~P6(a1,x14722,x14723)+P6(a1,f12(a1,x14721,x14722),f12(a1,x14721,x14723))
% 1.28/1.60 [1473]~P6(a112,x14732,x14733)+P6(a112,f12(a112,x14731,x14732),f12(a112,x14731,x14733))
% 1.28/1.60 [1474]~P6(a112,x14741,x14743)+P6(a112,f12(a112,x14741,x14742),f12(a112,x14743,x14742))
% 1.28/1.60 [1475]~P6(a112,x14751,x14753)+P6(a112,f7(a112,x14751,x14752),f7(a112,x14753,x14752))
% 1.28/1.60 [1476]~P6(a112,x14763,x14762)+P6(a112,f8(a112,x14761,x14762),f8(a112,x14761,x14763))
% 1.28/1.60 [1477]~P6(a112,x14771,x14773)+P6(a112,f8(a112,x14771,x14772),f8(a112,x14773,x14772))
% 1.28/1.60 [1478]~P6(a110,x14782,x14783)+P6(a110,f12(a110,x14781,x14782),f12(a110,x14781,x14783))
% 1.28/1.60 [1479]~P7(a112,x14792,x14793)+P7(a112,f12(a112,x14791,x14792),f12(a112,x14791,x14793))
% 1.28/1.60 [1480]~P7(a112,x14801,x14803)+P7(a112,f12(a112,x14801,x14802),f12(a112,x14803,x14802))
% 1.28/1.60 [1481]~P7(a110,x14811,x14813)+P7(a110,f12(a110,x14811,x14812),f12(a110,x14813,x14812))
% 1.28/1.60 [1616]~P6(a112,f8(a112,x16161,x16163),x16162)+P6(a112,x16161,f12(a112,x16162,x16163))
% 1.28/1.60 [1617]~P7(a112,f12(a112,x16171,x16173),x16172)+P7(a112,x16171,f8(a112,x16172,x16173))
% 1.28/1.60 [1618]~P6(a112,x16181,f12(a112,x16183,x16182))+P6(a112,f8(a112,x16181,x16182),x16183)
% 1.28/1.60 [1619]~P7(a112,x16191,f8(a112,x16193,x16192))+P7(a112,f12(a112,x16191,x16192),x16193)
% 1.28/1.60 [1732]P6(a112,x17321,x17322)+~P6(a112,f12(a112,x17323,x17321),f12(a112,x17323,x17322))
% 1.28/1.60 [1733]P7(a112,x17331,x17332)+~P7(a112,f12(a112,x17333,x17331),f12(a112,x17333,x17332))
% 1.28/1.60 [1013]~P14(x10131)+E(f8(x10131,x10132,f10(x10131,x10133)),f12(x10131,x10132,x10133))
% 1.28/1.60 [1074]~P3(x10741)+E(f24(x10741,f10(x10741,x10742),f10(x10741,x10743)),f24(x10741,x10742,x10743))
% 1.28/1.60 [1084]~P14(x10841)+E(f12(x10841,f8(x10841,x10842,x10843),x10843),x10842)
% 1.28/1.60 [1085]~P14(x10851)+E(f8(x10851,f12(x10851,x10852,x10853),x10853),x10852)
% 1.28/1.60 [1094]~P4(x10941)+E(f7(x10941,f6(x10941,x10942,x10943),x10943),f3(x10941))
% 1.28/1.60 [1126]~P16(x11261)+E(f10(x11261,f8(x11261,x11262,x11263)),f8(x11261,x11263,x11262))
% 1.28/1.60 [1154]~P14(x11541)+E(f12(x11541,f10(x11541,x11542),f12(x11541,x11542,x11543)),x11543)
% 1.28/1.60 [1176]~P3(x11761)+E(f24(x11761,x11762,f10(x11761,x11763)),f10(x11761,f24(x11761,x11762,x11763)))
% 1.28/1.60 [1177]~P46(x11771)+E(f24(x11771,f10(x11771,x11772),x11773),f10(x11771,f24(x11771,x11772,x11773)))
% 1.28/1.60 [1178]~P12(x11781)+E(f24(x11781,f10(x11781,x11782),x11783),f10(x11781,f24(x11781,x11782,x11783)))
% 1.28/1.60 [1210]~P4(x12101)+E(f6(x12101,f12(x12101,x12102,x12103),x12103),f6(x12101,x12102,x12103))
% 1.28/1.60 [1211]~P4(x12111)+E(f6(x12111,f12(x12111,x12112,x12113),x12112),f6(x12111,x12113,x12112))
% 1.28/1.60 [1212]~P4(x12121)+E(f6(x12121,f6(x12121,x12122,x12123),x12123),f6(x12121,x12122,x12123))
% 1.28/1.60 [1236]~P14(x12361)+E(f12(x12361,f10(x12361,x12362),f10(x12361,x12363)),f10(x12361,f12(x12361,x12363,x12362)))
% 1.28/1.60 [1237]~P16(x12371)+E(f12(x12371,f10(x12371,x12372),f10(x12371,x12373)),f10(x12371,f12(x12371,x12372,x12373)))
% 1.28/1.60 [1379]P7(a112,x13791,x13792)+~E(x13792,f12(a112,f12(a112,x13791,x13793),f4(a112)))
% 1.28/1.60 [1418]~P79(x14181,x14183,x14182)+P77(f20(x14181,f7(a110,x14182,x14183)))
% 1.28/1.60 [1419]~P78(x14191,x14193,x14192)+P77(f20(x14191,f6(a110,x14192,x14193)))
% 1.28/1.60 [1608]~P6(a112,x16082,x16083)+E(f8(a112,f12(a112,x16081,x16082),x16083),f8(a112,x16081,f8(a112,x16083,x16082)))
% 1.28/1.60 [1609]~P6(a112,x16093,x16092)+E(f12(a112,x16091,f8(a112,x16092,x16093)),f8(a112,f12(a112,x16091,x16092),x16093))
% 1.28/1.60 [1611]~P6(a112,x16112,x16111)+E(f12(a112,f8(a112,x16111,x16112),x16113),f8(a112,f12(a112,x16111,x16113),x16112))
% 1.28/1.60 [1669]P79(x16691,x16692,x16693)+~P77(f20(x16691,f7(a110,x16693,x16692)))
% 1.28/1.60 [1670]P78(x16701,x16702,x16703)+~P77(f20(x16701,f6(a110,x16703,x16702)))
% 1.28/1.60 [1697]~P6(a112,x16973,x16972)+P6(a112,x16971,f8(a112,f12(a112,x16972,x16971),x16973))
% 1.28/1.60 [1750]~P4(x17501)+E(f12(x17501,f20(f20(f11(x17501),x17502),f7(x17501,x17503,x17502)),f6(x17501,x17503,x17502)),x17503)
% 1.28/1.60 [1761]~P1(x17611)+P6(a1,f22(x17611,f12(x17611,x17612,x17613)),f12(a1,f22(x17611,x17612),f22(x17611,x17613)))
% 1.28/1.60 [1762]~P1(x17621)+P6(a1,f8(a1,f22(x17621,x17622),f22(x17621,x17623)),f22(x17621,f8(x17621,x17622,x17623)))
% 1.28/1.60 [1857]~P12(x18571)+P6(a1,f22(x18571,f24(x18571,x18572,x18573)),f20(f20(f11(a1),f22(x18571,x18572)),f52(x18573,x18571)))
% 1.28/1.60 [1858]~P12(x18581)+P6(a1,f22(x18581,f24(x18581,x18582,x18583)),f20(f20(f11(a1),f22(x18581,x18582)),f83(x18583,x18581)))
% 1.28/1.60 [1977]~P4(x19771)+E(f12(x19771,f20(f20(f11(x19771),f7(x19771,x19772,x19773)),x19773),f6(x19771,x19772,x19773)),x19772)
% 1.28/1.60 [920]~E(x9202,f3(a112))+E(f20(f20(f11(a112),x9201),x9202),f20(f20(f11(a112),x9203),x9202))
% 1.28/1.60 [922]~E(x9221,f3(a112))+E(f20(f20(f11(a112),x9221),x9222),f20(f20(f11(a112),x9221),x9223))
% 1.28/1.60 [945]~P48(x9451)+E(f20(f20(f11(x9451),x9452),x9453),f20(f20(f11(x9451),x9453),x9452))
% 1.28/1.60 [982]E(f6(a112,x9821,x9822),f3(a112))+~E(x9821,f20(f20(f11(a112),x9822),x9823))
% 1.28/1.60 [983]E(f6(a110,x9831,x9832),f3(a110))+~E(x9831,f20(f20(f11(a110),x9832),x9833))
% 1.28/1.60 [1070]~P11(x10701)+E(f6(f113(x10701),x10702,f10(f113(x10701),x10703)),f6(f113(x10701),x10702,x10703))
% 1.28/1.60 [1140]~P59(x11401)+E(f20(f20(f11(x11401),f10(x11401,x11402)),x11403),f20(f20(f11(x11401),x11402),f10(x11401,x11403)))
% 1.28/1.60 [1141]~P59(x11411)+E(f20(f20(f11(x11411),f10(x11411,x11412)),f10(x11411,x11413)),f20(f20(f11(x11411),x11412),x11413))
% 1.28/1.60 [1208]~P14(x12081)+E(f12(x12081,x12082,f12(x12081,f10(x12081,x12082),x12083)),x12083)
% 1.28/1.60 [1274]~P11(x12741)+E(f7(f113(x12741),x12742,f10(f113(x12741),x12743)),f10(f113(x12741),f7(f113(x12741),x12742,x12743)))
% 1.28/1.60 [1275]~P11(x12751)+E(f7(f113(x12751),f10(f113(x12751),x12752),x12753),f10(f113(x12751),f7(f113(x12751),x12752,x12753)))
% 1.28/1.60 [1276]~P11(x12761)+E(f6(f113(x12761),f10(f113(x12761),x12762),x12763),f10(f113(x12761),f6(f113(x12761),x12762,x12763)))
% 1.28/1.60 [1352]P7(a112,f3(a112),x13521)+P6(a112,f20(f20(f11(a112),x13522),x13521),f20(f20(f11(a112),x13523),x13521))
% 1.28/1.60 [1353]P7(a112,f3(a112),x13531)+P6(a112,f20(f20(f11(a112),x13531),x13532),f20(f20(f11(a112),x13531),x13533))
% 1.28/1.60 [1400]~P6(a112,x14002,x14003)+P6(a112,f20(f20(f11(a112),x14001),x14002),f20(f20(f11(a112),x14001),x14003))
% 1.28/1.60 [1402]~P6(a112,x14021,x14023)+P6(a112,f20(f20(f11(a112),x14021),x14022),f20(f20(f11(a112),x14023),x14022))
% 1.28/1.60 [1527]~P6(a1,f22(a2,x15272),x15273)+P6(a1,f22(a2,f20(f14(a2,x15271),x15272)),f45(x15271,x15273))
% 1.28/1.60 [1561]~P5(x15611)+E(f6(x15611,f10(x15611,f6(x15611,x15612,x15613)),x15613),f6(x15611,f10(x15611,x15612),x15613))
% 1.28/1.60 [1644]P7(a112,x16441,x16442)+~P7(a112,f20(f20(f11(a112),x16443),x16441),f20(f20(f11(a112),x16443),x16442))
% 1.28/1.60 [1645]P7(a112,x16451,x16452)+~P7(a112,f20(f20(f11(a112),x16451),x16453),f20(f20(f11(a112),x16452),x16453))
% 1.28/1.60 [1649]P7(a112,f3(a112),x16491)+~P7(a112,f20(f20(f11(a112),x16492),x16491),f20(f20(f11(a112),x16493),x16491))
% 1.28/1.60 [1650]P7(a112,f3(a112),x16501)+~P7(a112,f20(f20(f11(a112),x16501),x16502),f20(f20(f11(a112),x16501),x16503))
% 1.28/1.60 [1075]~P4(x10751)+E(f6(x10751,f20(f20(f11(x10751),x10752),x10753),x10753),f3(x10751))
% 1.28/1.60 [1076]~P4(x10761)+E(f6(x10761,f20(f20(f11(x10761),x10762),x10763),x10762),f3(x10761))
% 1.28/1.60 [1165]~P59(x11651)+E(f20(f20(f11(x11651),x11652),f10(x11651,x11653)),f10(x11651,f20(f20(f11(x11651),x11652),x11653)))
% 1.28/1.60 [1167]~P42(x11671)+E(f20(f20(f11(x11671),x11672),f10(x11671,x11673)),f10(x11671,f20(f20(f11(x11671),x11672),x11673)))
% 1.28/1.60 [1186]~P40(x11861)+E(f20(f20(f11(x11861),x11862),f20(f20(f11(x11861),x11862),x11863)),f20(f20(f11(x11861),x11862),x11863))
% 1.28/1.60 [1197]~P47(x11971)+E(f20(f14(x11971,f10(f113(x11971),x11972)),x11973),f10(x11971,f20(f14(x11971,x11972),x11973)))
% 1.28/1.60 [1209]~P44(x12091)+E(f22(x12091,f20(f20(f16(x12091),x12092),x12093)),f20(f20(f16(a1),f22(x12091,x12092)),x12093))
% 1.28/1.60 [1220]~P59(x12201)+E(f20(f20(f11(x12201),f10(x12201,x12202)),x12203),f10(x12201,f20(f20(f11(x12201),x12202),x12203)))
% 1.28/1.60 [1222]~P42(x12221)+E(f20(f20(f11(x12221),f10(x12221,x12222)),x12223),f10(x12221,f20(f20(f11(x12221),x12222),x12223)))
% 1.28/1.60 [1269]~E(x12691,f3(a112))+E(f7(a112,f20(f20(f11(a112),x12691),x12692),f20(f20(f11(a112),x12691),x12693)),f3(a112))
% 1.28/1.60 [1297]~P44(x12971)+E(f20(f20(f11(a1),f22(x12971,x12972)),f22(x12971,x12973)),f22(x12971,f20(f20(f11(x12971),x12972),x12973)))
% 1.28/1.60 [1351]E(x13511,f3(a112))+E(f7(a112,f20(f20(f11(a112),x13511),x13512),f20(f20(f11(a112),x13511),x13513)),f7(a112,x13512,x13513))
% 1.28/1.60 [1413]~P48(x14131)+E(f20(f20(f11(x14131),x14132),f20(f20(f16(x14131),x14132),x14133)),f20(f20(f16(x14131),x14132),f12(a112,x14133,f4(a112))))
% 1.28/1.60 [1414]~P43(x14141)+E(f20(f20(f11(x14141),x14142),f20(f20(f16(x14141),x14142),x14143)),f20(f20(f16(x14141),x14142),f12(a112,x14143,f4(a112))))
% 1.28/1.60 [1557]~P7(a112,f3(a112),x15571)+E(f7(a112,f20(f20(f11(a112),x15571),x15572),f20(f20(f11(a112),x15571),x15573)),f7(a112,x15572,x15573))
% 1.28/1.60 [1580]~P7(a110,f3(a110),x15803)+E(f7(a110,x15801,f20(f20(f11(a110),x15802),x15803)),f7(a110,f7(a110,x15801,x15802),x15803))
% 1.28/1.60 [1721]~P48(x17211)+E(f12(x17211,x17212,f20(f20(f11(x17211),x17213),x17212)),f20(f20(f11(x17211),f12(x17211,x17213,f4(x17211))),x17212))
% 1.28/1.60 [1722]~P48(x17221)+E(f12(x17221,f20(f20(f11(x17221),x17222),x17223),x17223),f20(f20(f11(x17221),f12(x17221,x17222,f4(x17221))),x17223))
% 1.28/1.60 [1730]~P3(x17301)+E(f24(x17301,f4(x17301),f20(f20(f16(x17301),x17302),x17303)),f20(f20(f16(x17301),f24(x17301,f4(x17301),x17302)),x17303))
% 1.28/1.60 [1749]~P23(x17491)+P6(a1,f22(x17491,f20(f20(f16(x17491),x17492),x17493)),f20(f20(f16(a1),f22(x17491,x17492)),x17493))
% 1.28/1.60 [1829]~P42(x18291)+P6(a1,f22(x18291,f20(f20(f11(x18291),x18292),x18293)),f20(f20(f11(a1),f22(x18291,x18293)),f85(x18292,x18291)))
% 1.28/1.60 [1830]~P42(x18301)+P6(a1,f22(x18301,f20(f20(f11(x18301),x18302),x18303)),f20(f20(f11(a1),f22(x18301,x18303)),f87(x18302,x18301)))
% 1.28/1.60 [1831]~P42(x18311)+P6(a1,f22(x18311,f20(f20(f11(x18311),x18312),x18313)),f20(f20(f11(a1),f22(x18311,x18312)),f22(x18311,x18313)))
% 1.28/1.60 [1832]~P42(x18321)+P6(a1,f22(x18321,f20(f20(f11(x18321),x18322),x18323)),f20(f20(f11(a1),f22(x18321,x18322)),f84(x18323,x18321)))
% 1.28/1.60 [1833]~P42(x18331)+P6(a1,f22(x18331,f20(f20(f11(x18331),x18332),x18333)),f20(f20(f11(a1),f22(x18331,x18332)),f86(x18333,x18331)))
% 1.28/1.60 [1906]~P56(x19061)+P6(x19061,f3(x19061),f12(x19061,f20(f20(f11(x19061),x19062),x19062),f20(f20(f11(x19061),x19063),x19063)))
% 1.28/1.60 [1976]~P4(x19761)+E(f12(x19761,f6(x19761,x19762,x19763),f20(f20(f11(x19761),f7(x19761,x19762,x19763)),x19763)),x19762)
% 1.28/1.60 [2019]~P73(x20191)+E(f20(f20(f11(x20191),f20(f20(f16(x20191),f10(x20191,f4(x20191))),x20192)),f20(f20(f16(x20191),x20193),x20192)),f20(f20(f16(x20191),f10(x20191,x20193)),x20192))
% 1.28/1.60 [2027]E(x20271,x20272)+~E(f20(f20(f11(a112),f12(a112,x20273,f4(a112))),x20271),f20(f20(f11(a112),f12(a112,x20273,f4(a112))),x20272))
% 1.28/1.60 [2034]~P56(x20341)+~P7(x20341,f12(x20341,f20(f20(f11(x20341),x20342),x20342),f20(f20(f11(x20341),x20343),x20343)),f3(x20341))
% 1.28/1.60 [2069]~P7(a110,f3(a110),x20693)+E(f12(a110,f20(f20(f11(a110),x20691),f6(a110,f7(a110,x20692,x20691),x20693)),f6(a110,x20692,x20691)),f6(a110,x20692,f20(f20(f11(a110),x20691),x20693)))
% 1.28/1.60 [2077]~P7(a112,x20772,x20773)+P7(a112,f20(f20(f11(a112),f12(a112,x20771,f4(a112))),x20772),f20(f20(f11(a112),f12(a112,x20771,f4(a112))),x20773))
% 1.28/1.60 [2093]~P42(x20931)+P6(a1,f22(x20931,f20(f20(f11(x20931),x20932),x20933)),f20(f20(f11(a1),f20(f20(f11(a1),f22(x20931,x20932)),f22(x20931,x20933))),f82(x20931)))
% 1.28/1.60 [2094]~P42(x20941)+P6(a1,f22(x20941,f20(f20(f11(x20941),x20942),x20943)),f20(f20(f11(a1),f20(f20(f11(a1),f22(x20941,x20942)),f22(x20941,x20943))),f81(x20941)))
% 1.28/1.60 [2104]P6(a112,x21041,x21042)+~P6(a112,f20(f20(f11(a112),f12(a112,x21043,f4(a112))),x21041),f20(f20(f11(a112),f12(a112,x21043,f4(a112))),x21042))
% 1.28/1.60 [1642]~P28(x16421)+E(f20(f20(f11(x16421),f20(f20(f16(x16421),x16422),x16423)),x16422),f20(f20(f11(x16421),x16422),f20(f20(f16(x16421),x16422),x16423)))
% 1.28/1.60 [1656]~P28(x16561)+E(f20(f20(f11(x16561),f20(f20(f16(x16561),x16562),x16563)),x16562),f20(f20(f16(x16561),x16562),f12(a112,x16563,f4(a112))))
% 1.28/1.60 [1657]~P48(x16571)+E(f20(f20(f11(x16571),f20(f20(f16(x16571),x16572),x16573)),x16572),f20(f20(f16(x16571),x16572),f12(a112,x16573,f4(a112))))
% 1.28/1.60 [1431]~P48(x14311)+E(f12(x14311,x14312,f12(x14311,x14313,x14314)),f12(x14311,x14313,f12(x14311,x14312,x14314)))
% 1.28/1.60 [1433]~P15(x14331)+E(f12(x14331,f12(x14331,x14332,x14333),x14334),f12(x14331,x14332,f12(x14331,x14333,x14334)))
% 1.28/1.60 [1434]~P48(x14341)+E(f12(x14341,f12(x14341,x14342,x14343),x14344),f12(x14341,x14342,f12(x14341,x14343,x14344)))
% 1.28/1.60 [1435]~P48(x14351)+E(f12(x14351,f12(x14351,x14352,x14353),x14354),f12(x14351,f12(x14351,x14352,x14354),x14353))
% 1.28/1.60 [1679]~P12(x16791)+E(f12(x16791,f24(x16791,x16792,x16793),f24(x16791,x16794,x16793)),f24(x16791,f12(x16791,x16792,x16794),x16793))
% 1.28/1.60 [1680]~P46(x16801)+E(f12(x16801,f24(x16801,x16802,x16803),f24(x16801,x16804,x16803)),f24(x16801,f12(x16801,x16802,x16804),x16803))
% 1.28/1.60 [999]~P34(x9992)+E(f20(f10(f116(x9991,x9992),x9993),x9994),f10(x9992,f20(x9993,x9994)))
% 1.28/1.60 [1850]~P5(x18501)+E(f6(x18501,f8(x18501,x18502,f6(x18501,x18503,x18504)),x18504),f6(x18501,f8(x18501,x18502,x18503),x18504))
% 1.28/1.60 [1852]~P5(x18521)+E(f6(x18521,f8(x18521,f6(x18521,x18522,x18523),x18524),x18523),f6(x18521,f8(x18521,x18522,x18524),x18523))
% 1.28/1.60 [1853]~P4(x18531)+E(f6(x18531,f12(x18531,x18532,f6(x18531,x18533,x18534)),x18534),f6(x18531,f12(x18531,x18532,x18533),x18534))
% 1.28/1.60 [1854]~P4(x18541)+E(f6(x18541,f12(x18541,f6(x18541,x18542,x18543),x18544),x18543),f6(x18541,f12(x18541,x18542,x18544),x18543))
% 1.28/1.60 [2004]~P4(x20041)+E(f6(x20041,f12(x20041,f6(x20041,x20042,x20043),f6(x20041,x20044,x20043)),x20043),f6(x20041,f12(x20041,x20042,x20044),x20043))
% 1.28/1.60 [2005]~P5(x20051)+E(f6(x20051,f8(x20051,f6(x20051,x20052,x20053),f6(x20051,x20054,x20053)),x20053),f6(x20051,f8(x20051,x20052,x20054),x20053))
% 1.28/1.60 [2064]~P4(x20641)+E(f12(x20641,f12(x20641,f20(f20(f11(x20641),x20642),f7(x20641,x20643,x20642)),f6(x20641,x20643,x20642)),x20644),f12(x20641,x20643,x20644))
% 1.28/1.60 [2101]~P4(x21011)+E(f12(x21011,f12(x21011,f20(f20(f11(x21011),f7(x21011,x21012,x21013)),x21013),f6(x21011,x21012,x21013)),x21014),f12(x21011,x21012,x21014))
% 1.28/1.60 [1396]~P48(x13961)+E(f20(f20(f11(x13961),x13962),f20(f20(f11(x13961),x13963),x13964)),f20(f20(f11(x13961),x13963),f20(f20(f11(x13961),x13962),x13964)))
% 1.28/1.60 [1411]~P46(x14111)+E(f24(x14111,f20(f20(f11(x14111),x14112),x14113),x14114),f20(f20(f11(x14111),x14112),f24(x14111,x14113,x14114)))
% 1.28/1.60 [1652]~P48(x16521)+E(f12(x16521,f20(f20(f11(x16521),x16522),x16523),f20(f20(f11(x16521),x16522),x16524)),f20(f20(f11(x16521),x16522),f12(x16521,x16523,x16524)))
% 1.28/1.60 [1654]~P42(x16541)+E(f12(x16541,f20(f20(f11(x16541),x16542),x16543),f20(f20(f11(x16541),x16542),x16544)),f20(f20(f11(x16541),x16542),f12(x16541,x16543,x16544)))
% 1.28/1.60 [1655]~P4(x16551)+E(f6(x16551,f20(f20(f11(x16551),x16552),x16553),f20(f20(f11(x16551),x16552),x16554)),f20(f20(f11(x16551),x16552),f6(x16551,x16553,x16554)))
% 1.28/1.60 [1754]~P49(x17541)+E(f12(x17541,f20(f14(x17541,x17542),x17543),f20(f14(x17541,x17544),x17543)),f20(f14(x17541,f12(f113(x17541),x17542,x17544)),x17543))
% 1.28/1.60 [1807]~P28(x18071)+E(f20(f20(f11(x18071),f20(f20(f16(x18071),x18072),x18073)),f20(f20(f16(x18071),x18072),x18074)),f20(f20(f16(x18071),x18072),f12(a112,x18073,x18074)))
% 1.28/1.60 [1808]~P48(x18081)+E(f20(f20(f11(x18081),f20(f20(f16(x18081),x18082),x18083)),f20(f20(f16(x18081),x18082),x18084)),f20(f20(f16(x18081),x18082),f12(a112,x18083,x18084)))
% 1.28/1.60 [1823]~P42(x18231)+E(f12(x18231,f20(f20(f11(x18231),x18232),x18233),f20(f20(f11(x18231),x18234),x18233)),f20(f20(f11(x18231),f12(x18231,x18232,x18234)),x18233))
% 1.28/1.60 [1824]~P50(x18241)+E(f12(x18241,f20(f20(f11(x18241),x18242),x18243),f20(f20(f11(x18241),x18244),x18243)),f20(f20(f11(x18241),f12(x18241,x18242,x18244)),x18243))
% 1.28/1.60 [1825]~P3(x18251)+E(f24(x18251,f20(f20(f16(x18251),x18252),x18253),f20(f20(f16(x18251),x18254),x18253)),f20(f20(f16(x18251),f24(x18251,x18252,x18254)),x18253))
% 1.28/1.60 [1826]~P48(x18261)+E(f12(x18261,f20(f20(f11(x18261),x18262),x18263),f20(f20(f11(x18261),x18264),x18263)),f20(f20(f11(x18261),f12(x18261,x18262,x18264)),x18263))
% 1.28/1.60 [1827]~P4(x18271)+E(f6(x18271,f20(f20(f11(x18271),x18272),x18273),f20(f20(f11(x18271),x18274),x18273)),f20(f20(f11(x18271),f6(x18271,x18272,x18274)),x18273))
% 1.28/1.60 [1828]~P4(x18281)+E(f6(x18281,f20(f20(f11(x18281),x18282),f6(x18281,x18283,x18284)),x18284),f6(x18281,f20(f20(f11(x18281),x18282),x18283),x18284))
% 1.28/1.60 [2002]~P4(x20021)+E(f6(x20021,f20(f20(f11(x20021),f6(x20021,x20022,x20023)),x20024),x20023),f6(x20021,f20(f20(f11(x20021),x20022),x20024),x20023))
% 1.28/1.60 [2050]~P4(x20501)+E(f6(x20501,f20(f20(f11(x20501),f6(x20501,x20502,x20503)),f6(x20501,x20504,x20503)),x20503),f6(x20501,f20(f20(f11(x20501),x20502),x20504),x20503))
% 1.28/1.60 [1612]~P11(x16121)+E(f7(f113(x16121),x16122,f20(f20(f11(f113(x16121)),x16123),x16124)),f7(f113(x16121),f7(f113(x16121),x16122,x16123),x16124))
% 1.28/1.60 [1631]~P48(x16311)+E(f20(f20(f16(x16311),f20(f20(f16(x16311),x16312),x16313)),x16314),f20(f20(f16(x16311),x16312),f20(f20(f11(a112),x16313),x16314)))
% 1.28/1.60 [1632]~P28(x16321)+E(f20(f20(f16(x16321),f20(f20(f16(x16321),x16322),x16323)),x16324),f20(f20(f16(x16321),x16322),f20(f20(f11(a112),x16323),x16324)))
% 1.28/1.60 [1640]~P48(x16401)+E(f20(f20(f11(x16401),f20(f20(f11(x16401),x16402),x16403)),x16404),f20(f20(f11(x16401),x16402),f20(f20(f11(x16401),x16403),x16404)))
% 1.28/1.60 [1641]~P19(x16411)+E(f20(f20(f11(x16411),f20(f20(f11(x16411),x16412),x16413)),x16414),f20(f20(f11(x16411),x16412),f20(f20(f11(x16411),x16413),x16414)))
% 1.28/1.60 [1662]~P4(x16621)+E(f6(x16621,f12(x16621,x16622,f20(f20(f11(x16621),x16623),x16624)),x16624),f6(x16621,x16622,x16624))
% 1.28/1.60 [1663]~P4(x16631)+E(f6(x16631,f12(x16631,x16632,f20(f20(f11(x16631),x16633),x16634)),x16633),f6(x16631,x16632,x16633))
% 1.28/1.60 [1806]~P48(x18061)+E(f20(f20(f11(x18061),f20(f20(f11(x18061),x18062),x18063)),x18064),f20(f20(f11(x18061),f20(f20(f11(x18061),x18062),x18064)),x18063))
% 1.28/1.60 [1923]~P48(x19231)+E(f20(f20(f11(x19231),f20(f20(f16(x19231),x19232),x19233)),f20(f20(f16(x19231),x19234),x19233)),f20(f20(f16(x19231),f20(f20(f11(x19231),x19232),x19234)),x19233))
% 1.28/1.60 [1924]~P22(x19241)+E(f20(f20(f11(x19241),f20(f20(f16(x19241),x19242),x19243)),f20(f20(f16(x19241),x19244),x19243)),f20(f20(f16(x19241),f20(f20(f11(x19241),x19242),x19244)),x19243))
% 1.28/1.60 [1970]~P49(x19701)+E(f12(f113(x19701),f20(f20(f11(f113(x19701)),x19702),x19703),f20(f20(f11(f113(x19701)),x19704),x19703)),f20(f20(f11(f113(x19701)),f12(f113(x19701),x19702,x19704)),x19703))
% 1.28/1.60 [2085]~P11(x20851)+E(f12(f113(x20851),f20(f20(f11(f113(x20851)),x20852),f6(f113(x20851),f7(f113(x20851),x20853,x20852),x20854)),f6(f113(x20851),x20853,x20852)),f6(f113(x20851),x20853,f20(f20(f11(f113(x20851)),x20852),x20854)))
% 1.28/1.60 [1863]~P48(x18631)+E(f20(f14(x18631,f20(f20(f16(f113(x18631)),x18632),x18633)),x18634),f20(f20(f16(x18631),f20(f14(x18631,x18632),x18634)),x18633))
% 1.28/1.60 [1942]~P49(x19421)+E(f20(f20(f11(x19421),f20(f14(x19421,x19422),x19423)),f20(f14(x19421,x19424),x19423)),f20(f14(x19421,f20(f20(f11(f113(x19421)),x19422),x19424)),x19423))
% 1.28/1.60 [1855]~P48(x18551)+E(f12(x18551,f12(x18551,x18552,x18553),f12(x18551,x18554,x18555)),f12(x18551,f12(x18551,x18552,x18554),f12(x18551,x18553,x18555)))
% 1.28/1.60 [1943]~P3(x19431)+E(f24(x19431,f20(f20(f11(x19431),x19432),x19433),f20(f20(f11(x19431),x19434),x19435)),f20(f20(f11(x19431),f24(x19431,x19432,x19434)),f24(x19431,x19433,x19435)))
% 1.28/1.60 [1989]~P48(x19891)+E(f20(f20(f11(x19891),f20(f20(f11(x19891),x19892),x19893)),f20(f20(f11(x19891),x19894),x19895)),f20(f20(f11(x19891),f20(f20(f11(x19891),x19892),x19894)),f20(f20(f11(x19891),x19893),x19895)))
% 1.28/1.60 [2073]~P59(x20731)+E(f12(x20731,f20(f20(f11(x20731),x20732),f8(x20731,x20733,x20734)),f20(f20(f11(x20731),f8(x20731,x20732,x20735)),x20734)),f8(x20731,f20(f20(f11(x20731),x20732),x20733),f20(f20(f11(x20731),x20735),x20734)))
% 1.28/1.60 [2110]~P42(x21101)+E(f12(x21101,f12(x21101,f20(f20(f11(x21101),f8(x21101,x21102,x21103)),f8(x21101,x21104,x21105)),f20(f20(f11(x21101),f8(x21101,x21102,x21103)),x21105)),f20(f20(f11(x21101),x21103),f8(x21101,x21104,x21105))),f8(x21101,f20(f20(f11(x21101),x21102),x21104),f20(f20(f11(x21101),x21103),x21105)))
% 1.28/1.60 [2063]~P70(x20631)+E(f12(x20631,f20(f20(f11(x20631),x20632),x20633),f12(x20631,f20(f20(f11(x20631),x20634),x20633),x20635)),f12(x20631,f20(f20(f11(x20631),f12(x20631,x20632,x20634)),x20633),x20635))
% 1.28/1.60 [1971]E(x19711,f3(a112))+E(x19711,f12(a112,f3(a112),f4(a112)))+~P7(a112,x19711,f12(a112,f12(a112,f3(a112),f4(a112)),f4(a112)))
% 1.28/1.60 [2109]P76(a500)+~P6(a1,f22(a2,f20(x21091,f100(x21091))),a114)+~P7(a1,f22(a2,f20(f14(a2,a115),f20(x21091,f101(x21091)))),f12(a1,f10(a1,a117),f24(a1,f4(a1),f19(a112,f12(a112,f101(x21091),f4(a112))))))
% 1.28/1.60 [942]E(x9421,x9422)+P7(a112,x9422,x9421)+P7(a112,x9421,x9422)
% 1.28/1.60 [943]E(x9431,x9432)+P7(a110,x9432,x9431)+P7(a110,x9431,x9432)
% 1.28/1.60 [1004]E(x10041,x10042)+P7(a1,x10041,x10042)+~P6(a1,x10041,x10042)
% 1.28/1.60 [1007]E(x10071,x10072)+P7(a112,x10071,x10072)+~P6(a112,x10071,x10072)
% 1.28/1.60 [1008]E(x10081,x10082)+P7(a110,x10081,x10082)+~P6(a110,x10081,x10082)
% 1.28/1.60 [1086]E(x10861,x10862)+~P6(a1,x10862,x10861)+~P6(a1,x10861,x10862)
% 1.28/1.60 [1087]E(x10871,x10872)+~P6(a112,x10872,x10871)+~P6(a112,x10871,x10872)
% 1.28/1.60 [1088]E(x10881,x10882)+~P6(a110,x10882,x10881)+~P6(a110,x10881,x10882)
% 1.28/1.60 [757]~P27(x7571)+~E(x7572,f3(x7571))+E(f10(x7571,x7572),x7572)
% 1.28/1.60 [759]~P1(x7591)+~E(x7592,f3(x7591))+E(f22(x7591,x7592),f3(a1))
% 1.28/1.60 [760]~P14(x7601)+~E(f3(x7601),x7602)+E(f10(x7601,x7602),f3(x7601))
% 1.28/1.60 [761]~P14(x7611)+~E(x7612,f3(x7611))+E(f10(x7611,x7612),f3(x7611))
% 1.28/1.60 [763]~P27(x7632)+~E(f10(x7632,x7631),x7631)+E(x7631,f3(x7632))
% 1.28/1.60 [769]~P1(x7692)+E(x7691,f3(x7692))+~E(f22(x7692,x7691),f3(a1))
% 1.28/1.60 [770]~P14(x7702)+~E(f10(x7702,x7701),f3(x7702))+E(x7701,f3(x7702))
% 1.28/1.60 [771]~P14(x7711)+~E(f10(x7711,x7712),f3(x7711))+E(f3(x7711),x7712)
% 1.28/1.60 [815]~E(x8152,f3(a112))+~E(x8151,f3(a112))+E(f12(a112,x8151,x8152),f3(a112))
% 1.28/1.60 [835]~P46(x8352)+E(f24(x8352,x8351,x8351),f4(x8352))+E(x8351,f3(x8352))
% 1.28/1.60 [836]~P4(x8362)+E(f7(x8362,x8361,x8361),f4(x8362))+E(x8361,f3(x8362))
% 1.28/1.60 [837]~P53(x8372)+E(f24(x8372,x8371,x8371),f4(x8372))+E(x8371,f3(x8372))
% 1.28/1.60 [855]~P53(x8551)+~E(x8552,f3(x8551))+E(f24(x8551,x8552,x8552),f3(x8551))
% 1.28/1.60 [856]~P27(x8561)+~E(x8562,f3(x8561))+E(f12(x8561,x8562,x8562),f3(x8561))
% 1.28/1.60 [907]~P1(x9072)+E(x9071,f3(x9072))+P7(a1,f3(a1),f22(x9072,x9071))
% 1.28/1.60 [919]~P1(x9191)+~E(x9192,f3(x9191))+P6(a1,f22(x9191,x9192),f3(a1))
% 1.28/1.60 [930]~P27(x9302)+~E(f12(x9302,x9301,x9301),f3(x9302))+E(x9301,f3(x9302))
% 1.28/1.60 [946]~P1(x9462)+~P8(x9462,x9461)+P7(a1,f3(a1),f53(x9461,x9462))
% 1.28/1.60 [947]~P1(x9472)+~P8(x9472,x9471)+P7(a1,f3(a1),f61(x9471,x9472))
% 1.28/1.60 [948]~P1(x9482)+~P8(x9482,x9481)+P7(a1,f3(a1),f65(x9481,x9482))
% 1.28/1.60 [949]~P1(x9492)+~P8(x9492,x9491)+P7(a1,f3(a1),f68(x9491,x9492))
% 1.28/1.60 [977]~P41(x9771)+P9(x9771,x9772)+P6(a112,f48(x9772,x9771),f50(x9772,x9771))
% 1.28/1.60 [978]~P41(x9781)+P10(x9781,x9782)+P6(a112,f62(x9782,x9781),f64(x9782,x9781))
% 1.28/1.60 [1012]~P1(x10122)+E(x10121,f3(x10122))+~P6(a1,f22(x10122,x10121),f3(a1))
% 1.28/1.60 [1014]~P1(x10142)+~E(x10141,f3(x10142))+~P7(a1,f3(a1),f22(x10142,x10141))
% 1.28/1.60 [1099]E(x10991,x10992)+~E(f8(a112,x10992,x10991),f3(a112))+~E(f8(a112,x10991,x10992),f3(a112))
% 1.28/1.60 [1133]~P27(x11331)+~P6(x11331,x11332,f3(x11331))+P6(x11331,x11332,f10(x11331,x11332))
% 1.28/1.60 [1134]~P52(x11341)+~P7(x11341,x11342,f3(x11341))+P7(x11341,x11342,f10(x11341,x11342))
% 1.28/1.60 [1135]~P27(x11351)+~P6(x11351,f3(x11351),x11352)+P6(x11351,f10(x11351,x11352),x11352)
% 1.28/1.60 [1136]~P27(x11361)+~P7(x11361,f3(x11361),x11362)+P7(x11361,f10(x11361,x11362),x11362)
% 1.28/1.60 [1142]~P31(x11421)+~P6(x11421,x11422,f3(x11421))+P6(x11421,f3(x11421),f10(x11421,x11422))
% 1.28/1.60 [1143]~P31(x11431)+~P7(x11431,x11432,f3(x11431))+P7(x11431,f3(x11431),f10(x11431,x11432))
% 1.28/1.60 [1144]~P31(x11441)+~P6(x11441,f3(x11441),x11442)+P6(x11441,f10(x11441,x11442),f3(x11441))
% 1.28/1.60 [1145]~P31(x11451)+~P7(x11451,f3(x11451),x11452)+P7(x11451,f10(x11451,x11452),f3(x11451))
% 1.28/1.60 [1150]~P27(x11501)+~P6(x11501,x11502,f10(x11501,x11502))+P6(x11501,x11502,f3(x11501))
% 1.28/1.60 [1151]~P52(x11511)+~P7(x11511,x11512,f10(x11511,x11512))+P7(x11511,x11512,f3(x11511))
% 1.28/1.60 [1152]~P27(x11521)+~P6(x11521,f10(x11521,x11522),x11522)+P6(x11521,f3(x11521),x11522)
% 1.28/1.60 [1153]~P27(x11531)+~P7(x11531,f10(x11531,x11532),x11532)+P7(x11531,f3(x11531),x11532)
% 1.28/1.60 [1172]~P31(x11721)+~P6(x11721,f3(x11721),f10(x11721,x11722))+P6(x11721,x11722,f3(x11721))
% 1.28/1.60 [1173]~P31(x11731)+~P7(x11731,f3(x11731),f10(x11731,x11732))+P7(x11731,x11732,f3(x11731))
% 1.28/1.60 [1174]~P31(x11741)+~P6(x11741,f10(x11741,x11742),f3(x11741))+P6(x11741,f3(x11741),x11742)
% 1.28/1.60 [1175]~P31(x11751)+~P7(x11751,f10(x11751,x11752),f3(x11751))+P7(x11751,f3(x11751),x11752)
% 1.28/1.60 [1218]~P7(a110,x12182,x12181)+E(f6(a110,x12181,x12182),x12181)+~P6(a110,x12181,f3(a110))
% 1.28/1.60 [1219]~P7(a110,x12191,x12192)+E(f6(a110,x12191,x12192),x12191)+~P6(a110,f3(a110),x12191)
% 1.28/1.60 [1224]~P7(a110,x12242,x12241)+~P6(a110,x12241,f3(a110))+E(f7(a110,x12241,x12242),f3(a110))
% 1.28/1.60 [1226]~P7(a110,x12261,x12262)+~P6(a110,f3(a110),x12261)+E(f7(a110,x12261,x12262),f3(a110))
% 1.28/1.60 [1309]~P6(a112,f13(x13091),x13092)+P6(a1,x13091,f19(a112,x13092))+~P6(a1,f3(a1),x13091)
% 1.28/1.60 [1310]~P6(a112,x13101,f18(x13102))+P6(a1,f19(a112,x13101),x13102)+~P6(a1,f3(a1),x13102)
% 1.28/1.60 [1311]~P7(a1,f3(a1),x13111)+~P7(a112,f3(a112),x13112)+P7(a1,f3(a1),f92(x13111,x13112))
% 1.28/1.60 [1312]~P7(a1,f3(a1),x13121)+~P7(a112,f3(a112),x13122)+P7(a1,f3(a1),f97(x13121,x13122))
% 1.28/1.60 [1324]P7(a112,f18(x13241),x13242)+~P7(a1,x13241,f19(a112,x13242))+~P6(a1,f3(a1),x13241)
% 1.28/1.60 [1327]~P27(x13271)+~P6(x13271,f3(x13271),x13272)+P6(x13271,f3(x13271),f12(x13271,x13272,x13272))
% 1.28/1.60 [1328]~P27(x13281)+~P7(x13281,f3(x13281),x13282)+P7(x13281,f3(x13281),f12(x13281,x13282,x13282))
% 1.28/1.60 [1329]~P27(x13291)+~P6(x13291,x13292,f3(x13291))+P6(x13291,f12(x13291,x13292,x13292),f3(x13291))
% 1.28/1.60 [1330]~P52(x13301)+~P7(x13301,x13302,f3(x13301))+P7(x13301,f12(x13301,x13302,x13302),f3(x13301))
% 1.28/1.60 [1331]~P27(x13311)+~P7(x13311,x13312,f3(x13311))+P7(x13311,f12(x13311,x13312,x13312),f3(x13311))
% 1.28/1.60 [1437]~P27(x14371)+~P6(x14371,f12(x14371,x14372,x14372),f3(x14371))+P6(x14371,x14372,f3(x14371))
% 1.28/1.60 [1438]~P52(x14381)+~P7(x14381,f12(x14381,x14382,x14382),f3(x14381))+P7(x14381,x14382,f3(x14381))
% 1.28/1.60 [1439]~P27(x14391)+~P7(x14391,f12(x14391,x14392,x14392),f3(x14391))+P7(x14391,x14392,f3(x14391))
% 1.28/1.60 [1440]~P27(x14401)+~P6(x14401,f3(x14401),f12(x14401,x14402,x14402))+P6(x14401,f3(x14401),x14402)
% 1.28/1.60 [1441]~P27(x14411)+~P7(x14411,f3(x14411),f12(x14411,x14412,x14412))+P7(x14411,f3(x14411),x14412)
% 1.28/1.60 [1444]~P6(a110,x14442,x14441)+~P7(a110,f3(a110),x14442)+P7(a110,f3(a110),f7(a110,x14441,x14442))
% 1.28/1.60 [1445]P7(a112,f7(a112,x14451,x14452),x14451)+~P7(a112,f3(a112),x14451)+~P7(a112,f4(a112),x14452)
% 1.28/1.60 [1446]P7(a112,f8(a112,x14461,x14462),x14461)+~P7(a112,f3(a112),x14461)+~P7(a112,f3(a112),x14462)
% 1.28/1.60 [1447]P7(a110,f7(a110,x14471,x14472),x14471)+~P7(a110,f3(a110),x14471)+~P7(a110,f4(a110),x14472)
% 1.28/1.60 [1450]~P6(a1,x14501,f3(a1))+~P6(a1,x14502,f3(a1))+P6(a1,f3(a1),f24(a1,x14501,x14502))
% 1.28/1.60 [1451]~P6(a110,x14511,f3(a110))+~P7(a110,x14512,f3(a110))+P6(a110,f3(a110),f7(a110,x14511,x14512))
% 1.28/1.60 [1452]~P6(a1,x14522,f3(a1))+~P6(a1,f3(a1),x14522)+P6(a1,f3(a1),f24(a1,x14521,x14522))
% 1.28/1.60 [1453]~P6(a1,x14531,f3(a1))+~P6(a1,f3(a1),x14531)+P6(a1,f3(a1),f24(a1,x14531,x14532))
% 1.28/1.60 [1454]~P6(a1,f3(a1),x14542)+~P6(a1,f3(a1),x14541)+P6(a1,f3(a1),f24(a1,x14541,x14542))
% 1.28/1.60 [1455]~P6(a110,f3(a110),x14552)+~P6(a110,f3(a110),x14551)+P6(a110,f3(a110),f12(a110,x14551,x14552))
% 1.28/1.60 [1456]~P6(a110,f3(a110),x14562)+~P6(a110,f3(a110),x14561)+P6(a110,f3(a110),f7(a110,x14561,x14562))
% 1.28/1.60 [1457]~P6(a110,f3(a110),x14571)+~P7(a110,f3(a110),x14572)+P6(a110,f3(a110),f7(a110,x14571,x14572))
% 1.28/1.60 [1458]~P6(a110,f3(a110),x14582)+~P6(a110,f3(a110),x14581)+P6(a110,f3(a110),f6(a110,x14581,x14582))
% 1.28/1.60 [1459]~P6(a110,x14591,f3(a110))+~P7(a110,f3(a110),x14592)+P6(a110,f7(a110,x14591,x14592),f3(a110))
% 1.28/1.60 [1460]~P7(a110,x14602,f3(a110))+~P6(a110,f3(a110),x14601)+P6(a110,f7(a110,x14601,x14602),f3(a110))
% 1.28/1.60 [1461]~P7(a110,x14612,f3(a110))+~P7(a110,f3(a110),x14611)+P7(a110,f7(a110,x14611,x14612),f3(a110))
% 1.28/1.60 [1463]~P7(a110,x14631,f3(a110))+~P7(a110,f3(a110),x14632)+P7(a110,f7(a110,x14631,x14632),f3(a110))
% 1.28/1.60 [1524]P6(a1,x15241,f3(a1))+P6(a1,f3(a1),x15242)+~P6(a1,f3(a1),f24(a1,x15242,x15241))
% 1.28/1.60 [1525]P6(a1,x15251,f3(a1))+P6(a1,f3(a1),x15252)+~P6(a1,f3(a1),f24(a1,x15251,x15252))
% 1.28/1.60 [1526]P7(a112,f3(a112),x15261)+P7(a112,f3(a112),x15262)+~P7(a112,f3(a112),f12(a112,x15262,x15261))
% 1.28/1.60 [1598]P6(a110,x15981,x15982)+~P7(a110,f3(a110),x15981)+~P7(a110,f3(a110),f7(a110,x15982,x15981))
% 1.28/1.60 [1599]P6(a110,x15991,x15992)+~P6(a110,f3(a110),x15992)+~P7(a110,f3(a110),f7(a110,x15992,x15991))
% 1.28/1.60 [1602]P6(a110,x16021,f3(a110))+~P7(a110,x16022,f3(a110))+~P6(a110,f3(a110),f7(a110,x16021,x16022))
% 1.28/1.60 [1603]P7(a110,x16031,f3(a110))+~P7(a110,f3(a110),x16032)+~P7(a110,f7(a110,x16031,x16032),f3(a110))
% 1.28/1.60 [1604]P7(a110,f3(a110),x16041)+~P7(a110,x16042,f3(a110))+~P7(a110,f7(a110,x16041,x16042),f3(a110))
% 1.28/1.60 [1605]P6(a110,f3(a110),x16051)+~P7(a110,f3(a110),x16052)+~P6(a110,f3(a110),f7(a110,x16051,x16052))
% 1.28/1.60 [1606]P7(a110,f3(a110),x16061)+~P6(a110,f3(a110),x16062)+~P7(a110,f3(a110),f7(a110,x16062,x16061))
% 1.28/1.60 [1692]E(f12(a110,x16921,x16922),f6(a110,x16921,x16922))+~P7(a110,f3(a110),x16921)+~P6(a110,f12(a110,x16921,x16922),f3(a110))
% 1.28/1.60 [773]~P33(x7731)+E(f9(x7731,x7732),f3(a112))+~E(x7732,f3(f113(x7731)))
% 1.28/1.60 [774]~P33(x7742)+~E(f9(x7742,x7741),f3(a112))+E(x7741,f3(f113(x7742)))
% 1.28/1.60 [1065]P7(a112,f55(x10652,x10651),x10652)+~P77(f20(x10651,x10652))+P77(f20(x10651,f3(a112)))
% 1.28/1.60 [1131]E(x11311,f3(a112))+E(x11312,f3(a112))+~E(f12(a112,x11312,x11311),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1132]E(x11321,f3(a112))+E(x11322,f3(a112))+~E(f12(a112,f3(a112),f4(a112)),f12(a112,x11322,x11321))
% 1.28/1.60 [1182]~E(x11822,f3(a112))+~E(x11821,f12(a112,f3(a112),f4(a112)))+E(f12(a112,x11821,x11822),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1183]~E(x11831,f3(a112))+~E(x11832,f12(a112,f3(a112),f4(a112)))+E(f12(a112,x11831,x11832),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1184]~E(x11842,f3(a112))+~E(x11841,f12(a112,f3(a112),f4(a112)))+E(f12(a112,f3(a112),f4(a112)),f12(a112,x11841,x11842))
% 1.28/1.60 [1185]~E(x11851,f3(a112))+~E(x11852,f12(a112,f3(a112),f4(a112)))+E(f12(a112,f3(a112),f4(a112)),f12(a112,x11851,x11852))
% 1.28/1.60 [1253]E(x12531,f3(a112))+E(x12531,f12(a112,f3(a112),f4(a112)))+~E(f12(a112,x12532,x12531),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1254]E(x12541,f3(a112))+E(x12541,f12(a112,f3(a112),f4(a112)))+~E(f12(a112,x12541,x12542),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1255]E(x12551,f3(a112))+E(x12551,f12(a112,f3(a112),f4(a112)))+~E(f12(a112,f3(a112),f4(a112)),f12(a112,x12552,x12551))
% 1.28/1.60 [1256]E(x12561,f3(a112))+E(x12561,f12(a112,f3(a112),f4(a112)))+~E(f12(a112,f3(a112),f4(a112)),f12(a112,x12561,x12562))
% 1.28/1.60 [1365]E(x13651,f12(a112,f3(a112),f4(a112)))+E(x13652,f12(a112,f3(a112),f4(a112)))+~E(f12(a112,x13651,x13652),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1366]E(x13661,f12(a112,f3(a112),f4(a112)))+E(x13662,f12(a112,f3(a112),f4(a112)))+~E(f12(a112,f3(a112),f4(a112)),f12(a112,x13661,x13662))
% 1.28/1.60 [1377]~P7(a112,x13771,x13772)+P7(a112,f12(a112,x13771,f4(a112)),x13772)+E(f12(a112,x13771,f4(a112)),x13772)
% 1.28/1.60 [1392]E(x13921,x13922)+P7(a112,x13921,x13922)+~P7(a112,x13921,f12(a112,x13922,f4(a112)))
% 1.28/1.60 [1393]E(x13931,x13932)+P7(a110,x13931,x13932)+~P7(a110,x13931,f12(a110,x13932,f4(a110)))
% 1.28/1.60 [1465]P7(a112,f44(x14652,x14651),x14652)+E(x14651,f3(a112))+~P7(a112,x14651,f12(a112,x14652,f4(a112)))
% 1.28/1.60 [1470]E(x14701,x14702)+~P6(a112,x14702,x14701)+~P7(a112,x14701,f12(a112,x14702,f4(a112)))
% 1.28/1.60 [1471]E(x14711,f3(a112))+~P7(a112,x14711,f12(a112,x14712,f4(a112)))+E(f12(a112,f44(x14712,x14711),f4(a112)),x14711)
% 1.28/1.60 [1490]~P41(x14901)+P9(x14901,x14902)+~P6(x14901,f20(x14902,f50(x14902,x14901)),f20(x14902,f48(x14902,x14901)))
% 1.28/1.60 [1491]~P41(x14911)+P10(x14911,x14912)+~P6(x14911,f20(x14912,f62(x14912,x14911)),f20(x14912,f64(x14912,x14911)))
% 1.28/1.60 [1553]P6(a112,x15531,x15532)+~P6(a112,x15531,f12(a112,x15532,f4(a112)))+E(x15531,f12(a112,x15532,f4(a112)))
% 1.28/1.60 [1720]E(f18(x17201),x17202)+~P6(a1,f19(a112,x17202),x17201)+~P7(a1,x17201,f12(a1,f19(a112,x17202),f4(a1)))
% 1.28/1.60 [1763]~P7(a1,f19(a112,x17632),x17631)+~P6(a1,x17631,f12(a1,f19(a112,x17632),f4(a1)))+E(f13(x17631),f12(a112,x17632,f4(a112)))
% 1.28/1.60 [796]~E(x7962,f4(a112))+~E(x7961,f4(a112))+E(f20(f20(f11(a112),x7961),x7962),f4(a112))
% 1.28/1.60 [848]~P72(x8481)+~E(x8482,f4(x8481))+E(f20(f20(f11(x8481),x8482),x8482),f4(x8481))
% 1.28/1.60 [871]E(x8711,f4(a112))+E(x8712,f3(a112))+~E(f20(f20(f11(a112),x8712),x8711),x8712)
% 1.28/1.60 [873]E(x8731,f3(a112))+E(x8732,f3(a112))+~E(f20(f20(f11(a112),x8732),x8731),f3(a112))
% 1.28/1.60 [917]~P72(x9171)+~E(x9172,f10(x9171,f4(x9171)))+E(f20(f20(f11(x9171),x9172),x9172),f4(x9171))
% 1.28/1.60 [1082]E(x10821,f4(a110))+~P7(a110,f3(a110),x10822)+~E(f20(f20(f11(a110),x10822),x10821),f4(a110))
% 1.28/1.60 [1083]E(x10831,f4(a110))+~P7(a110,f3(a110),x10831)+~E(f20(f20(f11(a110),x10831),x10832),f4(a110))
% 1.28/1.60 [1149]~P43(x11491)+~P74(x11491)+E(f20(f20(f16(x11491),f3(x11491)),f12(a112,x11492,f4(a112))),f3(x11491))
% 1.28/1.60 [1227]E(x12271,f3(a112))+E(x12272,f12(a112,f3(a112),f4(a112)))+~E(f20(f20(f16(a112),x12272),x12271),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1337]~P7(a1,f3(a1),x13371)+~P7(a112,f3(a112),x13372)+E(f20(f20(f16(a1),f92(x13371,x13372)),x13372),x13371)
% 1.28/1.60 [1338]~P7(a1,f3(a1),x13381)+~P7(a112,f3(a112),x13382)+E(f20(f20(f16(a1),f97(x13381,x13382)),x13382),x13381)
% 1.28/1.60 [1355]E(x13551,f3(a112))+P7(a112,f3(a112),x13552)+~P7(a112,f3(a112),f20(f20(f16(a112),x13552),x13551))
% 1.28/1.60 [1360]~E(x13602,f12(a112,f3(a112),f4(a112)))+~E(x13601,f12(a112,f3(a112),f4(a112)))+E(f20(f20(f11(a112),x13601),x13602),f12(a112,f3(a112),f4(a112)))
% 1.28/1.60 [1388]P7(a1,x13881,a28)+~P6(a1,f22(a2,x13882),a114)+~E(f22(a2,f20(f14(a2,a115),x13882)),f10(a1,x13881))
% 1.28/1.60 [1397]P7(a1,x13971,f4(a1))+~P6(a1,f22(a2,x13972),a114)+~E(f22(a2,f20(f14(a2,a115),x13972)),f10(a1,x13971))
% 1.28/1.60 [1415]~P6(a110,f3(a110),x14152)+~P6(a110,f3(a110),x14151)+P6(a110,f3(a110),f20(f20(f11(a110),x14151),x14152))
% 1.28/1.60 [1416]~P7(a1,f3(a1),x14162)+~P7(a1,f3(a1),x14161)+P7(a1,f3(a1),f20(f20(f11(a1),x14161),x14162))
% 1.28/1.60 [1417]~P7(a112,f3(a112),x14172)+~P7(a112,f3(a112),x14171)+P7(a112,f3(a112),f20(f20(f11(a112),x14171),x14172))
% 1.28/1.60 [1581]~P6(a1,f4(a1),x15811)+~P7(a112,f3(a112),x15812)+E(f18(f24(a1,x15811,f19(a112,x15812))),f7(a112,f18(x15811),x15812))
% 1.28/1.60 [1681]~P77(f20(x16811,x16812))+P77(f20(x16811,f3(a112)))+P77(f20(x16811,f12(a112,f55(x16812,x16811),f4(a112))))
% 1.28/1.60 [1805]P7(a1,f10(a1,a117),x18051)+~P6(a1,f22(a2,x18052),a114)+~P7(a1,f22(a2,f20(f14(a2,a115),x18052)),x18051)
% 1.28/1.60 [1963]~P7(a112,f12(a112,f3(a112),f4(a112)),x19632)+~P7(a112,f12(a112,f3(a112),f4(a112)),x19631)+P7(a112,x19631,f20(f20(f11(a112),x19632),x19631))
% 1.28/1.60 [1964]~P7(a112,f12(a112,f3(a112),f4(a112)),x19642)+~P7(a112,f12(a112,f3(a112),f4(a112)),x19641)+P7(a112,x19641,f20(f20(f11(a112),x19641),x19642))
% 1.28/1.60 [2020]~P6(a112,f12(a112,f3(a112),f4(a112)),x20202)+~P6(a112,f12(a112,f3(a112),f4(a112)),x20201)+P6(a112,f12(a112,f3(a112),f4(a112)),f20(f20(f11(a112),x20201),x20202))
% 1.28/1.60 [2021]~P7(a112,f12(a112,f3(a112),f4(a112)),x20211)+~P7(a112,f12(a112,f3(a112),f4(a112)),x20212)+P7(a112,f12(a112,f3(a112),f4(a112)),f20(f20(f11(a112),x20211),x20212))
% 1.28/1.60 [1298]~E(x12982,f3(a1))+~E(x12981,f3(a1))+E(f12(a1,f20(f20(f11(a1),x12981),x12981),f20(f20(f11(a1),x12982),x12982)),f3(a1))
% 1.28/1.60 [1856]~P6(a1,f3(a1),x18562)+~P6(a1,f3(a1),x18561)+P6(a112,f20(f20(f11(a112),f18(x18561)),f18(x18562)),f18(f20(f20(f11(a1),x18561),x18562)))
% 1.28/1.60 [1978]~P7(a112,f3(a112),x19782)+~P7(a110,f3(a110),x19781)+E(f7(a110,f20(f20(f16(a110),x19781),x19782),x19781),f20(f20(f16(a110),x19781),f8(a112,x19782,f12(a112,f3(a112),f4(a112)))))
% 1.28/1.60 [2092]P7(a1,f10(a1,a117),x20921)+~P6(a1,f22(a2,x20922),a114)+~P7(a1,f10(a1,f10(a1,f22(a2,f20(f14(a2,a115),x20922)))),x20921)
% 1.28/1.60 [2108]E(x21081,f3(a112))+E(x21082,f3(a2))+P7(a1,f22(a2,f12(a2,f4(a2),f20(f20(f11(a2),x21082),f20(f20(f16(a2),f90(x21081,x21082)),x21081)))),f4(a1))
% 1.28/1.60 [805]~E(x8052,x8053)+~P35(x8051)+P6(x8051,x8052,x8053)
% 1.28/1.60 [807]~E(x8072,x8073)+~P41(x8071)+P6(x8071,x8072,x8073)
% 1.28/1.60 [915]~P7(x9153,x9151,x9152)+~E(x9151,x9152)+~P37(x9153)
% 1.28/1.60 [916]~P7(x9163,x9161,x9162)+~E(x9161,x9162)+~P41(x9163)
% 1.28/1.60 [958]P6(x9581,x9583,x9582)+~P37(x9581)+P6(x9581,x9582,x9583)
% 1.28/1.60 [963]P7(x9631,x9633,x9632)+~P37(x9631)+P6(x9631,x9632,x9633)
% 1.28/1.60 [1020]~P35(x10201)+~P7(x10201,x10202,x10203)+P6(x10201,x10202,x10203)
% 1.28/1.60 [1022]~P41(x10221)+~P7(x10221,x10222,x10223)+P6(x10221,x10222,x10223)
% 1.28/1.60 [1105]~P7(x11051,x11053,x11052)+~P35(x11051)+~P6(x11051,x11052,x11053)
% 1.28/1.60 [1109]~P7(x11091,x11093,x11092)+~P35(x11091)+~P7(x11091,x11092,x11093)
% 1.28/1.60 [1112]~P7(x11121,x11123,x11122)+~P37(x11121)+~P6(x11121,x11122,x11123)
% 1.28/1.60 [1113]~P7(x11131,x11133,x11132)+~P37(x11131)+~P7(x11131,x11132,x11133)
% 1.28/1.60 [1114]~P7(x11141,x11143,x11142)+~P41(x11141)+~P7(x11141,x11142,x11143)
% 1.28/1.60 [1205]~P6(a1,x12051,x12053)+P6(a1,x12051,x12052)+~P6(a1,x12053,x12052)
% 1.28/1.60 [1206]~P6(a112,x12061,x12063)+P6(a112,x12061,x12062)+~P6(a112,x12063,x12062)
% 1.28/1.60 [1207]~P6(a110,x12071,x12073)+P6(a110,x12071,x12072)+~P6(a110,x12073,x12072)
% 1.28/1.60 [776]~P14(x7762)+~E(x7763,f10(x7762,x7761))+E(x7761,f10(x7762,x7763))
% 1.28/1.60 [778]~P14(x7781)+~E(f10(x7781,x7783),x7782)+E(f10(x7781,x7782),x7783)
% 1.28/1.60 [781]~P14(x7813)+E(x7811,x7812)+~E(f10(x7813,x7811),f10(x7813,x7812))
% 1.28/1.60 [782]~P39(x7823)+E(x7821,x7822)+~E(f10(x7823,x7821),f10(x7823,x7822))
% 1.28/1.60 [827]~E(x8272,x8273)+~P14(x8271)+E(f8(x8271,x8272,x8273),f3(x8271))
% 1.28/1.60 [828]~E(x8282,x8283)+~P16(x8281)+E(f8(x8281,x8282,x8283),f3(x8281))
% 1.28/1.60 [838]~P75(x8381)+~E(x8383,f3(x8381))+E(f12(x8381,x8382,x8383),x8382)
% 1.28/1.60 [896]~P14(x8961)+~E(x8963,f10(x8961,x8962))+E(f12(x8961,x8962,x8963),f3(x8961))
% 1.28/1.60 [897]~P14(x8971)+~E(x8972,f10(x8971,x8973))+E(f12(x8971,x8972,x8973),f3(x8971))
% 1.28/1.60 [924]~P75(x9242)+~E(f12(x9242,x9243,x9241),x9243)+E(x9241,f3(x9242))
% 1.28/1.60 [927]~P14(x9273)+E(x9271,x9272)+~E(f8(x9273,x9271,x9272),f3(x9273))
% 1.28/1.60 [928]~P16(x9283)+E(x9281,x9282)+~E(f8(x9283,x9281,x9282),f3(x9283))
% 1.28/1.60 [953]~P14(x9532)+~E(f12(x9532,x9533,x9531),f3(x9532))+E(x9531,f10(x9532,x9533))
% 1.28/1.60 [954]~P14(x9542)+~E(f12(x9542,x9541,x9543),f3(x9542))+E(x9541,f10(x9542,x9543))
% 1.28/1.60 [955]~P14(x9551)+~E(f12(x9551,x9552,x9553),f3(x9551))+E(f10(x9551,x9552),x9553)
% 1.28/1.60 [973]~P78(x9731,x9733,x9732)+~E(x9733,f3(a110))+P77(f20(x9731,x9732))
% 1.28/1.60 [1159]~P31(x11591)+~P6(x11591,x11593,x11592)+P6(x11591,f10(x11591,x11592),f10(x11591,x11593))
% 1.28/1.60 [1161]~P39(x11611)+~P6(x11611,x11613,x11612)+P6(x11611,f10(x11611,x11612),f10(x11611,x11613))
% 1.28/1.60 [1162]~P31(x11621)+~P7(x11621,x11623,x11622)+P7(x11621,f10(x11621,x11622),f10(x11621,x11623))
% 1.28/1.60 [1189]~P31(x11891)+~P6(x11891,x11893,f10(x11891,x11892))+P6(x11891,x11892,f10(x11891,x11893))
% 1.28/1.60 [1191]~P31(x11911)+~P7(x11911,x11913,f10(x11911,x11912))+P7(x11911,x11912,f10(x11911,x11913))
% 1.28/1.60 [1193]~P31(x11931)+~P6(x11931,f10(x11931,x11933),x11932)+P6(x11931,f10(x11931,x11932),x11933)
% 1.28/1.60 [1195]~P31(x11951)+~P7(x11951,f10(x11951,x11953),x11952)+P7(x11951,f10(x11951,x11952),x11953)
% 1.28/1.60 [1213]~P6(a112,x12133,x12131)+~E(f8(a112,x12131,x12133),x12132)+E(x12131,f12(a112,x12132,x12133))
% 1.28/1.60 [1214]~P6(a112,x12142,x12141)+~E(x12141,f12(a112,x12143,x12142))+E(f8(a112,x12141,x12142),x12143)
% 1.28/1.60 [1228]~P13(x12281)+P6(x12281,x12282,x12283)+P7(x12281,f3(x12281),f89(x12283,x12282,x12281))
% 1.28/1.60 [1229]~P13(x12291)+P6(x12291,x12292,x12293)+P7(x12291,f89(x12293,x12292,x12291),f4(x12291))
% 1.28/1.60 [1230]~P31(x12301)+P6(x12301,x12302,x12303)+~P6(x12301,f10(x12301,x12303),f10(x12301,x12302))
% 1.28/1.60 [1231]~P39(x12311)+P6(x12311,x12312,x12313)+~P6(x12311,f10(x12311,x12313),f10(x12311,x12312))
% 1.28/1.60 [1232]~P31(x12321)+P7(x12321,x12322,x12323)+~P7(x12321,f10(x12321,x12323),f10(x12321,x12322))
% 1.28/1.60 [1666]~P7(a112,x16663,x16661)+~P7(a112,x16663,x16662)+P7(a112,f8(a112,x16661,x16662),f8(a112,x16661,x16663))
% 1.28/1.60 [1667]~P6(a112,x16672,x16671)+~P7(a112,x16671,x16673)+P7(a112,f8(a112,x16671,x16672),f8(a112,x16673,x16672))
% 1.28/1.60 [1673]~P6(a110,x16733,x16731)+P6(a110,f7(a110,x16731,x16732),f7(a110,x16733,x16732))+~P7(a110,x16732,f3(a110))
% 1.28/1.60 [1674]~P6(a112,x16743,x16742)+P6(a112,f7(a112,x16741,x16742),f7(a112,x16741,x16743))+~P7(a112,f3(a112),x16743)
% 1.28/1.60 [1675]~P6(a110,x16751,x16753)+P6(a110,f7(a110,x16751,x16752),f7(a110,x16753,x16752))+~P7(a110,f3(a110),x16752)
% 1.28/1.60 [1752]~P6(a112,x17523,x17522)+~P6(a112,f12(a112,x17521,x17523),x17522)+P6(a112,x17521,f8(a112,x17522,x17523))
% 1.28/1.60 [1753]~P6(a112,x17532,x17533)+~P6(a112,x17531,f8(a112,x17533,x17532))+P6(a112,f12(a112,x17531,x17532),x17533)
% 1.28/1.60 [826]~P54(x8261)+~E(x8262,f3(f113(x8261)))+E(f20(f14(x8261,x8262),x8263),f3(x8261))
% 1.28/1.60 [940]~P54(x9401)+E(f15(x9401,x9402,x9403),f3(a112))+E(f20(f14(x9401,x9403),x9402),f3(x9401))
% 1.28/1.60 [981]~P79(x9811,x9812,x9813)+~E(x9812,f3(a110))+P77(f20(x9811,f3(a110)))
% 1.28/1.60 [1095]~P46(x10952)+E(x10951,f3(x10952))+E(f24(x10952,f10(x10952,x10953),f10(x10952,x10951)),f24(x10952,x10953,x10951))
% 1.28/1.60 [1137]~P1(x11371)+~P8(x11371,x11372)+P6(a1,f22(x11371,f20(x11372,x11373)),f53(x11372,x11371))
% 1.28/1.60 [1138]~P1(x11381)+~P8(x11381,x11382)+P6(a1,f22(x11381,f20(x11382,x11383)),f68(x11382,x11381))
% 1.28/1.60 [1187]~P46(x11872)+E(x11871,f3(x11872))+E(f24(x11872,x11873,f10(x11872,x11871)),f10(x11872,f24(x11872,x11873,x11871)))
% 1.28/1.60 [1251]~P12(x12512)+E(x12511,f3(x12512))+E(f24(a1,f22(x12512,x12513),f22(x12512,x12511)),f22(x12512,f24(x12512,x12513,x12511)))
% 1.28/1.60 [1252]~P12(x12521)+~P3(x12521)+E(f24(a1,f22(x12521,x12522),f22(x12521,x12523)),f22(x12521,f24(x12521,x12522,x12523)))
% 1.28/1.60 [1357]~E(x13573,f3(a112))+~P77(f20(x13571,x13572))+P77(f20(x13571,f6(a112,x13572,x13573)))
% 1.28/1.60 [1375]~E(x13753,f3(a112))+P77(f20(x13751,f7(a112,x13752,x13753)))+~P77(f20(x13751,f3(a112)))
% 1.28/1.60 [1436]~P7(a112,x14361,x14363)+~P7(a112,x14363,x14362)+P7(a112,f12(a112,x14361,f4(a112)),x14362)
% 1.28/1.60 [1449]~P7(a112,x14493,x14492)+P7(a112,x14491,f12(a112,x14492,f4(a112)))+~E(x14491,f12(a112,x14493,f4(a112)))
% 1.28/1.60 [1468]~P4(x14682)+E(x14681,f3(x14682))+E(f7(x14682,f12(x14682,x14683,x14681),x14681),f12(x14682,f7(x14682,x14683,x14681),f4(x14682)))
% 1.28/1.60 [1469]~P4(x14692)+E(x14691,f3(x14692))+E(f7(x14692,f12(x14692,x14691,x14693),x14691),f12(x14692,f7(x14692,x14693,x14691),f4(x14692)))
% 1.28/1.60 [1614]P7(a112,f76(x16141,x16142,x16143),x16141)+E(x16141,f3(a112))+P77(f20(x16143,f6(a112,x16142,x16141)))
% 1.28/1.60 [1615]P7(a112,f78(x16151,x16152,x16153),x16151)+E(x16151,f3(a112))+P77(f20(x16153,f7(a112,x16152,x16151)))
% 1.28/1.60 [1635]~E(x16353,f3(a112))+P77(f20(x16351,x16352))+~P77(f20(x16351,f6(a112,x16352,x16353)))
% 1.28/1.60 [1636]~E(x16362,f3(a112))+~P77(f20(x16361,f7(a112,x16363,x16362)))+P77(f20(x16361,f3(a112)))
% 1.28/1.60 [1687]P7(a112,f76(x16871,x16872,x16873),x16871)+~P77(f20(x16873,x16872))+P77(f20(x16873,f6(a112,x16872,x16871)))
% 1.28/1.60 [1725]P7(a112,f78(x17251,x17252,x17253),x17251)+P77(f20(x17253,f7(a112,x17252,x17251)))+~P77(f20(x17253,f3(a112)))
% 1.28/1.60 [1736]~P6(a112,x17362,x17363)+~P6(a112,x17362,x17361)+E(f8(a112,f8(a112,x17361,x17362),f8(a112,x17363,x17362)),f8(a112,x17361,x17363))
% 1.28/1.60 [1922]E(x19221,f3(a112))+P77(f20(x19222,f75(x19221,x19223,x19222)))+~P77(f20(x19222,f7(a112,x19223,x19221)))
% 1.28/1.60 [1927]E(x19271,f3(a112))+~P77(f20(x19272,f79(x19271,x19273,x19272)))+P77(f20(x19272,f7(a112,x19273,x19271)))
% 1.28/1.60 [1928]E(x19281,f3(a112))+~P77(f20(x19282,f76(x19281,x19283,x19282)))+P77(f20(x19282,f6(a112,x19283,x19281)))
% 1.28/1.60 [1953]P77(f20(x19531,f75(x19532,x19533,x19531)))+~P77(f20(x19531,f7(a112,x19533,x19532)))+P77(f20(x19531,f3(a112)))
% 1.28/1.60 [1960]~P77(f20(x19601,x19602))+~P77(f20(x19601,f76(x19603,x19602,x19601)))+P77(f20(x19601,f6(a112,x19602,x19603)))
% 1.28/1.60 [1965]~P77(f20(x19651,f79(x19653,x19652,x19651)))+P77(f20(x19651,f7(a112,x19652,x19653)))+~P77(f20(x19651,f3(a112)))
% 1.28/1.60 [1979]E(x19791,f3(a112))+E(f12(a112,f20(f20(f11(a112),x19791),f77(x19791,x19792,x19793)),f76(x19791,x19792,x19793)),x19792)+P77(f20(x19793,f6(a112,x19792,x19791)))
% 1.28/1.60 [1980]E(x19801,f3(a112))+E(f12(a112,f20(f20(f11(a112),x19801),f79(x19801,x19802,x19803)),f78(x19801,x19802,x19803)),x19802)+P77(f20(x19803,f7(a112,x19802,x19801)))
% 1.28/1.60 [1996]E(x19961,f3(a112))+P6(a112,f20(f20(f11(a112),x19961),f75(x19961,x19962,x19963)),x19962)+~P77(f20(x19963,f7(a112,x19962,x19961)))
% 1.28/1.60 [2003]~P77(f20(x20033,x20032))+E(f12(a112,f20(f20(f11(a112),x20031),f77(x20031,x20032,x20033)),f76(x20031,x20032,x20033)),x20032)+P77(f20(x20033,f6(a112,x20032,x20031)))
% 1.28/1.60 [2014]E(f12(a112,f20(f20(f11(a112),x20141),f79(x20141,x20142,x20143)),f78(x20141,x20142,x20143)),x20142)+P77(f20(x20143,f7(a112,x20142,x20141)))+~P77(f20(x20143,f3(a112)))
% 1.28/1.60 [2017]P6(a112,f20(f20(f11(a112),x20172),f75(x20172,x20173,x20171)),x20173)+~P77(f20(x20171,f7(a112,x20173,x20172)))+P77(f20(x20171,f3(a112)))
% 1.28/1.60 [2043]P7(a110,x20431,f93(x20432,x20433,x20431))+~P7(a110,x20431,f3(a110))+P77(f20(f20(x20433,f7(a110,x20432,x20431)),f6(a110,x20432,x20431)))
% 1.28/1.60 [2044]P7(a110,f94(x20441,x20442,x20443),x20443)+~P7(a110,f3(a110),x20443)+P77(f20(f20(x20442,f7(a110,x20441,x20443)),f6(a110,x20441,x20443)))
% 1.28/1.60 [2045]~P7(a110,f3(a110),x20453)+P6(a110,f3(a110),f94(x20451,x20452,x20453))+P77(f20(f20(x20452,f7(a110,x20451,x20453)),f6(a110,x20451,x20453)))
% 1.28/1.60 [2046]~P7(a110,x20463,f3(a110))+P6(a110,f93(x20461,x20462,x20463),f3(a110))+P77(f20(f20(x20462,f7(a110,x20461,x20463)),f6(a110,x20461,x20463)))
% 1.28/1.60 [2082]~P7(a110,x20821,f3(a110))+E(f12(a110,f20(f20(f11(a110),x20821),f96(x20822,x20823,x20821)),f93(x20822,x20823,x20821)),x20822)+P77(f20(f20(x20823,f7(a110,x20822,x20821)),f6(a110,x20822,x20821)))
% 1.28/1.60 [2083]~P7(a110,f3(a110),x20831)+E(f12(a110,f20(f20(f11(a110),x20831),f95(x20832,x20833,x20831)),f94(x20832,x20833,x20831)),x20832)+P77(f20(f20(x20833,f7(a110,x20832,x20831)),f6(a110,x20832,x20831)))
% 1.28/1.60 [2106]~P7(a110,x21063,f3(a110))+~P77(f20(f20(x21061,f96(x21062,x21061,x21063)),f93(x21062,x21061,x21063)))+P77(f20(f20(x21061,f7(a110,x21062,x21063)),f6(a110,x21062,x21063)))
% 1.28/1.60 [2107]~P7(a110,f3(a110),x21073)+~P77(f20(f20(x21071,f95(x21072,x21071,x21073)),f94(x21072,x21071,x21073)))+P77(f20(f20(x21071,f7(a110,x21072,x21073)),f6(a110,x21072,x21073)))
% 1.28/1.60 [846]~P71(x8461)+~E(x8463,f3(x8461))+E(f20(f20(f11(x8461),x8462),x8463),f3(x8461))
% 1.28/1.60 [847]~P71(x8471)+~E(x8472,f3(x8471))+E(f20(f20(f11(x8471),x8472),x8473),f3(x8471))
% 1.28/1.60 [926]~P72(x9262)+E(x9261,f3(x9262))+~E(f20(f20(f16(x9262),x9261),x9263),f3(x9262))
% 1.28/1.60 [985]~P54(x9851)+~E(x9852,f10(x9851,x9853))+E(f20(f20(f11(x9851),x9852),x9852),f20(f20(f11(x9851),x9853),x9853))
% 1.28/1.60 [1037]E(x10371,x10372)+E(x10373,f3(a1))+~E(f20(f20(f11(a1),x10373),x10371),f20(f20(f11(a1),x10373),x10372))
% 1.28/1.60 [1039]E(x10391,x10392)+E(x10393,f3(a112))+~E(f20(f20(f11(a112),x10393),x10391),f20(f20(f11(a112),x10393),x10392))
% 1.28/1.60 [1040]E(x10401,x10402)+E(x10403,f3(a1))+~E(f20(f20(f11(a1),x10401),x10403),f20(f20(f11(a1),x10402),x10403))
% 1.28/1.60 [1041]E(x10411,x10412)+E(x10413,f3(a112))+~E(f20(f20(f11(a112),x10411),x10413),f20(f20(f11(a112),x10412),x10413))
% 1.28/1.60 [1249]E(x12491,x12492)+~P7(a112,f3(a112),x12493)+~E(f20(f20(f11(a112),x12493),x12491),f20(f20(f11(a112),x12493),x12492))
% 1.28/1.60 [1319]~P45(x13191)+~P6(x13191,f3(x13191),x13192)+P6(x13191,f3(x13191),f20(f20(f16(x13191),x13192),x13193))
% 1.28/1.60 [1320]~P45(x13201)+~P6(x13201,f4(x13201),x13202)+P6(x13201,f4(x13201),f20(f20(f16(x13201),x13202),x13203))
% 1.28/1.60 [1321]~P45(x13211)+~P7(x13211,f3(x13211),x13212)+P7(x13211,f3(x13211),f20(f20(f16(x13211),x13212),x13213))
% 1.28/1.60 [1398]~E(x13982,f7(a112,x13983,x13981))+~P7(a112,f3(a112),x13981)+P6(a112,f20(f20(f11(a112),x13981),x13982),x13983)
% 1.28/1.60 [1620]~P6(a1,x16202,x16203)+~P7(a1,f3(a1),x16201)+P6(a1,f20(f20(f11(a1),x16201),x16202),f20(f20(f11(a1),x16201),x16203))
% 1.28/1.60 [1621]~P6(a1,x16211,x16213)+~P7(a1,f3(a1),x16212)+P6(a1,f20(f20(f11(a1),x16211),x16212),f20(f20(f11(a1),x16213),x16212))
% 1.28/1.60 [1623]~P7(a1,x16231,x16233)+~P7(a1,f3(a1),x16232)+P7(a1,f20(f20(f11(a1),x16231),x16232),f20(f20(f11(a1),x16233),x16232))
% 1.28/1.60 [1624]~P7(a1,x16242,x16243)+~P7(a1,f3(a1),x16241)+P7(a1,f20(f20(f11(a1),x16241),x16242),f20(f20(f11(a1),x16241),x16243))
% 1.28/1.60 [1628]~P7(a112,x16281,x16283)+~P7(a112,f3(a112),x16282)+P7(a112,f20(f20(f11(a112),x16281),x16282),f20(f20(f11(a112),x16283),x16282))
% 1.28/1.60 [1629]~P7(a112,x16292,x16293)+~P7(a112,f3(a112),x16291)+P7(a112,f20(f20(f11(a112),x16291),x16292),f20(f20(f11(a112),x16291),x16293))
% 1.28/1.60 [1630]~P7(a110,x16302,x16303)+~P7(a110,f3(a110),x16301)+P7(a110,f20(f20(f11(a110),x16301),x16302),f20(f20(f11(a110),x16301),x16303))
% 1.28/1.60 [1751]~P45(x17511)+~P7(x17511,f4(x17511),x17512)+P7(x17511,f4(x17511),f20(f20(f16(x17511),x17512),f12(a112,x17513,f4(a112))))
% 1.28/1.60 [1759]~P1(x17591)+~P8(x17591,x17592)+P6(a1,f22(x17591,f20(x17592,x17593)),f19(a112,f12(a112,f57(x17592,x17591),f4(a112))))
% 1.28/1.60 [1760]~P1(x17601)+~P8(x17601,x17602)+P7(a1,f22(x17601,f20(x17602,x17603)),f19(a112,f12(a112,f58(x17602,x17601),f4(a112))))
% 1.28/1.60 [1764]P6(a1,x17641,x17642)+~P7(a1,f3(a1),x17643)+~P6(a1,f20(f20(f11(a1),x17643),x17641),f20(f20(f11(a1),x17643),x17642))
% 1.28/1.60 [1765]P6(a1,x17651,x17652)+~P7(a1,f3(a1),x17653)+~P6(a1,f20(f20(f11(a1),x17651),x17653),f20(f20(f11(a1),x17652),x17653))
% 1.28/1.60 [1767]P6(a112,x17671,x17672)+~P7(a112,f3(a112),x17673)+~P6(a112,f20(f20(f11(a112),x17673),x17671),f20(f20(f11(a112),x17673),x17672))
% 1.28/1.60 [1768]P6(a112,x17681,x17682)+~P7(a112,f3(a112),x17683)+~P6(a112,f20(f20(f11(a112),x17681),x17683),f20(f20(f11(a112),x17682),x17683))
% 1.28/1.60 [1769]P7(a1,x17691,x17692)+~P7(a1,f3(a1),x17693)+~P7(a1,f20(f20(f11(a1),x17691),x17693),f20(f20(f11(a1),x17692),x17693))
% 1.28/1.60 [1771]P7(a112,x17711,x17712)+~P7(a112,f3(a112),x17713)+~P7(a112,f20(f20(f16(a112),x17713),x17711),f20(f20(f16(a112),x17713),x17712))
% 1.28/1.60 [1836]~E(x18363,f7(a112,x18361,x18362))+~P7(a112,f3(a112),x18362)+P7(a112,x18361,f20(f20(f11(a112),x18362),f12(a112,x18363,f4(a112))))
% 1.28/1.60 [1994]~P2(x19941)+~P7(x19941,x19942,x19943)+P7(x19941,x19942,f24(x19941,f12(x19941,x19942,x19943),f12(x19941,f4(x19941),f4(x19941))))
% 1.28/1.60 [1995]~P2(x19951)+~P7(x19951,x19952,x19953)+P7(x19951,f24(x19951,f12(x19951,x19952,x19953),f12(x19951,f4(x19951),f4(x19951))),x19953)
% 1.28/1.60 [2022]~P54(x20221)+~E(x20222,f10(x20221,x20223))+E(f20(f20(f16(x20221),x20222),f12(a112,f12(a112,f3(a112),f4(a112)),f4(a112))),f20(f20(f16(x20221),x20223),f12(a112,f12(a112,f3(a112),f4(a112)),f4(a112))))
% 1.28/1.60 [2051]~P13(x20511)+P6(x20511,x20512,x20513)+~P6(x20511,f20(f20(f11(x20511),f89(x20513,x20512,x20511)),x20512),x20513)
% 1.28/1.60 [2074]E(x20741,f3(a112))+P7(a112,x20742,f20(f20(f11(a112),x20741),f12(a112,f75(x20741,x20742,x20743),f4(a112))))+~P77(f20(x20743,f7(a112,x20742,x20741)))
% 1.28/1.60 [2078]P7(a112,x20782,f20(f20(f11(a112),x20783),f12(a112,f75(x20783,x20782,x20781),f4(a112))))+~P77(f20(x20781,f7(a112,x20782,x20783)))+P77(f20(x20781,f3(a112)))
% 1.28/1.60 [2086]~P1(x20861)+P8(x20861,x20862)+~P6(a1,f22(x20861,f20(x20862,f60(x20862,x20861,x20863))),f19(a112,f12(a112,x20863,f4(a112))))
% 1.28/1.60 [2087]~P1(x20871)+P8(x20871,x20872)+~P7(a1,f22(x20871,f20(x20872,f59(x20872,x20871,x20873))),f19(a112,f12(a112,x20873,f4(a112))))
% 1.28/1.60 [2090]~P1(x20902)+P7(a1,f3(a1),f30(x20901,x20902))+~P6(a1,f22(x20902,f20(x20901,f31(x20901,x20902,x20903))),f19(a112,f12(a112,x20903,f4(a112))))
% 1.28/1.60 [2091]~P1(x20912)+P7(a1,f3(a1),f34(x20911,x20912))+~P7(a1,f22(x20912,f20(x20911,f35(x20911,x20912,x20913))),f19(a112,f12(a112,x20913,f4(a112))))
% 1.28/1.60 [1090]~P4(x10902)+E(x10901,f3(x10902))+E(f7(x10902,f20(f20(f11(x10902),x10903),x10901),x10901),x10903)
% 1.28/1.60 [1091]~P4(x10912)+E(x10911,f3(x10912))+E(f7(x10912,f20(f20(f11(x10912),x10911),x10913),x10911),x10913)
% 1.28/1.60 [1658]~P57(x16582)+E(x16581,f3(x16582))+~E(f12(x16582,f20(f20(f11(x16582),x16583),x16583),f20(f20(f11(x16582),x16581),x16581)),f3(x16582))
% 1.28/1.60 [1659]~P57(x16592)+E(x16591,f3(x16592))+~E(f12(x16592,f20(f20(f11(x16592),x16591),x16591),f20(f20(f11(x16592),x16593),x16593)),f3(x16592))
% 1.28/1.60 [1735]~P45(x17351)+~P7(x17351,f4(x17351),x17352)+P7(x17351,f4(x17351),f20(f20(f11(x17351),x17352),f20(f20(f16(x17351),x17352),x17353)))
% 1.28/1.60 [1879]~P45(x18791)+~P7(x18791,f4(x18791),x18792)+P7(x18791,f20(f20(f16(x18791),x18792),x18793),f20(f20(f11(x18791),x18792),f20(f20(f16(x18791),x18792),x18793)))
% 1.28/1.60 [1907]~P57(x19072)+E(x19071,f3(x19072))+P7(x19072,f3(x19072),f12(x19072,f20(f20(f11(x19072),x19073),x19073),f20(f20(f11(x19072),x19071),x19071)))
% 1.28/1.60 [1908]~P57(x19082)+E(x19081,f3(x19082))+P7(x19082,f3(x19082),f12(x19082,f20(f20(f11(x19082),x19081),x19081),f20(f20(f11(x19082),x19083),x19083)))
% 1.28/1.60 [2016]~P1(x20161)+~P8(x20161,x20162)+P6(a1,f22(x20161,f12(x20161,f20(x20162,x20163),f10(x20161,f70(x20162,x20161)))),f65(x20162,x20161))
% 1.28/1.60 [2035]~P57(x20352)+E(x20351,f3(x20352))+~P6(x20352,f12(x20352,f20(f20(f11(x20352),x20353),x20353),f20(f20(f11(x20352),x20351),x20351)),f3(x20352))
% 1.28/1.60 [2036]~P57(x20362)+E(x20361,f3(x20362))+~P6(x20362,f12(x20362,f20(f20(f11(x20362),x20361),x20361),f20(f20(f11(x20362),x20363),x20363)),f3(x20362))
% 1.28/1.60 [2075]~P1(x20751)+~P8(x20751,x20752)+P6(a1,f22(x20751,f12(x20751,f20(x20752,x20753),f10(x20751,f20(x20752,f66(x20752,x20751))))),f61(x20752,x20751))
% 1.28/1.60 [1116]~P17(x11163)+E(x11161,x11162)+~E(f12(x11163,x11164,x11161),f12(x11163,x11164,x11162))
% 1.28/1.60 [1117]~P18(x11173)+E(x11171,x11172)+~E(f12(x11173,x11174,x11171),f12(x11173,x11174,x11172))
% 1.28/1.60 [1119]~P17(x11193)+E(x11191,x11192)+~E(f12(x11193,x11191,x11194),f12(x11193,x11192,x11194))
% 1.28/1.60 [1196]~P36(x11962)+~P7(f116(x11961,x11962),x11963,x11964)+P6(f116(x11961,x11962),x11963,x11964)
% 1.28/1.60 [1313]~P36(x13131)+~P7(f116(x13132,x13131),x13134,x13133)+~P6(f116(x13132,x13131),x13133,x13134)
% 1.28/1.60 [1376]~P7(a112,x13763,x13764)+P7(a112,x13761,x13762)+~E(f12(a112,x13763,x13762),f12(a112,x13761,x13764))
% 1.28/1.60 [1497]~P29(x14971)+~P6(x14971,x14973,x14974)+P6(x14971,f12(x14971,x14972,x14973),f12(x14971,x14972,x14974))
% 1.28/1.60 [1498]~P30(x14981)+~P6(x14981,x14983,x14984)+P6(x14981,f12(x14981,x14982,x14983),f12(x14981,x14982,x14984))
% 1.28/1.60 [1499]~P29(x14991)+~P6(x14991,x14992,x14994)+P6(x14991,f12(x14991,x14992,x14993),f12(x14991,x14994,x14993))
% 1.28/1.60 [1500]~P30(x15001)+~P6(x15001,x15002,x15004)+P6(x15001,f12(x15001,x15002,x15003),f12(x15001,x15004,x15003))
% 1.28/1.60 [1501]~P29(x15011)+~P7(x15011,x15013,x15014)+P7(x15011,f12(x15011,x15012,x15013),f12(x15011,x15012,x15014))
% 1.28/1.60 [1502]~P32(x15021)+~P7(x15021,x15023,x15024)+P7(x15021,f12(x15021,x15022,x15023),f12(x15021,x15022,x15024))
% 1.28/1.60 [1503]~P29(x15031)+~P7(x15031,x15032,x15034)+P7(x15031,f12(x15031,x15032,x15033),f12(x15031,x15034,x15033))
% 1.28/1.60 [1504]~P32(x15041)+~P7(x15041,x15042,x15044)+P7(x15041,f12(x15041,x15042,x15043),f12(x15041,x15044,x15043))
% 1.28/1.60 [1664]~P6(a112,x16642,x16644)+~P6(a112,x16641,x16643)+P6(a112,f12(a112,x16641,x16642),f12(a112,x16643,x16644))
% 1.28/1.60 [1665]~P7(a112,x16652,x16654)+~P7(a112,x16651,x16653)+P7(a112,f12(a112,x16651,x16652),f12(a112,x16653,x16654))
% 1.28/1.60 [1668]~P6(a110,x16682,x16684)+~P7(a110,x16681,x16683)+P7(a110,f12(a110,x16681,x16682),f12(a110,x16683,x16684))
% 1.28/1.60 [1742]~P29(x17421)+P6(x17421,x17422,x17423)+~P6(x17421,f12(x17421,x17424,x17422),f12(x17421,x17424,x17423))
% 1.28/1.60 [1744]~P29(x17441)+P6(x17441,x17442,x17443)+~P6(x17441,f12(x17441,x17442,x17444),f12(x17441,x17443,x17444))
% 1.28/1.60 [1746]~P29(x17461)+P7(x17461,x17462,x17463)+~P7(x17461,f12(x17461,x17464,x17462),f12(x17461,x17464,x17463))
% 1.28/1.60 [1748]~P29(x17481)+P7(x17481,x17482,x17483)+~P7(x17481,f12(x17481,x17482,x17484),f12(x17481,x17483,x17484))
% 1.28/1.60 [1881]~P1(x18811)+P8(x18811,x18812)+P6(a112,x18813,f74(x18814,x18812,x18813,x18811))
% 1.28/1.60 [1464]~P5(x14641)+~E(f6(x14641,x14642,x14643),f6(x14641,x14644,x14643))+E(f6(x14641,f10(x14641,x14642),x14643),f6(x14641,f10(x14641,x14644),x14643))
% 1.28/1.60 [2112]~P36(x21122)+P6(f116(x21121,x21122),x21123,x21124)+~P6(x21122,f20(x21123,f47(x21124,x21123,x21121,x21122)),f20(x21124,f47(x21124,x21123,x21121,x21122)))
% 1.28/1.60 [1613]~P6(a112,x16132,x16134)+~P6(a112,x16131,x16133)+P6(a112,f20(f20(f11(a112),x16131),x16132),f20(f20(f11(a112),x16133),x16134))
% 1.28/1.60 [2056]~P7(a112,x20564,x20561)+~P7(a112,f3(a112),x20563)+P7(a112,f12(a112,f20(f20(f11(a112),x20561),f6(a112,x20562,x20563)),x20564),f20(f20(f11(a112),x20561),x20563))
% 1.28/1.60 [2097]~P1(x20971)+P6(a1,f22(x20971,f20(x20972,x20973)),f30(x20972,x20971))+~P6(a1,f22(x20971,f20(x20972,f31(x20972,x20971,x20974))),f19(a112,f12(a112,x20974,f4(a112))))
% 1.28/1.60 [2098]~P1(x20981)+P6(a1,f22(x20981,f20(x20982,x20983)),f34(x20982,x20981))+~P7(a1,f22(x20981,f20(x20982,f35(x20982,x20981,x20984))),f19(a112,f12(a112,x20984,f4(a112))))
% 1.28/1.60 [2111]~P1(x21111)+P8(x21111,x21112)+~P6(a1,f22(x21111,f20(x21112,f74(x21113,x21112,x21114,x21111))),x21113)
% 1.28/1.60 [1343]~P4(x13431)+~E(x13432,f3(x13431))+E(f7(x13431,f20(f20(f11(x13431),x13432),x13433),f20(f20(f11(x13431),x13432),x13434)),f3(x13431))
% 1.28/1.60 [1420]~P3(x14202)+E(x14201,f3(x14202))+E(f24(x14202,f20(f20(f11(x14202),x14203),x14201),f20(f20(f11(x14202),x14204),x14201)),f24(x14202,x14203,x14204))
% 1.28/1.60 [1421]~P3(x14212)+E(x14211,f3(x14212))+E(f24(x14212,f20(f20(f11(x14212),x14211),x14213),f20(f20(f11(x14212),x14211),x14214)),f24(x14212,x14213,x14214))
% 1.28/1.60 [1422]~P4(x14222)+E(x14221,f3(x14222))+E(f7(x14222,f20(f20(f11(x14222),x14223),x14221),f20(f20(f11(x14222),x14224),x14221)),f7(x14222,x14223,x14224))
% 1.28/1.60 [1424]~P4(x14242)+E(x14241,f3(x14242))+E(f7(x14242,f20(f20(f11(x14242),x14241),x14243),f20(f20(f11(x14242),x14241),x14244)),f7(x14242,x14243,x14244))
% 1.28/1.60 [1837]~P11(x18372)+E(x18371,f3(x18372))+E(f24(x18372,f20(f20(f16(x18372),x18373),x18374),f20(f20(f16(x18372),x18371),x18374)),f20(f20(f16(x18372),f24(x18372,x18373,x18371)),x18374))
% 1.28/1.60 [1839]~P3(x18392)+E(x18391,f3(x18392))+E(f24(x18392,f12(x18392,x18393,f20(f20(f11(x18392),x18394),x18391)),x18391),f12(x18392,x18394,f24(x18392,x18393,x18391)))
% 1.28/1.60 [1840]~P11(x18402)+E(x18401,f3(x18402))+E(f24(x18402,f12(x18402,f20(f20(f11(x18402),x18401),x18403),x18404),x18401),f12(x18402,x18403,f24(x18402,x18404,x18401)))
% 1.28/1.60 [1841]~P3(x18412)+E(x18411,f3(x18412))+E(f24(x18412,f12(x18412,x18413,f20(f20(f11(x18412),x18414),x18411)),x18411),f12(x18412,f24(x18412,x18413,x18411),x18414))
% 1.28/1.60 [1842]~P11(x18422)+E(x18421,f3(x18422))+E(f24(x18422,f12(x18422,x18423,f20(f20(f11(x18422),x18421),x18424)),x18421),f12(x18422,f24(x18422,x18423,x18421),x18424))
% 1.28/1.60 [1843]~P4(x18432)+E(x18431,f3(x18432))+E(f7(x18432,f12(x18432,x18433,f20(f20(f11(x18432),x18434),x18431)),x18431),f12(x18432,x18434,f7(x18432,x18433,x18431)))
% 1.28/1.60 [1844]~P4(x18442)+E(x18441,f3(x18442))+E(f7(x18442,f12(x18442,x18443,f20(f20(f11(x18442),x18441),x18444)),x18441),f12(x18442,x18444,f7(x18442,x18443,x18441)))
% 1.28/1.60 [1268]~P36(x12681)+P6(x12681,f20(x12682,x12683),f20(x12684,x12683))+~P6(f116(x12685,x12681),x12682,x12684)
% 1.28/1.60 [1816]~E(x18162,x18164)+~P75(x18161)+E(f12(x18161,f20(f20(f11(x18161),x18162),x18163),f20(f20(f11(x18161),x18164),x18165)),f12(x18161,f20(f20(f11(x18161),x18162),x18165),f20(f20(f11(x18161),x18164),x18163)))
% 1.28/1.60 [2067]~P59(x20672)+~E(f12(x20672,f20(f20(f11(x20672),x20674),x20675),x20671),f12(x20672,f20(f20(f11(x20672),x20673),x20675),x20676))+E(x20671,f12(x20672,f20(f20(f11(x20672),f8(x20672,x20673,x20674)),x20675),x20676))
% 1.28/1.60 [2068]~P59(x20681)+~E(f12(x20681,f20(f20(f11(x20681),x20682),x20684),x20685),f12(x20681,f20(f20(f11(x20681),x20683),x20684),x20686))+E(f12(x20681,f20(f20(f11(x20681),f8(x20681,x20682,x20683)),x20684),x20685),x20686)
% 1.28/1.60 [2079]~P59(x20791)+~E(x20796,f12(x20791,f20(f20(f11(x20791),f8(x20791,x20792,x20795)),x20793),x20794))+E(f12(x20791,f20(f20(f11(x20791),x20792),x20793),x20794),f12(x20791,f20(f20(f11(x20791),x20795),x20793),x20796))
% 1.28/1.60 [2080]~P59(x20801)+~E(f12(x20801,f20(f20(f11(x20801),f8(x20801,x20802,x20805)),x20803),x20804),x20806)+E(f12(x20801,f20(f20(f11(x20801),x20802),x20803),x20804),f12(x20801,f20(f20(f11(x20801),x20805),x20803),x20806))
% 1.28/1.60 [1155]P7(a110,x11551,x11552)+P7(a110,x11552,x11551)+E(x11551,f3(a110))+~E(f7(a110,x11552,x11551),f3(a110))
% 1.28/1.60 [1163]P7(a110,x11632,x11631)+E(x11631,f3(a110))+P6(a110,x11632,f3(a110))+~E(f7(a110,x11632,x11631),f3(a110))
% 1.28/1.60 [1164]P7(a110,x11641,x11642)+E(x11641,f3(a110))+P6(a110,f3(a110),x11642)+~E(f7(a110,x11642,x11641),f3(a110))
% 1.28/1.60 [875]~P43(x8752)+~P74(x8752)+E(x8751,f3(a112))+E(f20(f20(f16(x8752),f3(x8752)),x8751),f3(x8752))
% 1.28/1.60 [888]~P43(x8881)+~P74(x8881)+~E(x8882,f3(a112))+E(f20(f20(f16(x8881),f3(x8881)),x8882),f4(x8881))
% 1.28/1.60 [972]~P72(x9722)+E(x9721,f4(x9722))+E(x9721,f10(x9722,f4(x9722)))+~E(f20(f20(f11(x9722),x9721),x9721),f4(x9722))
% 1.28/1.60 [1025]~E(x10252,f4(a110))+~E(x10251,f4(a110))+~P7(a110,f3(a110),x10251)+E(f20(f20(f11(a110),x10251),x10252),f4(a110))
% 1.28/1.60 [964]P7(x9643,x9641,x9642)+~P52(x9643)+E(x9641,x9642)+P7(x9643,x9642,x9641)
% 1.28/1.60 [970]P7(x9703,x9701,x9702)+~P37(x9703)+E(x9701,x9702)+P7(x9703,x9702,x9701)
% 1.28/1.60 [971]P7(x9711,x9712,x9713)+~E(x9712,x9713)+~P37(x9711)+P6(x9711,x9712,x9713)
% 1.28/1.60 [1028]~P41(x10283)+~P6(x10283,x10282,x10281)+E(x10281,x10282)+P7(x10283,x10282,x10281)
% 1.28/1.60 [1030]~P37(x10303)+~P6(x10303,x10301,x10302)+E(x10301,x10302)+P7(x10303,x10301,x10302)
% 1.28/1.60 [1036]~P41(x10363)+~P6(x10363,x10361,x10362)+E(x10361,x10362)+P7(x10363,x10361,x10362)
% 1.28/1.60 [1125]~P6(x11253,x11252,x11251)+~P6(x11253,x11251,x11252)+E(x11251,x11252)+~P41(x11253)
% 1.28/1.60 [1170]P7(x11701,x11703,x11702)+~P35(x11701)+~P6(x11701,x11703,x11702)+P6(x11701,x11702,x11703)
% 1.28/1.60 [797]~P38(x7973)+~P54(x7973)+E(x7971,x7972)+~E(f14(x7973,x7971),f14(x7973,x7972))
% 1.28/1.60 [857]~E(x8573,x8571)+~P46(x8572)+E(f24(x8572,x8573,x8571),f4(x8572))+E(x8571,f3(x8572))
% 1.28/1.60 [937]~P46(x9373)+E(x9371,x9372)+~E(f24(x9373,x9371,x9372),f4(x9373))+E(x9372,f3(x9373))
% 1.28/1.60 [1198]P78(x11981,x11982,x11983)+P7(a110,x11982,f3(a110))+P7(a110,f3(a110),x11982)+~P77(f20(x11981,x11983))
% 1.28/1.60 [1333]P79(x13332,x13331,x13333)+P7(a110,f98(x13333,x13331,x13332),x13331)+E(x13331,f3(a110))+P7(a110,x13331,f3(a110))
% 1.28/1.60 [1334]P78(x13342,x13341,x13343)+P7(a110,f103(x13343,x13341,x13342),x13341)+E(x13341,f3(a110))+P7(a110,x13341,f3(a110))
% 1.28/1.60 [1335]P79(x13352,x13351,x13353)+P7(a110,x13351,f104(x13353,x13351,x13352))+E(x13351,f3(a110))+P7(a110,f3(a110),x13351)
% 1.28/1.60 [1336]P78(x13362,x13361,x13363)+P7(a110,x13361,f107(x13363,x13361,x13362))+E(x13361,f3(a110))+P7(a110,f3(a110),x13361)
% 1.28/1.60 [1339]P79(x13392,x13391,x13393)+E(x13391,f3(a110))+P7(a110,x13391,f3(a110))+P6(a110,f3(a110),f98(x13393,x13391,x13392))
% 1.28/1.60 [1340]P78(x13402,x13401,x13403)+E(x13401,f3(a110))+P7(a110,x13401,f3(a110))+P6(a110,f3(a110),f103(x13403,x13401,x13402))
% 1.28/1.60 [1341]P79(x13412,x13411,x13413)+E(x13411,f3(a110))+P7(a110,f3(a110),x13411)+P6(a110,f104(x13413,x13411,x13412),f3(a110))
% 1.28/1.60 [1342]P78(x13422,x13421,x13423)+E(x13421,f3(a110))+P7(a110,f3(a110),x13421)+P6(a110,f107(x13423,x13421,x13422),f3(a110))
% 1.28/1.60 [1403]P78(x14031,x14032,x14033)+P7(a110,f103(x14033,x14032,x14031),x14032)+P7(a110,x14032,f3(a110))+~P77(f20(x14031,x14033))
% 1.28/1.60 [1404]P78(x14041,x14042,x14043)+P7(a110,x14042,f107(x14043,x14042,x14041))+P7(a110,f3(a110),x14042)+~P77(f20(x14041,x14043))
% 1.28/1.60 [1409]P78(x14091,x14092,x14093)+P7(a110,x14092,f3(a110))+P6(a110,f3(a110),f103(x14093,x14092,x14091))+~P77(f20(x14091,x14093))
% 1.28/1.60 [1410]P78(x14101,x14102,x14103)+P7(a110,f3(a110),x14102)+P6(a110,f107(x14103,x14102,x14101),f3(a110))+~P77(f20(x14101,x14103))
% 1.28/1.60 [1448]E(x14481,x14482)+~P6(a112,x14483,x14482)+~P6(a112,x14483,x14481)+~E(f8(a112,x14481,x14483),f8(a112,x14482,x14483))
% 1.28/1.60 [1528]~P2(x15281)+~P6(x15281,x15282,f3(x15281))+~P7(x15281,x15283,f3(x15281))+P6(x15281,f3(x15281),f24(x15281,x15282,x15283))
% 1.28/1.60 [1529]~P13(x15291)+~P6(x15291,x15293,f3(x15291))+~P6(x15291,x15292,f3(x15291))+P6(x15291,f3(x15291),f24(x15291,x15292,x15293))
% 1.28/1.60 [1530]~P2(x15301)+~P7(x15301,x15303,f3(x15301))+~P7(x15301,x15302,f3(x15301))+P7(x15301,f3(x15301),f24(x15301,x15302,x15303))
% 1.28/1.60 [1531]~P13(x15311)+~P7(x15311,x15313,f3(x15311))+~P7(x15311,x15312,f3(x15311))+P7(x15311,f3(x15311),f24(x15311,x15312,x15313))
% 1.28/1.60 [1532]~P2(x15321)+~P6(x15321,f3(x15321),x15322)+~P7(x15321,f3(x15321),x15323)+P6(x15321,f3(x15321),f24(x15321,x15322,x15323))
% 1.28/1.60 [1533]~P13(x15331)+~P6(x15331,f3(x15331),x15333)+~P6(x15331,f3(x15331),x15332)+P6(x15331,f3(x15331),f24(x15331,x15332,x15333))
% 1.28/1.60 [1535]~P2(x15351)+~P7(x15351,f3(x15351),x15353)+~P7(x15351,f3(x15351),x15352)+P7(x15351,f3(x15351),f24(x15351,x15352,x15353))
% 1.28/1.60 [1536]~P13(x15361)+~P7(x15361,f3(x15361),x15363)+~P7(x15361,f3(x15361),x15362)+P7(x15361,f3(x15361),f24(x15361,x15362,x15363))
% 1.28/1.60 [1539]~P24(x15391)+~P7(x15391,f3(x15391),x15393)+~P7(x15391,f3(x15391),x15392)+P7(x15391,f3(x15391),f12(x15391,x15392,x15393))
% 1.28/1.60 [1540]~P24(x15401)+~P6(x15401,x15403,f3(x15401))+~P6(x15401,x15402,f3(x15401))+P6(x15401,f12(x15401,x15402,x15403),f3(x15401))
% 1.28/1.60 [1541]~P24(x15411)+~P6(x15411,x15413,f3(x15411))+~P7(x15411,x15412,f3(x15411))+P7(x15411,f12(x15411,x15412,x15413),f3(x15411))
% 1.28/1.60 [1542]~P24(x15421)+~P6(x15421,x15422,f3(x15421))+~P7(x15421,x15423,f3(x15421))+P7(x15421,f12(x15421,x15422,x15423),f3(x15421))
% 1.28/1.60 [1543]~P24(x15431)+~P7(x15431,x15433,f3(x15431))+~P7(x15431,x15432,f3(x15431))+P7(x15431,f12(x15431,x15432,x15433),f3(x15431))
% 1.28/1.60 [1544]~P2(x15441)+~P6(x15441,x15442,f3(x15441))+~P7(x15441,f3(x15441),x15443)+P6(x15441,f24(x15441,x15442,x15443),f3(x15441))
% 1.28/1.60 [1545]~P2(x15451)+~P7(x15451,x15453,f3(x15451))+~P6(x15451,f3(x15451),x15452)+P6(x15451,f24(x15451,x15452,x15453),f3(x15451))
% 1.28/1.60 [1546]~P13(x15461)+~P6(x15461,x15463,f3(x15461))+~P6(x15461,f3(x15461),x15462)+P6(x15461,f24(x15461,x15462,x15463),f3(x15461))
% 1.28/1.60 [1547]~P13(x15471)+~P6(x15471,x15472,f3(x15471))+~P6(x15471,f3(x15471),x15473)+P6(x15471,f24(x15471,x15472,x15473),f3(x15471))
% 1.28/1.60 [1548]~P2(x15481)+~P7(x15481,x15483,f3(x15481))+~P7(x15481,f3(x15481),x15482)+P7(x15481,f24(x15481,x15482,x15483),f3(x15481))
% 1.28/1.60 [1549]~P2(x15491)+~P7(x15491,x15492,f3(x15491))+~P7(x15491,f3(x15491),x15493)+P7(x15491,f24(x15491,x15492,x15493),f3(x15491))
% 1.28/1.60 [1550]~P13(x15501)+~P7(x15501,x15503,f3(x15501))+~P7(x15501,f3(x15501),x15502)+P7(x15501,f24(x15501,x15502,x15503),f3(x15501))
% 1.28/1.60 [1551]~P13(x15511)+~P7(x15511,x15512,f3(x15511))+~P7(x15511,f3(x15511),x15513)+P7(x15511,f24(x15511,x15512,x15513),f3(x15511))
% 1.28/1.60 [1559]P79(x15592,x15591,x15593)+P7(a110,x15591,f104(x15593,x15591,x15592))+P7(a110,f98(x15593,x15591,x15592),x15591)+E(x15591,f3(a110))
% 1.28/1.60 [1560]P78(x15602,x15601,x15603)+P7(a110,x15601,f107(x15603,x15601,x15602))+P7(a110,f103(x15603,x15601,x15602),x15601)+E(x15601,f3(a110))
% 1.28/1.60 [1562]P79(x15622,x15621,x15623)+P7(a110,x15621,f104(x15623,x15621,x15622))+E(x15621,f3(a110))+P6(a110,f3(a110),f98(x15623,x15621,x15622))
% 1.28/1.60 [1563]P78(x15632,x15631,x15633)+P7(a110,x15631,f107(x15633,x15631,x15632))+E(x15631,f3(a110))+P6(a110,f3(a110),f103(x15633,x15631,x15632))
% 1.28/1.60 [1564]P79(x15642,x15641,x15643)+P7(a110,f98(x15643,x15641,x15642),x15641)+E(x15641,f3(a110))+P6(a110,f104(x15643,x15641,x15642),f3(a110))
% 1.28/1.60 [1565]P78(x15652,x15651,x15653)+P7(a110,f103(x15653,x15651,x15652),x15651)+E(x15651,f3(a110))+P6(a110,f107(x15653,x15651,x15652),f3(a110))
% 1.28/1.60 [1566]P79(x15662,x15661,x15663)+E(x15661,f3(a110))+P6(a110,f3(a110),f98(x15663,x15661,x15662))+P6(a110,f104(x15663,x15661,x15662),f3(a110))
% 1.28/1.60 [1567]P78(x15672,x15671,x15673)+E(x15671,f3(a110))+P6(a110,f3(a110),f103(x15673,x15671,x15672))+P6(a110,f107(x15673,x15671,x15672),f3(a110))
% 1.28/1.60 [1582]~P13(x15821)+~P6(x15821,f24(x15821,x15823,x15822),f3(x15821))+P6(x15821,x15822,f3(x15821))+P6(x15821,x15823,f3(x15821))
% 1.28/1.60 [1583]~P13(x15831)+~P7(x15831,f24(x15831,x15833,x15832),f3(x15831))+P7(x15831,x15832,f3(x15831))+P7(x15831,x15833,f3(x15831))
% 1.28/1.60 [1584]~P13(x15841)+~P6(x15841,f3(x15841),f24(x15841,x15843,x15842))+P6(x15841,x15842,f3(x15841))+P6(x15841,f3(x15841),x15843)
% 1.28/1.60 [1585]~P13(x15851)+~P6(x15851,f3(x15851),f24(x15851,x15852,x15853))+P6(x15851,x15852,f3(x15851))+P6(x15851,f3(x15851),x15853)
% 1.28/1.60 [1586]~P13(x15861)+P6(x15861,f3(x15861),x15862)+~P6(x15861,f3(x15861),f24(x15861,x15863,x15862))+P6(x15861,x15862,f3(x15861))
% 1.28/1.60 [1587]~P13(x15871)+P6(x15871,f3(x15871),x15872)+~P6(x15871,f3(x15871),f24(x15871,x15872,x15873))+P6(x15871,x15872,f3(x15871))
% 1.28/1.60 [1588]~P13(x15881)+~P7(x15881,f3(x15881),f24(x15881,x15883,x15882))+P7(x15881,x15882,f3(x15881))+P7(x15881,f3(x15881),x15883)
% 1.28/1.60 [1589]~P13(x15891)+~P7(x15891,f3(x15891),f24(x15891,x15892,x15893))+P7(x15891,x15892,f3(x15891))+P7(x15891,f3(x15891),x15893)
% 1.28/1.60 [1590]~P13(x15901)+P7(x15901,f3(x15901),x15902)+~P7(x15901,f3(x15901),f24(x15901,x15903,x15902))+P7(x15901,x15902,f3(x15901))
% 1.28/1.60 [1591]~P13(x15911)+P7(x15911,f3(x15911),x15912)+~P7(x15911,f3(x15911),f24(x15911,x15912,x15913))+P7(x15911,x15912,f3(x15911))
% 1.28/1.60 [1592]~P13(x15921)+P6(x15921,f3(x15921),x15922)+~P6(x15921,f24(x15921,x15923,x15922),f3(x15921))+P6(x15921,x15922,f3(x15921))
% 1.28/1.60 [1593]~P13(x15931)+P6(x15931,f3(x15931),x15932)+~P6(x15931,f24(x15931,x15932,x15933),f3(x15931))+P6(x15931,x15932,f3(x15931))
% 1.28/1.60 [1594]~P13(x15941)+P7(x15941,f3(x15941),x15942)+~P7(x15941,f24(x15941,x15943,x15942),f3(x15941))+P7(x15941,x15942,f3(x15941))
% 1.28/1.60 [1595]~P13(x15951)+P7(x15951,f3(x15951),x15952)+~P7(x15951,f24(x15951,x15952,x15953),f3(x15951))+P7(x15951,x15952,f3(x15951))
% 1.28/1.60 [1596]~P13(x15961)+~P6(x15961,f24(x15961,x15962,x15963),f3(x15961))+P6(x15961,f3(x15961),x15962)+P6(x15961,f3(x15961),x15963)
% 1.28/1.60 [1597]~P13(x15971)+~P7(x15971,f24(x15971,x15972,x15973),f3(x15971))+P7(x15971,f3(x15971),x15972)+P7(x15971,f3(x15971),x15973)
% 1.28/1.60 [1651]P78(x16511,x16512,x16513)+P7(a110,x16512,f107(x16513,x16512,x16511))+P7(a110,f103(x16513,x16512,x16511),x16512)+~P77(f20(x16511,x16513))
% 1.28/1.60 [1660]P78(x16601,x16602,x16603)+P7(a110,x16602,f107(x16603,x16602,x16601))+P6(a110,f3(a110),f103(x16603,x16602,x16601))+~P77(f20(x16601,x16603))
% 1.28/1.60 [1661]P78(x16611,x16612,x16613)+P7(a110,f103(x16613,x16612,x16611),x16612)+P6(a110,f107(x16613,x16612,x16611),f3(a110))+~P77(f20(x16611,x16613))
% 1.28/1.60 [1671]P78(x16711,x16712,x16713)+P6(a110,f3(a110),f103(x16713,x16712,x16711))+P6(a110,f107(x16713,x16712,x16711),f3(a110))+~P77(f20(x16711,x16713))
% 1.28/1.60 [1809]~P6(a110,x18092,x18093)+P6(a110,f7(a110,x18091,x18092),f7(a110,x18091,x18093))+~P7(a110,x18091,f3(a110))+~P7(a110,f3(a110),x18092)
% 1.28/1.60 [1810]~P6(a110,x18103,x18102)+P6(a110,f7(a110,x18101,x18102),f7(a110,x18101,x18103))+~P6(a110,f3(a110),x18101)+~P7(a110,f3(a110),x18103)
% 1.28/1.60 [1938]~P6(a112,x19383,x19381)+P6(a112,x19381,x19382)+~P6(a112,x19383,x19382)+~P6(a112,f8(a112,x19381,x19383),f8(a112,x19382,x19383))
% 1.28/1.60 [1939]~P6(a112,x19393,x19391)+P7(a112,x19391,x19392)+~P6(a112,x19393,x19392)+~P7(a112,f8(a112,x19391,x19393),f8(a112,x19392,x19393))
% 1.28/1.60 [1100]~P54(x11002)+~E(f15(x11002,x11003,x11001),f3(a112))+~E(f20(f14(x11002,x11001),x11003),f3(x11002))+E(x11001,f3(f113(x11002)))
% 1.28/1.60 [1215]P79(x12151,x12152,x12153)+P7(a110,x12152,f3(a110))+P7(a110,f3(a110),x12152)+~P77(f20(x12151,f3(a110)))
% 1.28/1.60 [1308]~P6(a112,x13083,f55(x13082,x13081))+~P77(f20(x13081,x13082))+~P77(f20(x13081,x13083))+P77(f20(x13081,f3(a112)))
% 1.28/1.60 [1429]P79(x14291,x14292,x14293)+P7(a110,f98(x14293,x14292,x14291),x14292)+P7(a110,x14292,f3(a110))+~P77(f20(x14291,f3(a110)))
% 1.28/1.60 [1430]P79(x14301,x14302,x14303)+P7(a110,x14302,f104(x14303,x14302,x14301))+P7(a110,f3(a110),x14302)+~P77(f20(x14301,f3(a110)))
% 1.28/1.60 [1442]P79(x14421,x14422,x14423)+P7(a110,x14422,f3(a110))+P6(a110,f3(a110),f98(x14423,x14422,x14421))+~P77(f20(x14421,f3(a110)))
% 1.28/1.60 [1443]P79(x14431,x14432,x14433)+P7(a110,f3(a110),x14432)+P6(a110,f104(x14433,x14432,x14431),f3(a110))+~P77(f20(x14431,f3(a110)))
% 1.28/1.60 [1672]P79(x16721,x16722,x16723)+P7(a110,x16722,f104(x16723,x16722,x16721))+P7(a110,f98(x16723,x16722,x16721),x16722)+~P77(f20(x16721,f3(a110)))
% 1.28/1.60 [1677]P79(x16771,x16772,x16773)+P7(a110,x16772,f104(x16773,x16772,x16771))+P6(a110,f3(a110),f98(x16773,x16772,x16771))+~P77(f20(x16771,f3(a110)))
% 1.28/1.60 [1678]P79(x16781,x16782,x16783)+P7(a110,f98(x16783,x16782,x16781),x16782)+P6(a110,f104(x16783,x16782,x16781),f3(a110))+~P77(f20(x16781,f3(a110)))
% 1.28/1.60 [1682]P79(x16821,x16822,x16823)+P6(a110,f3(a110),f98(x16823,x16822,x16821))+P6(a110,f104(x16823,x16822,x16821),f3(a110))+~P77(f20(x16821,f3(a110)))
% 1.28/1.60 [1755]P79(x17552,x17551,x17553)+E(x17551,f3(a110))+P7(a110,x17551,f3(a110))+~P77(f20(x17552,f99(x17553,x17551,x17552)))
% 1.28/1.60 [1756]P78(x17562,x17561,x17563)+E(x17561,f3(a110))+P7(a110,x17561,f3(a110))+~P77(f20(x17562,f103(x17563,x17561,x17562)))
% 1.28/1.60 [1757]P79(x17572,x17571,x17573)+E(x17571,f3(a110))+P7(a110,f3(a110),x17571)+~P77(f20(x17572,f105(x17573,x17571,x17572)))
% 1.28/1.60 [1758]P78(x17582,x17581,x17583)+E(x17581,f3(a110))+P7(a110,f3(a110),x17581)+~P77(f20(x17582,f107(x17583,x17581,x17582)))
% 1.28/1.60 [1847]P78(x18471,x18472,x18473)+P7(a110,x18472,f3(a110))+~P77(f20(x18471,x18473))+~P77(f20(x18471,f103(x18473,x18472,x18471)))
% 1.28/1.60 [1848]P78(x18481,x18482,x18483)+P7(a110,f3(a110),x18482)+~P77(f20(x18481,x18483))+~P77(f20(x18481,f107(x18483,x18482,x18481)))
% 1.28/1.60 [1861]P79(x18611,x18612,x18613)+P7(a110,x18612,f3(a110))+~P77(f20(x18611,f99(x18613,x18612,x18611)))+~P77(f20(x18611,f3(a110)))
% 1.28/1.60 [1862]P79(x18621,x18622,x18623)+P7(a110,f3(a110),x18622)+~P77(f20(x18621,f105(x18623,x18622,x18621)))+~P77(f20(x18621,f3(a110)))
% 1.28/1.60 [1901]P79(x19013,x19011,x19012)+E(x19011,f3(a110))+P7(a110,x19011,f3(a110))+E(f12(a110,f20(f20(f11(a110),x19011),f99(x19012,x19011,x19013)),f98(x19012,x19011,x19013)),x19012)
% 1.28/1.60 [1902]P78(x19023,x19021,x19022)+E(x19021,f3(a110))+P7(a110,x19021,f3(a110))+E(f12(a110,f20(f20(f11(a110),x19021),f106(x19022,x19021,x19023)),f103(x19022,x19021,x19023)),x19022)
% 1.28/1.60 [1903]P79(x19033,x19031,x19032)+E(x19031,f3(a110))+P7(a110,f3(a110),x19031)+E(f12(a110,f20(f20(f11(a110),x19031),f105(x19032,x19031,x19033)),f104(x19032,x19031,x19033)),x19032)
% 1.28/1.60 [1904]P78(x19043,x19041,x19042)+E(x19041,f3(a110))+P7(a110,f3(a110),x19041)+E(f12(a110,f20(f20(f11(a110),x19041),f108(x19042,x19041,x19043)),f107(x19042,x19041,x19043)),x19042)
% 1.28/1.60 [1910]P79(x19102,x19101,x19103)+P7(a110,x19101,f104(x19103,x19101,x19102))+E(x19101,f3(a110))+~P77(f20(x19102,f99(x19103,x19101,x19102)))
% 1.28/1.60 [1911]P78(x19112,x19111,x19113)+P7(a110,x19111,f107(x19113,x19111,x19112))+E(x19111,f3(a110))+~P77(f20(x19112,f103(x19113,x19111,x19112)))
% 1.28/1.60 [1912]P79(x19122,x19121,x19123)+P7(a110,f98(x19123,x19121,x19122),x19121)+E(x19121,f3(a110))+~P77(f20(x19122,f105(x19123,x19121,x19122)))
% 1.28/1.60 [1913]P78(x19132,x19131,x19133)+P7(a110,f103(x19133,x19131,x19132),x19131)+E(x19131,f3(a110))+~P77(f20(x19132,f107(x19133,x19131,x19132)))
% 1.28/1.60 [1918]P79(x19182,x19181,x19183)+E(x19181,f3(a110))+P6(a110,f3(a110),f98(x19183,x19181,x19182))+~P77(f20(x19182,f105(x19183,x19181,x19182)))
% 1.28/1.60 [1919]P78(x19192,x19191,x19193)+E(x19191,f3(a110))+P6(a110,f3(a110),f103(x19193,x19191,x19192))+~P77(f20(x19192,f107(x19193,x19191,x19192)))
% 1.28/1.60 [1920]P79(x19202,x19201,x19203)+E(x19201,f3(a110))+P6(a110,f104(x19203,x19201,x19202),f3(a110))+~P77(f20(x19202,f99(x19203,x19201,x19202)))
% 1.28/1.60 [1921]P78(x19212,x19211,x19213)+E(x19211,f3(a110))+P6(a110,f107(x19213,x19211,x19212),f3(a110))+~P77(f20(x19212,f103(x19213,x19211,x19212)))
% 1.28/1.60 [1925]P78(x19253,x19251,x19252)+P7(a110,x19251,f3(a110))+~P77(f20(x19253,x19252))+E(f12(a110,f20(f20(f11(a110),x19251),f106(x19252,x19251,x19253)),f103(x19252,x19251,x19253)),x19252)
% 1.28/1.60 [1926]P78(x19263,x19261,x19262)+P7(a110,f3(a110),x19261)+~P77(f20(x19263,x19262))+E(f12(a110,f20(f20(f11(a110),x19261),f108(x19262,x19261,x19263)),f107(x19262,x19261,x19263)),x19262)
% 1.28/1.60 [1940]P79(x19403,x19401,x19402)+P7(a110,x19401,f3(a110))+E(f12(a110,f20(f20(f11(a110),x19401),f99(x19402,x19401,x19403)),f98(x19402,x19401,x19403)),x19402)+~P77(f20(x19403,f3(a110)))
% 1.28/1.60 [1941]P79(x19413,x19411,x19412)+P7(a110,f3(a110),x19411)+E(f12(a110,f20(f20(f11(a110),x19411),f105(x19412,x19411,x19413)),f104(x19412,x19411,x19413)),x19412)+~P77(f20(x19413,f3(a110)))
% 1.28/1.60 [1947]P78(x19471,x19472,x19473)+P7(a110,x19472,f107(x19473,x19472,x19471))+~P77(f20(x19471,x19473))+~P77(f20(x19471,f103(x19473,x19472,x19471)))
% 1.28/1.60 [1948]P78(x19481,x19482,x19483)+P7(a110,f103(x19483,x19482,x19481),x19482)+~P77(f20(x19481,x19483))+~P77(f20(x19481,f107(x19483,x19482,x19481)))
% 1.28/1.60 [1949]P78(x19491,x19492,x19493)+P6(a110,f3(a110),f103(x19493,x19492,x19491))+~P77(f20(x19491,x19493))+~P77(f20(x19491,f107(x19493,x19492,x19491)))
% 1.28/1.60 [1950]P78(x19501,x19502,x19503)+P6(a110,f107(x19503,x19502,x19501),f3(a110))+~P77(f20(x19501,x19503))+~P77(f20(x19501,f103(x19503,x19502,x19501)))
% 1.28/1.60 [1954]P79(x19541,x19542,x19543)+P7(a110,x19542,f104(x19543,x19542,x19541))+~P77(f20(x19541,f99(x19543,x19542,x19541)))+~P77(f20(x19541,f3(a110)))
% 1.28/1.60 [1955]P79(x19551,x19552,x19553)+P7(a110,f98(x19553,x19552,x19551),x19552)+~P77(f20(x19551,f105(x19553,x19552,x19551)))+~P77(f20(x19551,f3(a110)))
% 1.28/1.60 [1956]P79(x19561,x19562,x19563)+P6(a110,f3(a110),f98(x19563,x19562,x19561))+~P77(f20(x19561,f105(x19563,x19562,x19561)))+~P77(f20(x19561,f3(a110)))
% 1.28/1.60 [1957]P79(x19571,x19572,x19573)+P6(a110,f104(x19573,x19572,x19571),f3(a110))+~P77(f20(x19571,f99(x19573,x19572,x19571)))+~P77(f20(x19571,f3(a110)))
% 1.28/1.60 [1966]P79(x19663,x19661,x19662)+P7(a110,x19661,f104(x19662,x19661,x19663))+E(x19661,f3(a110))+E(f12(a110,f20(f20(f11(a110),x19661),f99(x19662,x19661,x19663)),f98(x19662,x19661,x19663)),x19662)
% 1.28/1.60 [1967]P78(x19673,x19671,x19672)+P7(a110,x19671,f107(x19672,x19671,x19673))+E(x19671,f3(a110))+E(f12(a110,f20(f20(f11(a110),x19671),f106(x19672,x19671,x19673)),f103(x19672,x19671,x19673)),x19672)
% 1.28/1.60 [1968]P79(x19683,x19681,x19682)+P7(a110,f98(x19682,x19681,x19683),x19681)+E(x19681,f3(a110))+E(f12(a110,f20(f20(f11(a110),x19681),f105(x19682,x19681,x19683)),f104(x19682,x19681,x19683)),x19682)
% 1.28/1.60 [1969]P78(x19693,x19691,x19692)+P7(a110,f103(x19692,x19691,x19693),x19691)+E(x19691,f3(a110))+E(f12(a110,f20(f20(f11(a110),x19691),f108(x19692,x19691,x19693)),f107(x19692,x19691,x19693)),x19692)
% 1.28/1.60 [1972]P79(x19723,x19721,x19722)+E(x19721,f3(a110))+P6(a110,f3(a110),f98(x19722,x19721,x19723))+E(f12(a110,f20(f20(f11(a110),x19721),f105(x19722,x19721,x19723)),f104(x19722,x19721,x19723)),x19722)
% 1.28/1.60 [1973]P78(x19733,x19731,x19732)+E(x19731,f3(a110))+P6(a110,f3(a110),f103(x19732,x19731,x19733))+E(f12(a110,f20(f20(f11(a110),x19731),f108(x19732,x19731,x19733)),f107(x19732,x19731,x19733)),x19732)
% 1.28/1.60 [1974]P79(x19743,x19741,x19742)+E(x19741,f3(a110))+P6(a110,f104(x19742,x19741,x19743),f3(a110))+E(f12(a110,f20(f20(f11(a110),x19741),f99(x19742,x19741,x19743)),f98(x19742,x19741,x19743)),x19742)
% 1.28/1.60 [1975]P78(x19753,x19751,x19752)+E(x19751,f3(a110))+P6(a110,f107(x19752,x19751,x19753),f3(a110))+E(f12(a110,f20(f20(f11(a110),x19751),f106(x19752,x19751,x19753)),f103(x19752,x19751,x19753)),x19752)
% 1.28/1.60 [1990]P78(x19903,x19901,x19902)+P7(a110,x19901,f107(x19902,x19901,x19903))+~P77(f20(x19903,x19902))+E(f12(a110,f20(f20(f11(a110),x19901),f106(x19902,x19901,x19903)),f103(x19902,x19901,x19903)),x19902)
% 1.28/1.60 [1991]P78(x19913,x19911,x19912)+P7(a110,f103(x19912,x19911,x19913),x19911)+~P77(f20(x19913,x19912))+E(f12(a110,f20(f20(f11(a110),x19911),f108(x19912,x19911,x19913)),f107(x19912,x19911,x19913)),x19912)
% 1.28/1.60 [1992]P78(x19923,x19921,x19922)+P6(a110,f3(a110),f103(x19922,x19921,x19923))+~P77(f20(x19923,x19922))+E(f12(a110,f20(f20(f11(a110),x19921),f108(x19922,x19921,x19923)),f107(x19922,x19921,x19923)),x19922)
% 1.28/1.60 [1993]P78(x19933,x19931,x19932)+P6(a110,f107(x19932,x19931,x19933),f3(a110))+~P77(f20(x19933,x19932))+E(f12(a110,f20(f20(f11(a110),x19931),f106(x19932,x19931,x19933)),f103(x19932,x19931,x19933)),x19932)
% 1.28/1.60 [1997]P79(x19973,x19971,x19972)+P7(a110,x19971,f104(x19972,x19971,x19973))+E(f12(a110,f20(f20(f11(a110),x19971),f99(x19972,x19971,x19973)),f98(x19972,x19971,x19973)),x19972)+~P77(f20(x19973,f3(a110)))
% 1.28/1.60 [1998]P79(x19983,x19981,x19982)+P7(a110,f98(x19982,x19981,x19983),x19981)+E(f12(a110,f20(f20(f11(a110),x19981),f105(x19982,x19981,x19983)),f104(x19982,x19981,x19983)),x19982)+~P77(f20(x19983,f3(a110)))
% 1.28/1.60 [1999]P79(x19993,x19991,x19992)+P6(a110,f3(a110),f98(x19992,x19991,x19993))+E(f12(a110,f20(f20(f11(a110),x19991),f105(x19992,x19991,x19993)),f104(x19992,x19991,x19993)),x19992)+~P77(f20(x19993,f3(a110)))
% 1.28/1.60 [2000]P79(x20003,x20001,x20002)+P6(a110,f104(x20002,x20001,x20003),f3(a110))+E(f12(a110,f20(f20(f11(a110),x20001),f99(x20002,x20001,x20003)),f98(x20002,x20001,x20003)),x20002)+~P77(f20(x20003,f3(a110)))
% 1.28/1.60 [2025]P79(x20252,x20251,x20253)+E(x20251,f3(a110))+~P77(f20(x20252,f99(x20253,x20251,x20252)))+~P77(f20(x20252,f105(x20253,x20251,x20252)))
% 1.28/1.60 [2026]P78(x20262,x20261,x20263)+E(x20261,f3(a110))+~P77(f20(x20262,f103(x20263,x20261,x20262)))+~P77(f20(x20262,f107(x20263,x20261,x20262)))
% 1.28/1.60 [2028]P78(x20281,x20282,x20283)+~P77(f20(x20281,x20283))+~P77(f20(x20281,f103(x20283,x20282,x20281)))+~P77(f20(x20281,f107(x20283,x20282,x20281)))
% 1.28/1.60 [2029]P79(x20291,x20292,x20293)+~P77(f20(x20291,f99(x20293,x20292,x20291)))+~P77(f20(x20291,f105(x20293,x20292,x20291)))+~P77(f20(x20291,f3(a110)))
% 1.28/1.60 [2030]P79(x20303,x20301,x20302)+E(x20301,f3(a110))+E(f12(a110,f20(f20(f11(a110),x20301),f99(x20302,x20301,x20303)),f98(x20302,x20301,x20303)),x20302)+~P77(f20(x20303,f105(x20302,x20301,x20303)))
% 1.28/1.60 [2031]P78(x20313,x20311,x20312)+E(x20311,f3(a110))+E(f12(a110,f20(f20(f11(a110),x20311),f106(x20312,x20311,x20313)),f103(x20312,x20311,x20313)),x20312)+~P77(f20(x20313,f107(x20312,x20311,x20313)))
% 1.28/1.60 [2032]P79(x20323,x20321,x20322)+E(x20321,f3(a110))+E(f12(a110,f20(f20(f11(a110),x20321),f105(x20322,x20321,x20323)),f104(x20322,x20321,x20323)),x20322)+~P77(f20(x20323,f99(x20322,x20321,x20323)))
% 1.28/1.60 [2033]P78(x20333,x20331,x20332)+E(x20331,f3(a110))+E(f12(a110,f20(f20(f11(a110),x20331),f108(x20332,x20331,x20333)),f107(x20332,x20331,x20333)),x20332)+~P77(f20(x20333,f103(x20332,x20331,x20333)))
% 1.28/1.60 [2040]P78(x20403,x20401,x20402)+~P77(f20(x20403,x20402))+E(f12(a110,f20(f20(f11(a110),x20401),f106(x20402,x20401,x20403)),f103(x20402,x20401,x20403)),x20402)+~P77(f20(x20403,f107(x20402,x20401,x20403)))
% 1.28/1.60 [2041]P78(x20413,x20411,x20412)+~P77(f20(x20413,x20412))+E(f12(a110,f20(f20(f11(a110),x20411),f108(x20412,x20411,x20413)),f107(x20412,x20411,x20413)),x20412)+~P77(f20(x20413,f103(x20412,x20411,x20413)))
% 1.28/1.60 [2048]P79(x20483,x20481,x20482)+E(f12(a110,f20(f20(f11(a110),x20481),f99(x20482,x20481,x20483)),f98(x20482,x20481,x20483)),x20482)+~P77(f20(x20483,f105(x20482,x20481,x20483)))+~P77(f20(x20483,f3(a110)))
% 1.28/1.60 [2049]P79(x20493,x20491,x20492)+E(f12(a110,f20(f20(f11(a110),x20491),f105(x20492,x20491,x20493)),f104(x20492,x20491,x20493)),x20492)+~P77(f20(x20493,f99(x20492,x20491,x20493)))+~P77(f20(x20493,f3(a110)))
% 1.28/1.60 [2052]P79(x20523,x20521,x20522)+E(x20521,f3(a110))+E(f12(a110,f20(f20(f11(a110),x20521),f105(x20522,x20521,x20523)),f104(x20522,x20521,x20523)),x20522)+E(f12(a110,f20(f20(f11(a110),x20521),f99(x20522,x20521,x20523)),f98(x20522,x20521,x20523)),x20522)
% 1.28/1.60 [2053]P78(x20533,x20531,x20532)+E(x20531,f3(a110))+E(f12(a110,f20(f20(f11(a110),x20531),f108(x20532,x20531,x20533)),f107(x20532,x20531,x20533)),x20532)+E(f12(a110,f20(f20(f11(a110),x20531),f106(x20532,x20531,x20533)),f103(x20532,x20531,x20533)),x20532)
% 1.28/1.60 [2059]P78(x20593,x20591,x20592)+~P77(f20(x20593,x20592))+E(f12(a110,f20(f20(f11(a110),x20591),f108(x20592,x20591,x20593)),f107(x20592,x20591,x20593)),x20592)+E(f12(a110,f20(f20(f11(a110),x20591),f106(x20592,x20591,x20593)),f103(x20592,x20591,x20593)),x20592)
% 1.28/1.60 [2062]P79(x20623,x20621,x20622)+E(f12(a110,f20(f20(f11(a110),x20621),f105(x20622,x20621,x20623)),f104(x20622,x20621,x20623)),x20622)+E(f12(a110,f20(f20(f11(a110),x20621),f99(x20622,x20621,x20623)),f98(x20622,x20621,x20623)),x20622)+~P77(f20(x20623,f3(a110)))
% 1.28/1.60 [932]~P60(x9322)+E(x9321,f3(x9322))+E(x9323,f3(x9322))+~E(f20(f20(f11(x9322),x9323),x9321),f3(x9322))
% 1.28/1.60 [933]~P71(x9332)+E(x9331,f3(x9332))+E(x9333,f3(x9332))+~E(f20(f20(f11(x9332),x9333),x9331),f3(x9332))
% 1.28/1.60 [1139]~P54(x11393)+E(x11391,x11392)+E(x11391,f10(x11393,x11392))+~E(f20(f20(f11(x11393),x11391),x11391),f20(f20(f11(x11393),x11392),x11392))
% 1.28/1.60 [1492]~P45(x14921)+~P7(x14921,f4(x14921),x14922)+~P7(a112,f3(a112),x14923)+P7(x14921,f4(x14921),f20(f20(f16(x14921),x14922),x14923))
% 1.28/1.60 [1505]~P57(x15051)+~P6(x15051,x15053,f3(x15051))+~P6(x15051,x15052,f3(x15051))+P6(x15051,f3(x15051),f20(f20(f11(x15051),x15052),x15053))
% 1.28/1.60 [1507]~P67(x15071)+~P6(x15071,x15073,f3(x15071))+~P6(x15071,x15072,f3(x15071))+P6(x15071,f3(x15071),f20(f20(f11(x15071),x15072),x15073))
% 1.28/1.60 [1508]~P57(x15081)+~P7(x15081,x15083,f3(x15081))+~P7(x15081,x15082,f3(x15081))+P7(x15081,f3(x15081),f20(f20(f11(x15081),x15082),x15083))
% 1.28/1.60 [1509]~P57(x15091)+~P6(x15091,f3(x15091),x15093)+~P6(x15091,f3(x15091),x15092)+P6(x15091,f3(x15091),f20(f20(f11(x15091),x15092),x15093))
% 1.28/1.60 [1510]~P66(x15101)+~P6(x15101,f3(x15101),x15103)+~P6(x15101,f3(x15101),x15102)+P6(x15101,f3(x15101),f20(f20(f11(x15101),x15102),x15103))
% 1.28/1.60 [1511]~P67(x15111)+~P6(x15111,f3(x15111),x15113)+~P6(x15111,f3(x15111),x15112)+P6(x15111,f3(x15111),f20(f20(f11(x15111),x15112),x15113))
% 1.28/1.60 [1512]~P62(x15121)+~P7(x15121,f3(x15121),x15123)+~P7(x15121,f3(x15121),x15122)+P7(x15121,f3(x15121),f20(f20(f11(x15121),x15122),x15123))
% 1.28/1.60 [1513]~P45(x15131)+~P7(x15131,f4(x15131),x15133)+~P7(x15131,f4(x15131),x15132)+P7(x15131,f4(x15131),f20(f20(f11(x15131),x15132),x15133))
% 1.28/1.60 [1515]~P57(x15151)+~P6(x15151,x15153,f3(x15151))+~P6(x15151,f3(x15151),x15152)+P6(x15151,f20(f20(f11(x15151),x15152),x15153),f3(x15151))
% 1.28/1.60 [1516]~P57(x15161)+~P6(x15161,x15162,f3(x15161))+~P6(x15161,f3(x15161),x15163)+P6(x15161,f20(f20(f11(x15161),x15162),x15163),f3(x15161))
% 1.28/1.60 [1518]~P66(x15181)+~P6(x15181,x15183,f3(x15181))+~P6(x15181,f3(x15181),x15182)+P6(x15181,f20(f20(f11(x15181),x15182),x15183),f3(x15181))
% 1.28/1.60 [1520]~P66(x15201)+~P6(x15201,x15202,f3(x15201))+~P6(x15201,f3(x15201),x15203)+P6(x15201,f20(f20(f11(x15201),x15202),x15203),f3(x15201))
% 1.28/1.60 [1522]~P62(x15221)+~P7(x15221,x15223,f3(x15221))+~P7(x15221,f3(x15221),x15222)+P7(x15221,f20(f20(f11(x15221),x15222),x15223),f3(x15221))
% 1.28/1.60 [1523]~P62(x15231)+~P7(x15231,x15232,f3(x15231))+~P7(x15231,f3(x15231),x15233)+P7(x15231,f20(f20(f11(x15231),x15232),x15233),f3(x15231))
% 1.28/1.60 [1568]~P57(x15681)+P6(x15681,x15682,f3(x15681))+P6(x15681,x15683,f3(x15681))+~P6(x15681,f20(f20(f11(x15681),x15683),x15682),f3(x15681))
% 1.28/1.60 [1569]~P57(x15691)+P6(x15691,x15692,f3(x15691))+P6(x15691,f3(x15691),x15693)+~P6(x15691,f3(x15691),f20(f20(f11(x15691),x15693),x15692))
% 1.28/1.60 [1570]~P57(x15701)+P6(x15701,x15702,f3(x15701))+P6(x15701,f3(x15701),x15703)+~P6(x15701,f3(x15701),f20(f20(f11(x15701),x15702),x15703))
% 1.28/1.60 [1571]~P57(x15711)+P6(x15711,f3(x15711),x15712)+P6(x15711,x15712,f3(x15711))+~P6(x15711,f3(x15711),f20(f20(f11(x15711),x15713),x15712))
% 1.28/1.60 [1572]~P57(x15721)+P6(x15721,f3(x15721),x15722)+P6(x15721,x15722,f3(x15721))+~P6(x15721,f3(x15721),f20(f20(f11(x15721),x15722),x15723))
% 1.28/1.60 [1573]~P57(x15731)+P6(x15731,f3(x15731),x15732)+P6(x15731,x15732,f3(x15731))+~P6(x15731,f20(f20(f11(x15731),x15733),x15732),f3(x15731))
% 1.28/1.60 [1574]~P57(x15741)+P6(x15741,f3(x15741),x15742)+P6(x15741,x15742,f3(x15741))+~P6(x15741,f20(f20(f11(x15741),x15742),x15743),f3(x15741))
% 1.28/1.60 [1575]~P57(x15751)+P6(x15751,f3(x15751),x15752)+P6(x15751,f3(x15751),x15753)+~P6(x15751,f20(f20(f11(x15751),x15752),x15753),f3(x15751))
% 1.28/1.60 [1600]~P7(a1,x16001,x16003)+P7(a1,x16001,a117)+~P6(a1,f22(a2,x16002),a114)+~E(f22(a2,f20(f14(a2,a115),x16002)),f10(a1,x16003))
% 1.28/1.60 [1601]~P7(a1,x16011,x16013)+P7(a1,x16011,a39)+~P6(a1,f22(a2,x16012),a114)+~E(f22(a2,f20(f14(a2,a115),x16012)),f10(a1,x16013))
% 1.28/1.60 [1646]~P62(x16461)+P7(x16461,f3(x16461),x16462)+~P7(x16461,f3(x16461),x16463)+~P7(x16461,f3(x16461),f20(f20(f11(x16461),x16463),x16462))
% 1.28/1.60 [1647]~P62(x16471)+P7(x16471,f3(x16471),x16472)+~P7(x16471,f3(x16471),x16473)+~P7(x16471,f3(x16471),f20(f20(f11(x16471),x16472),x16473))
% 1.28/1.60 [1898]~P45(x18981)+~P6(x18981,x18982,f4(x18981))+~P6(x18981,f3(x18981),x18982)+P6(x18981,f20(f20(f16(x18981),x18982),f12(a112,x18983,f4(a112))),x18982)
% 1.28/1.60 [1905]~P45(x19051)+~P7(x19051,x19052,f4(x19051))+~P7(x19051,f3(x19051),x19052)+P7(x19051,f20(f20(f16(x19051),x19052),f12(a112,x19053,f4(a112))),f4(x19051))
% 1.28/1.60 [2039]E(x20391,f7(a112,x20392,x20393))+~P7(a112,f3(a112),x20393)+~P6(a112,f20(f20(f11(a112),x20393),x20391),x20392)+~P7(a112,x20392,f20(f20(f11(a112),x20393),f12(a112,x20391,f4(a112))))
% 1.28/1.60 [2054]~P1(x20541)+P8(x20541,x20542)+~P7(a1,f3(a1),x20543)+~P6(a1,f22(x20541,f20(x20542,f63(x20542,x20541,x20543))),x20543)
% 1.28/1.60 [2055]~P1(x20551)+P8(x20551,x20552)+~P7(a1,f3(a1),x20553)+~P6(a1,f22(x20551,f20(x20552,f72(x20552,x20553,x20551))),x20553)
% 1.28/1.60 [2084]~P54(x20843)+E(x20841,x20842)+E(x20841,f10(x20843,x20842))+~E(f20(f20(f16(x20843),x20841),f12(a112,f12(a112,f3(a112),f4(a112)),f4(a112))),f20(f20(f16(x20843),x20842),f12(a112,f12(a112,f3(a112),f4(a112)),f4(a112))))
% 1.28/1.60 [1350]~P57(x13501)+~E(x13503,f3(x13501))+~E(x13502,f3(x13501))+E(f12(x13501,f20(f20(f11(x13501),x13502),x13502),f20(f20(f11(x13501),x13503),x13503)),f3(x13501))
% 1.28/1.60 [1724]~P7(a110,x17242,x17243)+~P7(a110,f3(a110),x17243)+P6(a110,f4(a110),x17241)+~E(f12(a110,x17242,f20(f20(f11(a110),x17243),x17241)),x17243)
% 1.28/1.60 [1731]~P6(a110,f3(a110),x17312)+~P7(a110,f3(a110),x17313)+P6(a110,x17311,f4(a110))+~E(f12(a110,x17312,f20(f20(f11(a110),x17313),x17311)),x17313)
% 1.28/1.60 [1909]~P57(x19091)+~E(x19093,f3(x19091))+~E(x19092,f3(x19091))+P6(x19091,f12(x19091,f20(f20(f11(x19091),x19092),x19092),f20(f20(f11(x19091),x19093),x19093)),f3(x19091))
% 1.28/1.60 [1958]~P45(x19581)+~P7(x19581,x19582,f4(x19581))+~P7(x19581,f3(x19581),x19582)+P7(x19581,f20(f20(f11(x19581),x19582),f20(f20(f16(x19581),x19582),x19583)),f20(f20(f16(x19581),x19582),x19583))
% 1.28/1.60 [2015]~P7(a110,x20152,x20153)+~P7(a110,f3(a110),x20153)+P6(a110,f3(a110),x20151)+~P6(a110,f3(a110),f12(a110,f20(f20(f11(a110),x20153),x20151),x20152))
% 1.28/1.60 [2018]P6(a110,x20181,f3(a110))+~P6(a110,f3(a110),x20182)+~P7(a110,f3(a110),x20183)+~P7(a110,f12(a110,f20(f20(f11(a110),x20183),x20181),x20182),f3(a110))
% 1.28/1.60 [2038]~P57(x20382)+~E(x20381,f3(x20382))+~E(x20383,f3(x20382))+~P7(x20382,f3(x20382),f12(x20382,f20(f20(f11(x20382),x20383),x20383),f20(f20(f11(x20382),x20381),x20381)))
% 1.28/1.60 [1238]~P41(x12381)+~P6(x12381,x12384,x12383)+P6(x12381,x12382,x12383)+~P6(x12381,x12382,x12384)
% 1.28/1.60 [1239]~P35(x12391)+~P6(x12391,x12392,x12394)+P6(x12391,x12392,x12393)+~P6(x12391,x12394,x12393)
% 1.28/1.60 [1240]~P41(x12401)+~P7(x12401,x12404,x12403)+P7(x12401,x12402,x12403)+~P6(x12401,x12402,x12404)
% 1.28/1.60 [1241]~P41(x12411)+~P7(x12411,x12412,x12414)+P7(x12411,x12412,x12413)+~P6(x12411,x12414,x12413)
% 1.28/1.60 [1242]~P41(x12421)+~P7(x12421,x12424,x12423)+P7(x12421,x12422,x12423)+~P7(x12421,x12422,x12424)
% 1.28/1.60 [1243]~P35(x12431)+~P7(x12431,x12432,x12434)+P7(x12431,x12432,x12433)+~P6(x12431,x12434,x12433)
% 1.28/1.60 [1244]~P35(x12441)+~P7(x12441,x12444,x12443)+P7(x12441,x12442,x12443)+~P6(x12441,x12442,x12444)
% 1.28/1.60 [1245]~P35(x12451)+~P7(x12451,x12452,x12454)+P7(x12451,x12452,x12453)+~P7(x12451,x12454,x12453)
% 1.28/1.60 [865]~P3(x8652)+~E(x8654,f3(x8652))+~E(x8651,f3(x8652))+E(x8651,f24(x8652,x8653,x8654))
% 1.28/1.60 [866]~P3(x8661)+~E(x8663,f3(x8661))+~E(x8664,f3(x8661))+E(f24(x8661,x8662,x8663),x8664)
% 1.28/1.60 [938]~P3(x9382)+E(x9381,f3(x9382))+~E(x9381,f24(x9382,x9384,x9383))+~E(x9383,f3(x9382))
% 1.28/1.60 [939]~P3(x9392)+E(x9391,f3(x9392))+~E(f24(x9392,x9394,x9393),x9391)+~E(x9393,f3(x9392))
% 1.28/1.60 [1203]~P41(x12031)+~P9(x12031,x12032)+~P6(a112,x12034,x12033)+P6(x12031,f20(x12032,x12033),f20(x12032,x12034))
% 1.28/1.60 [1204]~P41(x12041)+~P10(x12041,x12042)+~P6(a112,x12043,x12044)+P6(x12041,f20(x12042,x12043),f20(x12042,x12044))
% 1.28/1.60 [1361]~P36(x13612)+P7(f116(x13611,x13612),x13614,x13613)+~P6(f116(x13611,x13612),x13614,x13613)+P6(f116(x13611,x13612),x13613,x13614)
% 1.28/1.60 [1484]~P24(x14841)+~P6(x14841,x14842,x14843)+~P6(x14841,f3(x14841),x14844)+P6(x14841,x14842,f12(x14841,x14843,x14844))
% 1.28/1.60 [1485]~P24(x14851)+~P6(x14851,x14852,x14854)+~P6(x14851,f3(x14851),x14853)+P6(x14851,x14852,f12(x14851,x14853,x14854))
% 1.28/1.60 [1486]~P45(x14861)+~P7(x14861,x14862,x14864)+~P7(x14861,f3(x14861),x14863)+P7(x14861,x14862,f12(x14861,x14863,x14864))
% 1.28/1.60 [1487]~P24(x14871)+~P6(x14871,x14872,x14874)+~P7(x14871,f3(x14871),x14873)+P7(x14871,x14872,f12(x14871,x14873,x14874))
% 1.28/1.60 [1488]~P24(x14881)+~P7(x14881,x14882,x14884)+~P6(x14881,f3(x14881),x14883)+P7(x14881,x14882,f12(x14881,x14883,x14884))
% 1.28/1.60 [1726]~P13(x17261)+~P6(x17261,x17264,x17262)+~P6(x17261,x17263,f3(x17261))+P6(x17261,f24(x17261,x17262,x17263),f24(x17261,x17264,x17263))
% 1.28/1.60 [1727]~P2(x17271)+~P7(x17271,x17274,x17272)+~P7(x17271,x17273,f3(x17271))+P7(x17271,f24(x17271,x17272,x17273),f24(x17271,x17274,x17273))
% 1.28/1.60 [1728]~P13(x17281)+~P6(x17281,x17282,x17284)+~P6(x17281,f3(x17281),x17283)+P6(x17281,f24(x17281,x17282,x17283),f24(x17281,x17284,x17283))
% 1.28/1.60 [1729]~P2(x17291)+~P7(x17291,x17292,x17294)+~P7(x17291,f3(x17291),x17293)+P7(x17291,f24(x17291,x17292,x17293),f24(x17291,x17294,x17293))
% 1.28/1.60 [1717]~P1(x17172)+E(x17171,f3(x17172))+~P6(a1,x17173,f3(a1))+~P6(a1,f22(x17172,x17171),f20(f20(f11(a1),x17173),f22(x17172,x17174)))
% 1.28/1.60 [1046]~P46(x10462)+E(x10461,f3(x10462))+E(x10463,f24(x10462,x10464,x10461))+~E(f20(f20(f11(x10462),x10463),x10461),x10464)
% 1.28/1.60 [1047]~P3(x10472)+E(x10471,f3(x10472))+E(x10473,f24(x10472,x10474,x10471))+~E(f20(f20(f11(x10472),x10473),x10471),x10474)
% 1.28/1.60 [1049]~P46(x10492)+E(x10491,f3(x10492))+E(f24(x10492,x10493,x10491),x10494)+~E(x10493,f20(f20(f11(x10492),x10494),x10491))
% 1.28/1.60 [1050]~P3(x10502)+E(x10501,f3(x10502))+E(f24(x10502,x10503,x10501),x10504)+~E(x10503,f20(f20(f11(x10502),x10504),x10501))
% 1.28/1.60 [1053]~P46(x10532)+~E(f24(x10532,x10533,x10531),x10534)+E(x10531,f3(x10532))+E(x10533,f20(f20(f11(x10532),x10534),x10531))
% 1.28/1.60 [1054]~P3(x10542)+~E(f24(x10542,x10543,x10541),x10544)+E(x10541,f3(x10542))+E(x10543,f20(f20(f11(x10542),x10544),x10541))
% 1.28/1.60 [1055]~P46(x10552)+~E(x10553,f24(x10552,x10554,x10551))+E(x10551,f3(x10552))+E(f20(f20(f11(x10552),x10553),x10551),x10554)
% 1.28/1.60 [1056]~P3(x10562)+~E(x10563,f24(x10562,x10564,x10561))+E(x10561,f3(x10562))+E(f20(f20(f11(x10562),x10563),x10561),x10564)
% 1.28/1.60 [1059]~P3(x10592)+~E(x10591,f3(x10592))+E(x10591,f24(x10592,x10593,x10594))+~E(f20(f20(f11(x10592),x10591),x10594),x10593)
% 1.28/1.60 [1060]~P3(x10601)+~E(x10604,f3(x10601))+E(f24(x10601,x10602,x10603),x10604)+~E(x10602,f20(f20(f11(x10601),x10604),x10603))
% 1.28/1.60 [1325]~P45(x13253)+E(x13251,x13252)+~P7(x13253,f4(x13253),x13254)+~E(f20(f20(f16(x13253),x13254),x13251),f20(f20(f16(x13253),x13254),x13252))
% 1.28/1.60 [1688]~P45(x16881)+~P6(a112,x16883,x16884)+~P7(x16881,f4(x16881),x16882)+P6(x16881,f20(f20(f16(x16881),x16882),x16883),f20(f20(f16(x16881),x16882),x16884))
% 1.28/1.60 [1689]~P45(x16891)+~P6(a112,x16893,x16894)+~P6(x16891,f4(x16891),x16892)+P6(x16891,f20(f20(f16(x16891),x16892),x16893),f20(f20(f16(x16891),x16892),x16894))
% 1.28/1.60 [1691]~P45(x16911)+~P7(a112,x16913,x16914)+~P7(x16911,f4(x16911),x16912)+P7(x16911,f20(f20(f16(x16911),x16912),x16913),f20(f20(f16(x16911),x16912),x16914))
% 1.28/1.60 [1698]~P57(x16981)+~P6(x16981,x16984,x16983)+~P7(x16981,x16982,f3(x16981))+P6(x16981,f20(f20(f11(x16981),x16982),x16983),f20(f20(f11(x16981),x16982),x16984))
% 1.28/1.60 [1699]~P67(x16991)+~P6(x16991,x16994,x16993)+~P6(x16991,x16992,f3(x16991))+P6(x16991,f20(f20(f11(x16991),x16992),x16993),f20(f20(f11(x16991),x16992),x16994))
% 1.28/1.60 [1700]~P67(x17001)+~P6(x17001,x17004,x17002)+~P6(x17001,x17003,f3(x17001))+P6(x17001,f20(f20(f11(x17001),x17002),x17003),f20(f20(f11(x17001),x17004),x17003))
% 1.28/1.60 [1704]~P57(x17041)+~P7(x17041,x17044,x17042)+~P7(x17041,x17043,f3(x17041))+P7(x17041,f20(f20(f11(x17041),x17042),x17043),f20(f20(f11(x17041),x17044),x17043))
% 1.28/1.60 [1705]~P57(x17051)+~P7(x17051,x17054,x17053)+~P7(x17051,x17052,f3(x17051))+P7(x17051,f20(f20(f11(x17051),x17052),x17053),f20(f20(f11(x17051),x17052),x17054))
% 1.28/1.60 [1706]~P57(x17061)+~P6(x17061,x17063,x17064)+~P7(x17061,f3(x17061),x17062)+P6(x17061,f20(f20(f11(x17061),x17062),x17063),f20(f20(f11(x17061),x17062),x17064))
% 1.28/1.60 [1707]~P69(x17071)+~P6(x17071,x17073,x17074)+~P6(x17071,f3(x17071),x17072)+P6(x17071,f20(f20(f11(x17071),x17072),x17073),f20(f20(f11(x17071),x17072),x17074))
% 1.28/1.60 [1708]~P68(x17081)+~P6(x17081,x17083,x17084)+~P6(x17081,f3(x17081),x17082)+P6(x17081,f20(f20(f11(x17081),x17082),x17083),f20(f20(f11(x17081),x17082),x17084))
% 1.28/1.60 [1709]~P69(x17091)+~P6(x17091,x17092,x17094)+~P6(x17091,f3(x17091),x17093)+P6(x17091,f20(f20(f11(x17091),x17092),x17093),f20(f20(f11(x17091),x17094),x17093))
% 1.28/1.60 [1710]~P45(x17101)+~P6(x17101,x17102,x17104)+~P6(x17101,f3(x17101),x17102)+P6(x17101,f20(f20(f16(x17101),x17102),x17103),f20(f20(f16(x17101),x17104),x17103))
% 1.28/1.60 [1712]~P62(x17121)+~P7(x17121,x17123,x17124)+~P7(x17121,f3(x17121),x17122)+P7(x17121,f20(f20(f11(x17121),x17122),x17123),f20(f20(f11(x17121),x17122),x17124))
% 1.28/1.60 [1713]~P55(x17131)+~P7(x17131,x17133,x17134)+~P7(x17131,f3(x17131),x17132)+P7(x17131,f20(f20(f11(x17131),x17132),x17133),f20(f20(f11(x17131),x17132),x17134))
% 1.28/1.60 [1714]~P57(x17141)+~P7(x17141,x17142,x17144)+~P7(x17141,f3(x17141),x17143)+P7(x17141,f20(f20(f11(x17141),x17142),x17143),f20(f20(f11(x17141),x17144),x17143))
% 1.28/1.60 [1715]~P62(x17151)+~P7(x17151,x17152,x17154)+~P7(x17151,f3(x17151),x17153)+P7(x17151,f20(f20(f11(x17151),x17152),x17153),f20(f20(f11(x17151),x17154),x17153))
% 1.28/1.60 [1716]~P57(x17161)+~P7(x17161,x17163,x17164)+~P7(x17161,f3(x17161),x17162)+P7(x17161,f20(f20(f11(x17161),x17162),x17163),f20(f20(f11(x17161),x17162),x17164))
% 1.28/1.60 [1773]~P2(x17731)+~P7(x17731,x17734,f3(x17731))+P6(x17731,x17732,f24(x17731,x17733,x17734))+~P6(x17731,x17733,f20(f20(f11(x17731),x17732),x17734))
% 1.28/1.60 [1774]~P2(x17741)+~P7(x17741,x17744,f3(x17741))+P7(x17741,x17742,f24(x17741,x17743,x17744))+~P7(x17741,x17743,f20(f20(f11(x17741),x17742),x17744))
% 1.28/1.60 [1776]~P13(x17761)+~P7(x17761,f3(x17761),x17764)+P6(x17761,x17762,f24(x17761,x17763,x17764))+~P6(x17761,f20(f20(f11(x17761),x17762),x17764),x17763)
% 1.28/1.60 [1777]~P2(x17771)+~P7(x17771,f3(x17771),x17774)+P6(x17771,x17772,f24(x17771,x17773,x17774))+~P6(x17771,f20(f20(f11(x17771),x17772),x17774),x17773)
% 1.28/1.60 [1779]~P13(x17791)+~P7(x17791,f3(x17791),x17794)+P7(x17791,x17792,f24(x17791,x17793,x17794))+~P7(x17791,f20(f20(f11(x17791),x17792),x17794),x17793)
% 1.28/1.60 [1780]~P2(x17801)+~P7(x17801,f3(x17801),x17804)+P7(x17801,x17802,f24(x17801,x17803,x17804))+~P7(x17801,f20(f20(f11(x17801),x17802),x17804),x17803)
% 1.28/1.60 [1781]~P2(x17811)+~P7(x17811,x17813,f3(x17811))+P6(x17811,f24(x17811,x17812,x17813),x17814)+~P6(x17811,f20(f20(f11(x17811),x17814),x17813),x17812)
% 1.28/1.60 [1782]~P2(x17821)+~P7(x17821,x17823,f3(x17821))+P7(x17821,f24(x17821,x17822,x17823),x17824)+~P7(x17821,f20(f20(f11(x17821),x17824),x17823),x17822)
% 1.28/1.60 [1784]~P13(x17841)+~P7(x17841,f3(x17841),x17843)+P6(x17841,f24(x17841,x17842,x17843),x17844)+~P6(x17841,x17842,f20(f20(f11(x17841),x17844),x17843))
% 1.28/1.60 [1785]~P2(x17851)+~P7(x17851,f3(x17851),x17853)+P6(x17851,f24(x17851,x17852,x17853),x17854)+~P6(x17851,x17852,f20(f20(f11(x17851),x17854),x17853))
% 1.28/1.60 [1787]~P13(x17871)+~P7(x17871,f3(x17871),x17873)+P7(x17871,f24(x17871,x17872,x17873),x17874)+~P7(x17871,x17872,f20(f20(f11(x17871),x17874),x17873))
% 1.28/1.60 [1788]~P2(x17881)+~P7(x17881,f3(x17881),x17883)+P7(x17881,f24(x17881,x17882,x17883),x17884)+~P7(x17881,x17882,f20(f20(f11(x17881),x17884),x17883))
% 1.28/1.60 [1793]~P2(x17931)+~P7(x17931,x17934,f3(x17931))+~P6(x17931,x17933,f24(x17931,x17932,x17934))+P6(x17931,x17932,f20(f20(f11(x17931),x17933),x17934))
% 1.28/1.60 [1794]~P2(x17941)+~P7(x17941,x17944,f3(x17941))+~P7(x17941,x17943,f24(x17941,x17942,x17944))+P7(x17941,x17942,f20(f20(f11(x17941),x17943),x17944))
% 1.28/1.60 [1795]~P13(x17951)+~P7(x17951,f3(x17951),x17954)+~P6(x17951,f24(x17951,x17952,x17954),x17953)+P6(x17951,x17952,f20(f20(f11(x17951),x17953),x17954))
% 1.28/1.60 [1796]~P2(x17961)+~P7(x17961,f3(x17961),x17964)+~P6(x17961,f24(x17961,x17962,x17964),x17963)+P6(x17961,x17962,f20(f20(f11(x17961),x17963),x17964))
% 1.28/1.60 [1797]~P13(x17971)+~P7(x17971,f3(x17971),x17974)+~P7(x17971,f24(x17971,x17972,x17974),x17973)+P7(x17971,x17972,f20(f20(f11(x17971),x17973),x17974))
% 1.28/1.60 [1798]~P2(x17981)+~P7(x17981,f3(x17981),x17984)+~P7(x17981,f24(x17981,x17982,x17984),x17983)+P7(x17981,x17982,f20(f20(f11(x17981),x17983),x17984))
% 1.28/1.60 [1799]~P2(x17991)+~P7(x17991,x17993,f3(x17991))+~P6(x17991,f24(x17991,x17994,x17993),x17992)+P6(x17991,f20(f20(f11(x17991),x17992),x17993),x17994)
% 1.28/1.60 [1800]~P2(x18001)+~P7(x18001,x18003,f3(x18001))+~P7(x18001,f24(x18001,x18004,x18003),x18002)+P7(x18001,f20(f20(f11(x18001),x18002),x18003),x18004)
% 1.28/1.60 [1801]~P13(x18011)+~P7(x18011,f3(x18011),x18013)+~P6(x18011,x18012,f24(x18011,x18014,x18013))+P6(x18011,f20(f20(f11(x18011),x18012),x18013),x18014)
% 1.28/1.60 [1802]~P2(x18021)+~P7(x18021,f3(x18021),x18023)+~P6(x18021,x18022,f24(x18021,x18024,x18023))+P6(x18021,f20(f20(f11(x18021),x18022),x18023),x18024)
% 1.28/1.60 [1803]~P13(x18031)+~P7(x18031,f3(x18031),x18033)+~P7(x18031,x18032,f24(x18031,x18034,x18033))+P7(x18031,f20(f20(f11(x18031),x18032),x18033),x18034)
% 1.28/1.60 [1804]~P2(x18041)+~P7(x18041,f3(x18041),x18043)+~P7(x18041,x18042,f24(x18041,x18044,x18043))+P7(x18041,f20(f20(f11(x18041),x18042),x18043),x18044)
% 1.28/1.60 [1811]P7(x18111,x18113,x18112)+~P57(x18111)+P7(x18111,x18112,x18113)+~P7(x18111,f20(f20(f11(x18111),x18114),x18112),f20(f20(f11(x18111),x18114),x18113))
% 1.28/1.60 [1812]P7(x18121,x18123,x18122)+~P57(x18121)+P7(x18121,x18122,x18123)+~P7(x18121,f20(f20(f11(x18121),x18122),x18124),f20(f20(f11(x18121),x18123),x18124))
% 1.28/1.60 [1817]~P57(x18171)+P7(x18171,x18172,x18173)+P7(x18171,x18174,f3(x18171))+~P7(x18171,f20(f20(f11(x18171),x18172),x18174),f20(f20(f11(x18171),x18173),x18174))
% 1.28/1.60 [1818]~P57(x18181)+P7(x18181,x18182,x18183)+P7(x18181,x18184,f3(x18181))+~P7(x18181,f20(f20(f11(x18181),x18184),x18182),f20(f20(f11(x18181),x18184),x18183))
% 1.28/1.60 [1819]~P57(x18191)+P7(x18191,x18192,x18193)+P7(x18191,f3(x18191),x18194)+~P7(x18191,f20(f20(f11(x18191),x18194),x18193),f20(f20(f11(x18191),x18194),x18192))
% 1.28/1.60 [1820]~P57(x18201)+P7(x18201,x18202,x18203)+P7(x18201,f3(x18201),x18204)+~P7(x18201,f20(f20(f11(x18201),x18203),x18204),f20(f20(f11(x18201),x18202),x18204))
% 1.28/1.60 [1834]~P57(x18341)+P7(x18341,f3(x18341),x18342)+P7(x18341,x18342,f3(x18341))+~P7(x18341,f20(f20(f11(x18341),x18343),x18342),f20(f20(f11(x18341),x18344),x18342))
% 1.28/1.60 [1835]~P57(x18351)+P7(x18351,f3(x18351),x18352)+P7(x18351,x18352,f3(x18351))+~P7(x18351,f20(f20(f11(x18351),x18352),x18353),f20(f20(f11(x18351),x18352),x18354))
% 1.28/1.60 [1865]~P45(x18653)+P6(a112,x18651,x18652)+~P7(x18653,f4(x18653),x18654)+~P6(x18653,f20(f20(f16(x18653),x18654),x18651),f20(f20(f16(x18653),x18654),x18652))
% 1.28/1.60 [1867]~P45(x18673)+P7(a112,x18671,x18672)+~P7(x18673,f4(x18673),x18674)+~P7(x18673,f20(f20(f16(x18673),x18674),x18671),f20(f20(f16(x18673),x18674),x18672))
% 1.28/1.60 [1868]~P57(x18681)+P6(x18681,x18682,x18683)+~P7(x18681,x18684,f3(x18681))+~P6(x18681,f20(f20(f11(x18681),x18684),x18683),f20(f20(f11(x18681),x18684),x18682))
% 1.28/1.60 [1869]~P57(x18691)+P7(x18691,x18692,x18693)+~P7(x18691,x18694,f3(x18691))+~P7(x18691,f20(f20(f11(x18691),x18694),x18693),f20(f20(f11(x18691),x18694),x18692))
% 1.28/1.60 [1870]~P57(x18701)+P6(x18701,x18702,x18703)+~P7(x18701,f3(x18701),x18704)+~P6(x18701,f20(f20(f11(x18701),x18704),x18702),f20(f20(f11(x18701),x18704),x18703))
% 1.28/1.60 [1871]~P62(x18711)+P6(x18711,x18712,x18713)+~P7(x18711,f3(x18711),x18714)+~P6(x18711,f20(f20(f11(x18711),x18714),x18712),f20(f20(f11(x18711),x18714),x18713))
% 1.28/1.60 [1872]~P62(x18721)+P6(x18721,x18722,x18723)+~P7(x18721,f3(x18721),x18724)+~P6(x18721,f20(f20(f11(x18721),x18722),x18724),f20(f20(f11(x18721),x18723),x18724))
% 1.28/1.60 [1873]~P57(x18731)+P7(x18731,x18732,x18733)+~P7(x18731,f3(x18731),x18734)+~P7(x18731,f20(f20(f11(x18731),x18734),x18732),f20(f20(f11(x18731),x18734),x18733))
% 1.28/1.60 [1874]~P62(x18741)+P7(x18741,x18742,x18743)+~P6(x18741,f3(x18741),x18744)+~P7(x18741,f20(f20(f11(x18741),x18744),x18742),f20(f20(f11(x18741),x18744),x18743))
% 1.28/1.60 [1875]~P63(x18751)+P7(x18751,x18752,x18753)+~P6(x18751,f3(x18751),x18754)+~P7(x18751,f20(f20(f11(x18751),x18754),x18752),f20(f20(f11(x18751),x18754),x18753))
% 1.28/1.60 [1876]~P45(x18761)+P7(x18761,x18762,x18763)+~P6(x18761,f3(x18761),x18763)+~P7(x18761,f20(f20(f16(x18761),x18762),x18764),f20(f20(f16(x18761),x18763),x18764))
% 1.28/1.60 [1877]~P62(x18771)+P7(x18771,x18772,x18773)+~P6(x18771,f3(x18771),x18774)+~P7(x18771,f20(f20(f11(x18771),x18772),x18774),f20(f20(f11(x18771),x18773),x18774))
% 1.28/1.60 [1878]~P63(x18781)+P7(x18781,x18782,x18783)+~P6(x18781,f3(x18781),x18784)+~P7(x18781,f20(f20(f11(x18781),x18782),x18784),f20(f20(f11(x18781),x18783),x18784))
% 1.28/1.60 [2057]~P7(a110,x20574,x20571)+~P6(a110,f3(a110),x20574)+~P7(a110,f3(a110),x20573)+P6(a110,f3(a110),f12(a110,f20(f20(f11(a110),x20571),f6(a110,x20572,x20573)),x20574))
% 1.28/1.60 [2058]~P7(a110,x20581,x20584)+~P6(a110,x20584,f3(a110))+~P7(a110,f3(a110),x20583)+P6(a110,f12(a110,f20(f20(f11(a110),x20581),f6(a110,x20582,x20583)),x20584),f3(a110))
% 1.28/1.60 [2066]~P77(f20(x20661,x20664))+~P6(a112,f20(f20(f11(a112),x20663),x20664),x20662)+~P7(a112,x20662,f20(f20(f11(a112),x20663),f12(a112,x20664,f4(a112))))+P77(f20(x20661,f7(a112,x20662,x20663)))
% 1.28/1.60 [2070]~P7(a110,x20701,x20704)+~P6(a110,x20704,f3(a110))+~P7(a110,f3(a110),x20702)+P7(a110,f20(f20(f11(a110),x20701),x20702),f12(a110,f20(f20(f11(a110),x20701),f6(a110,x20703,x20702)),x20704))
% 1.28/1.60 [2071]~P7(a110,x20714,x20711)+~P6(a110,f3(a110),x20714)+~P7(a110,f3(a110),x20713)+P7(a110,f12(a110,f20(f20(f11(a110),x20711),f6(a110,x20712,x20713)),x20714),f20(f20(f11(a110),x20711),x20713))
% 1.28/1.60 [2081]~P45(x20811)+P6(x20811,x20812,x20813)+~P6(x20811,f3(x20811),x20813)+~P6(x20811,f20(f20(f16(x20811),x20812),f12(a112,x20814,f4(a112))),f20(f20(f16(x20811),x20813),f12(a112,x20814,f4(a112))))
% 1.28/1.60 [2099]~P1(x20991)+~P7(a1,f3(a1),x20994)+~P6(a1,f22(x20991,f20(x20992,f33(x20992,x20991,x20994))),x20994)+P6(a1,f22(x20991,f20(x20992,x20993)),f19(a112,f12(a112,f32(x20992,x20991),f4(a112))))
% 1.28/1.60 [2100]~P1(x21001)+~P7(a1,f3(a1),x21004)+~P6(a1,f22(x21001,f20(x21002,f37(x21002,x21001,x21004))),x21004)+P7(a1,f22(x21001,f20(x21002,x21003)),f19(a112,f12(a112,f36(x21002,x21001),f4(a112))))
% 1.28/1.60 [2113]~P1(x21131)+P8(x21131,x21132)+~P7(a1,f3(a1),x21133)+~P6(a1,f22(x21131,f12(x21131,f20(x21132,f71(x21132,x21131,x21133,x21134)),f10(x21131,x21134))),x21133)
% 1.28/1.60 [2114]~P1(x21141)+P8(x21141,x21142)+~P7(a1,f3(a1),x21143)+~P6(a1,f22(x21141,f12(x21141,f20(x21142,f67(x21142,x21141,x21143,x21144)),f10(x21141,f20(x21142,x21144)))),x21143)
% 1.28/1.60 [1406]~P31(x14061)+~P6(x14061,x14064,x14065)+P6(x14061,x14062,x14063)+~E(f8(x14061,x14064,x14065),f8(x14061,x14062,x14063))
% 1.28/1.60 [1408]~P31(x14081)+~P7(x14081,x14084,x14085)+P7(x14081,x14082,x14083)+~E(f8(x14081,x14084,x14085),f8(x14081,x14082,x14083))
% 1.28/1.60 [1693]~P30(x16931)+~P6(x16931,x16933,x16935)+~P6(x16931,x16932,x16934)+P6(x16931,f12(x16931,x16932,x16933),f12(x16931,x16934,x16935))
% 1.28/1.60 [1694]~P32(x16941)+~P6(x16941,x16943,x16945)+~P7(x16941,x16942,x16944)+P7(x16941,f12(x16941,x16942,x16943),f12(x16941,x16944,x16945))
% 1.28/1.60 [1695]~P32(x16951)+~P6(x16951,x16952,x16954)+~P7(x16951,x16953,x16955)+P7(x16951,f12(x16951,x16952,x16953),f12(x16951,x16954,x16955))
% 1.28/1.60 [1696]~P32(x16961)+~P7(x16961,x16963,x16965)+~P7(x16961,x16962,x16964)+P7(x16961,f12(x16961,x16962,x16963),f12(x16961,x16964,x16965))
% 1.28/1.60 [1951]~P1(x19511)+~P7(a1,f22(x19511,x19513),x19515)+~P7(a1,f22(x19511,x19512),x19514)+P7(a1,f22(x19511,f12(x19511,x19512,x19513)),f12(a1,x19514,x19515))
% 1.28/1.60 [1931]~P42(x19311)+~P7(a1,f22(x19311,x19313),x19315)+~P7(a1,f22(x19311,x19312),x19314)+P7(a1,f22(x19311,f20(f20(f11(x19311),x19312),x19313)),f20(f20(f11(a1),x19314),x19315))
% 1.28/1.60 [2024]~P75(x20245)+E(x20241,x20242)+E(x20243,x20244)+~E(f12(x20245,f20(f20(f11(x20245),x20243),x20241),f20(f20(f11(x20245),x20244),x20242)),f12(x20245,f20(f20(f11(x20245),x20243),x20242),f20(f20(f11(x20245),x20244),x20241)))
% 1.28/1.60 [2047]~P11(x20472)+E(x20471,f3(x20472))+E(x20473,f3(x20472))+E(f24(x20472,f12(x20472,f20(f20(f11(x20472),x20474),x20471),f20(f20(f11(x20472),x20475),x20473)),f20(f20(f11(x20472),x20473),x20471)),f12(x20472,f24(x20472,x20474,x20473),f24(x20472,x20475,x20471)))
% 1.28/1.60 [1961]~P4(x19611)+~E(f6(x19611,x19613,x19614),f6(x19611,x19616,x19614))+~E(f6(x19611,x19612,x19614),f6(x19611,x19615,x19614))+E(f6(x19611,f12(x19611,x19612,x19613),x19614),f6(x19611,f12(x19611,x19615,x19616),x19614))
% 1.28/1.60 [1962]~P5(x19621)+~E(f6(x19621,x19623,x19624),f6(x19621,x19626,x19624))+~E(f6(x19621,x19622,x19624),f6(x19621,x19625,x19624))+E(f6(x19621,f8(x19621,x19622,x19623),x19624),f6(x19621,f8(x19621,x19625,x19626),x19624))
% 1.28/1.60 [1959]~P4(x19591)+~E(f6(x19591,x19593,x19594),f6(x19591,x19596,x19594))+~E(f6(x19591,x19592,x19594),f6(x19591,x19595,x19594))+E(f6(x19591,f20(f20(f11(x19591),x19592),x19593),x19594),f6(x19591,f20(f20(f11(x19591),x19595),x19596),x19594))
% 1.28/1.60 [1362]~P24(x13622)+~P6(x13622,f3(x13622),x13623)+~P6(x13622,f3(x13622),x13621)+~E(f12(x13622,x13623,x13621),f3(x13622))+E(x13621,f3(x13622))
% 1.28/1.60 [1363]~P24(x13632)+~P6(x13632,f3(x13632),x13633)+~P6(x13632,f3(x13632),x13631)+~E(f12(x13632,x13631,x13633),f3(x13632))+E(x13631,f3(x13632))
% 1.28/1.60 [1493]E(x14931,f97(x14932,x14933))+~P7(a1,f3(a1),x14932)+~P7(a1,f3(a1),x14931)+~P7(a112,f3(a112),x14933)+~E(f20(f20(f16(a1),x14931),x14933),x14932)
% 1.28/1.60 [1718]~P52(x17181)+~P6(x17181,x17182,f4(x17181))+~P6(x17181,f3(x17181),x17182)+~P6(x17181,f3(x17181),x17183)+P6(x17181,f20(f20(f11(x17181),x17182),x17183),x17183)
% 1.28/1.60 [1719]~P52(x17191)+~P6(x17191,x17193,f4(x17191))+~P6(x17191,f3(x17191),x17193)+~P6(x17191,f3(x17191),x17192)+P6(x17191,f20(f20(f11(x17191),x17192),x17193),x17192)
% 1.28/1.60 [1576]~P13(x15761)+P7(x15761,f3(x15761),x15762)+~P6(x15761,x15763,f3(x15761))+P7(x15761,x15762,f3(x15761))+P6(x15761,x15763,f24(x15761,x15764,x15762))
% 1.28/1.60 [1577]~P13(x15771)+P7(x15771,f3(x15771),x15772)+~P7(x15771,x15773,f3(x15771))+P7(x15771,x15772,f3(x15771))+P7(x15771,x15773,f24(x15771,x15774,x15772))
% 1.28/1.60 [1578]~P13(x15781)+P7(x15781,f3(x15781),x15782)+~P6(x15781,f3(x15781),x15784)+P7(x15781,x15782,f3(x15781))+P6(x15781,f24(x15781,x15783,x15782),x15784)
% 1.28/1.60 [1579]~P13(x15791)+P7(x15791,f3(x15791),x15792)+~P7(x15791,f3(x15791),x15794)+P7(x15791,x15792,f3(x15791))+P7(x15791,f24(x15791,x15793,x15792),x15794)
% 1.28/1.60 [1683]~P13(x16831)+P7(x16831,f3(x16831),x16833)+P6(x16831,x16832,f3(x16831))+~P6(x16831,x16832,f24(x16831,x16834,x16833))+P7(x16831,x16833,f3(x16831))
% 1.28/1.60 [1684]~P13(x16841)+P7(x16841,f3(x16841),x16843)+P7(x16841,x16842,f3(x16841))+~P7(x16841,x16842,f24(x16841,x16844,x16843))+P7(x16841,x16843,f3(x16841))
% 1.28/1.60 [1685]~P13(x16851)+P7(x16851,f3(x16851),x16852)+P7(x16851,x16852,f3(x16851))+~P6(x16851,f24(x16851,x16854,x16852),x16853)+P6(x16851,f3(x16851),x16853)
% 1.28/1.60 [1686]~P13(x16861)+P7(x16861,f3(x16861),x16862)+P7(x16861,x16862,f3(x16861))+~P7(x16861,f24(x16861,x16864,x16862),x16863)+P7(x16861,f3(x16861),x16863)
% 1.28/1.60 [1838]~P45(x18381)+~P7(x18381,x18382,x18384)+~P6(x18381,f3(x18381),x18382)+~P7(a112,f3(a112),x18383)+P7(x18381,f20(f20(f16(x18381),x18382),x18383),f20(f20(f16(x18381),x18384),x18383))
% 1.28/1.60 [1845]~P45(x18451)+~P6(a112,x18454,x18453)+~P6(x18451,x18452,f4(x18451))+~P6(x18451,f3(x18451),x18452)+P6(x18451,f20(f20(f16(x18451),x18452),x18453),f20(f20(f16(x18451),x18452),x18454))
% 1.28/1.60 [1846]~P45(x18461)+~P7(a112,x18464,x18463)+~P7(x18461,x18462,f4(x18461))+~P7(x18461,f3(x18461),x18462)+P7(x18461,f20(f20(f16(x18461),x18462),x18463),f20(f20(f16(x18461),x18462),x18464))
% 1.28/1.60 [1882]~P13(x18821)+~P6(x18821,x18823,f3(x18821))+P7(x18821,x18822,f3(x18821))+P6(x18821,x18823,f24(x18821,x18824,x18822))+~P6(x18821,f20(f20(f11(x18821),x18823),x18822),x18824)
% 1.28/1.60 [1883]~P13(x18831)+~P7(x18831,x18833,f3(x18831))+P7(x18831,x18832,f3(x18831))+P7(x18831,x18833,f24(x18831,x18834,x18832))+~P7(x18831,f20(f20(f11(x18831),x18833),x18832),x18834)
% 1.28/1.60 [1884]~P13(x18841)+~P6(x18841,f3(x18841),x18844)+P7(x18841,x18842,f3(x18841))+P6(x18841,f24(x18841,x18843,x18842),x18844)+~P6(x18841,x18843,f20(f20(f11(x18841),x18844),x18842))
% 1.28/1.60 [1885]~P13(x18851)+~P7(x18851,f3(x18851),x18854)+P7(x18851,x18852,f3(x18851))+P7(x18851,f24(x18851,x18853,x18852),x18854)+~P7(x18851,x18853,f20(f20(f11(x18851),x18854),x18852))
% 1.28/1.60 [1886]~P13(x18861)+~P6(x18861,x18863,f3(x18861))+P7(x18861,f3(x18861),x18862)+P6(x18861,x18863,f24(x18861,x18864,x18862))+~P6(x18861,x18864,f20(f20(f11(x18861),x18863),x18862))
% 1.28/1.60 [1887]~P13(x18871)+~P7(x18871,x18873,f3(x18871))+P7(x18871,f3(x18871),x18872)+P7(x18871,x18873,f24(x18871,x18874,x18872))+~P7(x18871,x18874,f20(f20(f11(x18871),x18873),x18872))
% 1.28/1.60 [1888]~P13(x18881)+~P7(x18881,x18882,f3(x18881))+P7(x18881,f3(x18881),x18882)+P6(x18881,x18883,f24(x18881,x18884,x18882))+~P6(x18881,x18884,f20(f20(f11(x18881),x18883),x18882))
% 1.28/1.60 [1889]~P13(x18891)+~P7(x18891,x18892,f3(x18891))+P7(x18891,f3(x18891),x18892)+P7(x18891,x18893,f24(x18891,x18894,x18892))+~P7(x18891,x18894,f20(f20(f11(x18891),x18893),x18892))
% 1.28/1.60 [1890]~P13(x18901)+~P7(x18901,x18902,f3(x18901))+P7(x18901,f3(x18901),x18902)+P6(x18901,f24(x18901,x18903,x18902),x18904)+~P6(x18901,f20(f20(f11(x18901),x18904),x18902),x18903)
% 1.28/1.60 [1891]~P13(x18911)+~P7(x18911,x18912,f3(x18911))+P7(x18911,f3(x18911),x18912)+P7(x18911,f24(x18911,x18913,x18912),x18914)+~P7(x18911,f20(f20(f11(x18911),x18914),x18912),x18913)
% 1.28/1.60 [1892]~P13(x18921)+~P6(x18921,f3(x18921),x18924)+P7(x18921,f3(x18921),x18922)+P6(x18921,f24(x18921,x18923,x18922),x18924)+~P6(x18921,f20(f20(f11(x18921),x18924),x18922),x18923)
% 1.28/1.60 [1893]~P13(x18931)+~P7(x18931,f3(x18931),x18934)+P7(x18931,f3(x18931),x18932)+P7(x18931,f24(x18931,x18933,x18932),x18934)+~P7(x18931,f20(f20(f11(x18931),x18934),x18932),x18933)
% 1.28/1.60 [1894]~P13(x18941)+~P7(x18941,x18942,f3(x18941))+~P6(x18941,x18944,f24(x18941,x18943,x18942))+P7(x18941,f3(x18941),x18942)+P6(x18941,x18943,f20(f20(f11(x18941),x18944),x18942))
% 1.28/1.60 [1895]~P13(x18951)+~P7(x18951,x18952,f3(x18951))+~P7(x18951,x18954,f24(x18951,x18953,x18952))+P7(x18951,f3(x18951),x18952)+P7(x18951,x18953,f20(f20(f11(x18951),x18954),x18952))
% 1.28/1.60 [1896]~P13(x18961)+~P7(x18961,x18962,f3(x18961))+~P6(x18961,f24(x18961,x18964,x18962),x18963)+P7(x18961,f3(x18961),x18962)+P6(x18961,f20(f20(f11(x18961),x18963),x18962),x18964)
% 1.28/1.60 [1897]~P13(x18971)+~P7(x18971,x18972,f3(x18971))+~P7(x18971,f24(x18971,x18974,x18972),x18973)+P7(x18971,f3(x18971),x18972)+P7(x18971,f20(f20(f11(x18971),x18973),x18972),x18974)
% 1.28/1.60 [1981]~P45(x19813)+E(x19811,x19812)+~P6(x19813,f3(x19813),x19812)+~P6(x19813,f3(x19813),x19811)+~E(f20(f20(f16(x19813),x19811),f12(a112,x19814,f4(a112))),f20(f20(f16(x19813),x19812),f12(a112,x19814,f4(a112))))
% 1.28/1.60 [1982]~P13(x19821)+~P6(x19821,x19823,x19824)+~P6(x19821,x19822,f3(x19821))+P6(x19821,f24(x19821,x19822,x19823),f24(x19821,x19822,x19824))+~P7(x19821,f3(x19821),f20(f20(f11(x19821),x19823),x19824))
% 1.28/1.60 [1983]~P2(x19831)+~P7(x19831,x19833,x19834)+~P7(x19831,x19832,f3(x19831))+P7(x19831,f24(x19831,x19832,x19833),f24(x19831,x19832,x19834))+~P7(x19831,f3(x19831),f20(f20(f11(x19831),x19833),x19834))
% 1.28/1.60 [1984]~P2(x19841)+~P6(x19841,x19844,x19843)+~P6(x19841,f3(x19841),x19842)+P6(x19841,f24(x19841,x19842,x19843),f24(x19841,x19842,x19844))+~P7(x19841,f3(x19841),f20(f20(f11(x19841),x19843),x19844))
% 1.28/1.60 [1985]~P2(x19851)+~P7(x19851,x19854,x19853)+~P7(x19851,f3(x19851),x19852)+P7(x19851,f24(x19851,x19852,x19853),f24(x19851,x19852,x19854))+~P7(x19851,f3(x19851),f20(f20(f11(x19851),x19853),x19854))
% 1.28/1.60 [2006]~P13(x20061)+~P7(x20061,x20064,f3(x20061))+P6(x20061,x20062,f24(x20061,x20063,x20064))+~P6(x20061,x20063,f20(f20(f11(x20061),x20062),x20064))+~P6(x20061,f20(f20(f11(x20061),x20062),x20064),x20063)
% 1.28/1.60 [2007]~P13(x20071)+~P6(x20071,x20072,f3(x20071))+P6(x20071,x20072,f24(x20071,x20073,x20074))+~P6(x20071,x20073,f20(f20(f11(x20071),x20072),x20074))+~P6(x20071,f20(f20(f11(x20071),x20072),x20074),x20073)
% 1.28/1.60 [2008]~P13(x20081)+~P7(x20081,x20084,f3(x20081))+P7(x20081,x20082,f24(x20081,x20083,x20084))+~P7(x20081,x20083,f20(f20(f11(x20081),x20082),x20084))+~P7(x20081,f20(f20(f11(x20081),x20082),x20084),x20083)
% 1.28/1.60 [2009]~P13(x20091)+~P7(x20091,x20092,f3(x20091))+P7(x20091,x20092,f24(x20091,x20093,x20094))+~P7(x20091,x20093,f20(f20(f11(x20091),x20092),x20094))+~P7(x20091,f20(f20(f11(x20091),x20092),x20094),x20093)
% 1.28/1.60 [2010]~P13(x20101)+~P7(x20101,x20103,f3(x20101))+P6(x20101,f24(x20101,x20102,x20103),x20104)+~P6(x20101,x20102,f20(f20(f11(x20101),x20104),x20103))+~P6(x20101,f20(f20(f11(x20101),x20104),x20103),x20102)
% 1.28/1.60 [2011]~P13(x20111)+~P7(x20111,x20113,f3(x20111))+P7(x20111,f24(x20111,x20112,x20113),x20114)+~P7(x20111,x20112,f20(f20(f11(x20111),x20114),x20113))+~P7(x20111,f20(f20(f11(x20111),x20114),x20113),x20112)
% 1.28/1.60 [2012]~P13(x20121)+~P6(x20121,f3(x20121),x20124)+P6(x20121,f24(x20121,x20122,x20123),x20124)+~P6(x20121,x20122,f20(f20(f11(x20121),x20124),x20123))+~P6(x20121,f20(f20(f11(x20121),x20124),x20123),x20122)
% 1.28/1.60 [2013]~P13(x20131)+~P7(x20131,f3(x20131),x20134)+P7(x20131,f24(x20131,x20132,x20133),x20134)+~P7(x20131,x20132,f20(f20(f11(x20131),x20134),x20133))+~P7(x20131,f20(f20(f11(x20131),x20134),x20133),x20132)
% 1.28/1.60 [1356]~P11(x13562)+E(f24(x13562,x13564,x13561),f24(x13562,x13565,x13563))+E(x13561,f3(x13562))+E(x13563,f3(x13562))+~E(f20(f20(f11(x13562),x13564),x13563),f20(f20(f11(x13562),x13565),x13561))
% 1.28/1.60 [1359]~P11(x13592)+~E(f24(x13592,x13594,x13593),f24(x13592,x13595,x13591))+E(x13591,f3(x13592))+E(x13593,f3(x13592))+E(f20(f20(f11(x13592),x13594),x13591),f20(f20(f11(x13592),x13595),x13593))
% 1.28/1.60 [1986]~P7(a112,x19865,x19861)+E(x19861,f3(a112))+P77(f20(x19862,x19863))+~P77(f20(x19862,f7(a112,x19864,x19861)))+~E(x19864,f12(a112,f20(f20(f11(a112),x19861),x19863),x19865))
% 1.28/1.60 [1987]~P7(a112,x19873,x19871)+E(x19871,f3(a112))+P77(f20(x19872,x19873))+~P77(f20(x19872,f6(a112,x19874,x19871)))+~E(x19874,f12(a112,f20(f20(f11(a112),x19871),x19875),x19873))
% 1.28/1.60 [2088]P6(a110,x20881,x20882)+~P7(a110,x20883,x20884)+~P7(a110,x20883,x20885)+~P6(a110,x20884,f3(a110))+~P6(a110,f12(a110,f20(f20(f11(a110),x20883),x20882),x20885),f12(a110,f20(f20(f11(a110),x20883),x20881),x20884))
% 1.28/1.60 [2089]P6(a110,x20891,x20892)+~P7(a110,x20893,x20894)+~P7(a110,x20895,x20894)+~P6(a110,f3(a110),x20895)+~P6(a110,f12(a110,f20(f20(f11(a110),x20894),x20891),x20895),f12(a110,f20(f20(f11(a110),x20894),x20892),x20893))
% 1.28/1.60 [1772]~P75(x17724)+E(x17721,x17722)+~E(x17725,x17726)+E(x17723,f3(x17724))+~E(f12(x17724,x17725,f20(f20(f11(x17724),x17723),x17721)),f12(x17724,x17726,f20(f20(f11(x17724),x17723),x17722)))
% 1.28/1.60 [1332]~P24(x13321)+~P6(x13321,f3(x13321),x13323)+~P6(x13321,f3(x13321),x13322)+~E(x13323,f3(x13321))+~E(x13322,f3(x13321))+E(f12(x13321,x13322,x13323),f3(x13321))
% 1.28/1.60 [974]~P58(x9742)+~P60(x9742)+~P61(x9742)+~P43(x9742)+E(x9741,f3(x9742))+~E(f20(f20(f16(x9742),x9741),x9743),f3(x9742))
% 1.28/1.60 [975]~P58(x9752)+~P60(x9752)+~P61(x9752)+~P43(x9752)+~E(x9751,f3(a112))+~E(f20(f20(f16(x9752),x9753),x9751),f3(x9752))
% 1.28/1.60 [1723]~P45(x17233)+E(x17231,x17232)+~P6(x17233,f3(x17233),x17232)+~P6(x17233,f3(x17233),x17231)+~P7(a112,f3(a112),x17234)+~E(f20(f20(f16(x17233),x17231),x17234),f20(f20(f16(x17233),x17232),x17234))
% 1.28/1.60 [1791]~P7(a110,x17911,x17914)+E(f7(a110,x17912,x17911),x17913)+E(x17911,f3(a110))+P7(a110,f3(a110),x17911)+~P6(a110,x17914,f3(a110))+~E(x17912,f12(a110,f20(f20(f11(a110),x17911),x17913),x17914))
% 1.28/1.60 [1792]~P7(a110,x17921,x17923)+E(f6(a110,x17922,x17921),x17923)+E(x17921,f3(a110))+P7(a110,f3(a110),x17921)+~P6(a110,x17923,f3(a110))+~E(x17922,f12(a110,f20(f20(f11(a110),x17921),x17924),x17923))
% 1.28/1.60 [1859]~P7(a110,x18594,x18591)+E(f7(a110,x18592,x18591),x18593)+E(x18591,f3(a110))+~P6(a110,f3(a110),x18594)+~P7(a110,f3(a110),x18591)+~E(x18592,f12(a110,f20(f20(f11(a110),x18591),x18593),x18594))
% 1.28/1.60 [1860]~P7(a110,x18603,x18601)+E(f6(a110,x18602,x18601),x18603)+E(x18601,f3(a110))+~P6(a110,f3(a110),x18603)+~P7(a110,f3(a110),x18601)+~E(x18602,f12(a110,f20(f20(f11(a110),x18601),x18604),x18603))
% 1.28/1.60 [1944]~P2(x19441)+~P6(x19441,x19445,x19443)+~P6(x19441,x19442,x19444)+~P6(x19441,f3(x19441),x19442)+~P7(x19441,f3(x19441),x19445)+P6(x19441,f24(x19441,x19442,x19443),f24(x19441,x19444,x19445))
% 1.28/1.60 [1945]~P2(x19451)+~P6(x19451,x19455,x19453)+~P7(x19451,x19452,x19454)+~P6(x19451,f3(x19451),x19452)+~P7(x19451,f3(x19451),x19455)+P7(x19451,f24(x19451,x19452,x19453),f24(x19451,x19454,x19455))
% 1.28/1.60 [1946]~P2(x19461)+~P6(x19461,x19462,x19464)+~P7(x19461,x19465,x19463)+~P7(x19461,f3(x19461),x19465)+~P7(x19461,f3(x19461),x19462)+P7(x19461,f24(x19461,x19462,x19463),f24(x19461,x19464,x19465))
% 1.28/1.60 [1932]~P69(x19321)+~P6(x19321,x19323,x19325)+~P6(x19321,x19322,x19324)+~P6(x19321,f3(x19321),x19323)+~P6(x19321,f3(x19321),x19324)+P6(x19321,f20(f20(f11(x19321),x19322),x19323),f20(f20(f11(x19321),x19324),x19325))
% 1.28/1.60 [1933]~P69(x19331)+~P6(x19331,x19333,x19335)+~P6(x19331,x19332,x19334)+~P6(x19331,f3(x19331),x19333)+~P6(x19331,f3(x19331),x19332)+P6(x19331,f20(f20(f11(x19331),x19332),x19333),f20(f20(f11(x19331),x19334),x19335))
% 1.28/1.60 [1934]~P62(x19341)+~P6(x19341,x19343,x19345)+~P7(x19341,x19342,x19344)+~P6(x19341,f3(x19341),x19342)+~P7(x19341,f3(x19341),x19343)+P7(x19341,f20(f20(f11(x19341),x19342),x19343),f20(f20(f11(x19341),x19344),x19345))
% 1.28/1.60 [1935]~P62(x19351)+~P6(x19351,x19352,x19354)+~P7(x19351,x19353,x19355)+~P6(x19351,f3(x19351),x19353)+~P7(x19351,f3(x19351),x19352)+P7(x19351,f20(f20(f11(x19351),x19352),x19353),f20(f20(f11(x19351),x19354),x19355))
% 1.28/1.60 [1936]~P62(x19361)+~P7(x19361,x19363,x19365)+~P7(x19361,x19362,x19364)+~P6(x19361,f3(x19361),x19363)+~P6(x19361,f3(x19361),x19362)+P7(x19361,f20(f20(f11(x19361),x19362),x19363),f20(f20(f11(x19361),x19364),x19365))
% 1.28/1.60 [1937]~P62(x19371)+~P7(x19371,x19373,x19375)+~P7(x19371,x19372,x19374)+~P6(x19371,f3(x19371),x19373)+~P7(x19371,f3(x19371),x19374)+P7(x19371,f20(f20(f11(x19371),x19372),x19373),f20(f20(f11(x19371),x19374),x19375))
% 1.28/1.60 [1914]~P79(x19141,x19144,x19143)+~P7(a110,x19144,x19145)+~P6(a110,x19145,f3(a110))+~P7(a110,x19144,f3(a110))+P77(f20(x19141,x19142))+~E(x19143,f12(a110,f20(f20(f11(a110),x19144),x19142),x19145))
% 1.28/1.60 [1915]~P78(x19151,x19154,x19153)+~P7(a110,x19154,x19152)+~P6(a110,x19152,f3(a110))+~P7(a110,x19154,f3(a110))+P77(f20(x19151,x19152))+~E(x19153,f12(a110,f20(f20(f11(a110),x19154),x19155),x19152))
% 1.28/1.60 [1916]~P79(x19161,x19164,x19163)+~P7(a110,x19165,x19164)+~P6(a110,f3(a110),x19165)+~P7(a110,f3(a110),x19164)+P77(f20(x19161,x19162))+~E(x19163,f12(a110,f20(f20(f11(a110),x19164),x19162),x19165))
% 1.28/1.60 [1917]~P78(x19171,x19174,x19173)+~P7(a110,x19172,x19174)+~P6(a110,f3(a110),x19172)+~P7(a110,f3(a110),x19174)+P77(f20(x19171,x19172))+~E(x19173,f12(a110,f20(f20(f11(a110),x19174),x19175),x19172))
% 1.28/1.60 [2102]~P7(a110,x21025,x21023)+~P6(a110,x21023,f3(a110))+~P7(a110,x21025,f3(a110))+P77(f20(f20(x21021,x21022),x21023))+~P77(f20(f20(x21021,f7(a110,x21024,x21025)),f6(a110,x21024,x21025)))+~E(x21024,f12(a110,f20(f20(f11(a110),x21025),x21022),x21023))
% 1.28/1.60 [2103]~P7(a110,x21033,x21035)+~P6(a110,f3(a110),x21033)+~P7(a110,f3(a110),x21035)+P77(f20(f20(x21031,x21032),x21033))+~P77(f20(f20(x21031,f7(a110,x21034,x21035)),f6(a110,x21034,x21035)))+~E(x21034,f12(a110,f20(f20(f11(a110),x21035),x21032),x21033))
% 1.28/1.60 [918]~P58(x9182)+~P60(x9182)+~P61(x9182)+~P43(x9182)+~E(x9183,f3(x9182))+E(x9181,f3(a112))+E(f20(f20(f16(x9182),x9183),x9181),f3(x9182))
% 1.28/1.60 [1929]~P7(a110,x19294,x19291)+~P7(a110,x19291,x19294)+E(f7(a110,x19292,x19291),x19293)+E(x19291,f3(a110))+~P6(a110,x19294,f3(a110))+~P6(a110,f3(a110),x19294)+~E(x19292,f12(a110,f20(f20(f11(a110),x19291),x19293),x19294))
% 1.28/1.60 [1930]~P7(a110,x19303,x19301)+~P7(a110,x19301,x19303)+E(f6(a110,x19302,x19301),x19303)+E(x19301,f3(a110))+~P6(a110,x19303,f3(a110))+~P6(a110,f3(a110),x19303)+~E(x19302,f12(a110,f20(f20(f11(a110),x19301),x19304),x19303))
% 1.28/1.60 [2060]~P64(x20601)+~P6(x20601,x20605,x20606)+~P6(x20601,x20603,x20606)+~P6(x20601,f3(x20601),x20604)+~P6(x20601,f3(x20601),x20602)+~E(f12(x20601,x20602,x20604),f4(x20601))+P6(x20601,f12(x20601,f20(f20(f11(x20601),x20602),x20603),f20(f20(f11(x20601),x20604),x20605)),x20606)
% 1.28/1.60 [2061]~P65(x20611)+~P7(x20611,x20615,x20616)+~P7(x20611,x20613,x20616)+~P6(x20611,f3(x20611),x20614)+~P6(x20611,f3(x20611),x20612)+~E(f12(x20611,x20612,x20614),f4(x20611))+P7(x20611,f12(x20611,f20(f20(f11(x20611),x20612),x20613),f20(f20(f11(x20611),x20614),x20615)),x20616)
% 1.28/1.60 [2095]~P6(a110,x20955,x20953)+~P7(a110,x20956,x20955)+P6(a110,x20951,x20952)+~P6(a110,f3(a110),x20954)+~P7(a110,f3(a110),x20955)+~P6(a110,f3(a110),f12(a110,f20(f20(f11(a110),x20955),x20952),x20956))+~E(f12(a110,f20(f20(f11(a110),x20953),x20951),x20954),f12(a110,f20(f20(f11(a110),x20955),x20952),x20956))
% 1.28/1.60 [2096]~P6(a110,x20965,x20963)+~P7(a110,x20964,x20963)+P6(a110,x20961,x20962)+~P6(a110,f3(a110),x20966)+~P7(a110,f3(a110),x20965)+~P7(a110,f12(a110,f20(f20(f11(a110),x20965),x20961),x20966),f3(a110))+~E(f12(a110,f20(f20(f11(a110),x20963),x20962),x20964),f12(a110,f20(f20(f11(a110),x20965),x20961),x20966))
% 1.28/1.60 %EqnAxiom
% 1.28/1.60 [1]E(x11,x11)
% 1.28/1.60 [2]E(x22,x21)+~E(x21,x22)
% 1.28/1.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.28/1.60 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 1.28/1.60 [5]~E(x51,x52)+E(f13(x51),f13(x52))
% 1.28/1.60 [6]~E(x61,x62)+E(f22(x61,x63),f22(x62,x63))
% 1.28/1.60 [7]~E(x71,x72)+E(f22(x73,x71),f22(x73,x72))
% 1.28/1.60 [8]~E(x81,x82)+E(f4(x81),f4(x82))
% 1.28/1.60 [9]~E(x91,x92)+E(f12(x91,x93,x94),f12(x92,x93,x94))
% 1.28/1.60 [10]~E(x101,x102)+E(f12(x103,x101,x104),f12(x103,x102,x104))
% 1.28/1.60 [11]~E(x111,x112)+E(f12(x113,x114,x111),f12(x113,x114,x112))
% 1.28/1.60 [12]~E(x121,x122)+E(f20(x121,x123),f20(x122,x123))
% 1.28/1.60 [13]~E(x131,x132)+E(f20(x133,x131),f20(x133,x132))
% 1.28/1.60 [14]~E(x141,x142)+E(f11(x141),f11(x142))
% 1.28/1.60 [15]~E(x151,x152)+E(f18(x151),f18(x152))
% 1.28/1.60 [16]~E(x161,x162)+E(f10(x161,x163),f10(x162,x163))
% 1.28/1.60 [17]~E(x171,x172)+E(f10(x173,x171),f10(x173,x172))
% 1.28/1.60 [18]~E(x181,x182)+E(f104(x181,x183,x184),f104(x182,x183,x184))
% 1.28/1.60 [19]~E(x191,x192)+E(f104(x193,x191,x194),f104(x193,x192,x194))
% 1.28/1.60 [20]~E(x201,x202)+E(f104(x203,x204,x201),f104(x203,x204,x202))
% 1.28/1.60 [21]~E(x211,x212)+E(f7(x211,x213,x214),f7(x212,x213,x214))
% 1.28/1.60 [22]~E(x221,x222)+E(f7(x223,x221,x224),f7(x223,x222,x224))
% 1.28/1.60 [23]~E(x231,x232)+E(f7(x233,x234,x231),f7(x233,x234,x232))
% 1.28/1.60 [24]~E(x241,x242)+E(f8(x241,x243,x244),f8(x242,x243,x244))
% 1.28/1.60 [25]~E(x251,x252)+E(f8(x253,x251,x254),f8(x253,x252,x254))
% 1.28/1.60 [26]~E(x261,x262)+E(f8(x263,x264,x261),f8(x263,x264,x262))
% 1.28/1.60 [27]~E(x271,x272)+E(f6(x271,x273,x274),f6(x272,x273,x274))
% 1.28/1.60 [28]~E(x281,x282)+E(f6(x283,x281,x284),f6(x283,x282,x284))
% 1.28/1.60 [29]~E(x291,x292)+E(f6(x293,x294,x291),f6(x293,x294,x292))
% 1.28/1.60 [30]~E(x301,x302)+E(f24(x301,x303,x304),f24(x302,x303,x304))
% 1.28/1.60 [31]~E(x311,x312)+E(f24(x313,x311,x314),f24(x313,x312,x314))
% 1.28/1.60 [32]~E(x321,x322)+E(f24(x323,x324,x321),f24(x323,x324,x322))
% 1.28/1.60 [33]~E(x331,x332)+E(f103(x331,x333,x334),f103(x332,x333,x334))
% 1.28/1.60 [34]~E(x341,x342)+E(f103(x343,x341,x344),f103(x343,x342,x344))
% 1.28/1.60 [35]~E(x351,x352)+E(f103(x353,x354,x351),f103(x353,x354,x352))
% 1.28/1.60 [36]~E(x361,x362)+E(f67(x361,x363,x364,x365),f67(x362,x363,x364,x365))
% 1.28/1.60 [37]~E(x371,x372)+E(f67(x373,x371,x374,x375),f67(x373,x372,x374,x375))
% 1.28/1.60 [38]~E(x381,x382)+E(f67(x383,x384,x381,x385),f67(x383,x384,x382,x385))
% 1.28/1.60 [39]~E(x391,x392)+E(f67(x393,x394,x395,x391),f67(x393,x394,x395,x392))
% 1.28/1.60 [40]~E(x401,x402)+E(f19(x401,x403),f19(x402,x403))
% 1.28/1.60 [41]~E(x411,x412)+E(f19(x413,x411),f19(x413,x412))
% 1.28/1.60 [42]~E(x421,x422)+E(f54(x421),f54(x422))
% 1.28/1.60 [43]~E(x431,x432)+E(f105(x431,x433,x434),f105(x432,x433,x434))
% 1.28/1.60 [44]~E(x441,x442)+E(f105(x443,x441,x444),f105(x443,x442,x444))
% 1.28/1.60 [45]~E(x451,x452)+E(f105(x453,x454,x451),f105(x453,x454,x452))
% 1.28/1.60 [46]~E(x461,x462)+E(f16(x461),f16(x462))
% 1.28/1.60 [47]~E(x471,x472)+E(f113(x471),f113(x472))
% 1.28/1.60 [48]~E(x481,x482)+E(f94(x481,x483,x484),f94(x482,x483,x484))
% 1.28/1.60 [49]~E(x491,x492)+E(f94(x493,x491,x494),f94(x493,x492,x494))
% 1.28/1.60 [50]~E(x501,x502)+E(f94(x503,x504,x501),f94(x503,x504,x502))
% 1.28/1.60 [51]~E(x511,x512)+E(f5(x511,x513),f5(x512,x513))
% 1.28/1.60 [52]~E(x521,x522)+E(f5(x523,x521),f5(x523,x522))
% 1.28/1.60 [53]~E(x531,x532)+E(f76(x531,x533,x534),f76(x532,x533,x534))
% 1.28/1.60 [54]~E(x541,x542)+E(f76(x543,x541,x544),f76(x543,x542,x544))
% 1.28/1.60 [55]~E(x551,x552)+E(f76(x553,x554,x551),f76(x553,x554,x552))
% 1.28/1.60 [56]~E(x561,x562)+E(f102(x561),f102(x562))
% 1.28/1.60 [57]~E(x571,x572)+E(f41(x571),f41(x572))
% 1.28/1.60 [58]~E(x581,x582)+E(f50(x581,x583),f50(x582,x583))
% 1.28/1.60 [59]~E(x591,x592)+E(f50(x593,x591),f50(x593,x592))
% 1.28/1.60 [60]~E(x601,x602)+E(f49(x601,x603),f49(x602,x603))
% 1.28/1.60 [61]~E(x611,x612)+E(f49(x613,x611),f49(x613,x612))
% 1.28/1.60 [62]~E(x621,x622)+E(f69(x621),f69(x622))
% 1.28/1.60 [63]~E(x631,x632)+E(f70(x631,x633),f70(x632,x633))
% 1.28/1.60 [64]~E(x641,x642)+E(f70(x643,x641),f70(x643,x642))
% 1.28/1.60 [65]~E(x651,x652)+E(f116(x651,x653),f116(x652,x653))
% 1.28/1.60 [66]~E(x661,x662)+E(f116(x663,x661),f116(x663,x662))
% 1.28/1.60 [67]~E(x671,x672)+E(f32(x671,x673),f32(x672,x673))
% 1.28/1.60 [68]~E(x681,x682)+E(f32(x683,x681),f32(x683,x682))
% 1.28/1.60 [69]~E(x691,x692)+E(f99(x691,x693,x694),f99(x692,x693,x694))
% 1.28/1.60 [70]~E(x701,x702)+E(f99(x703,x701,x704),f99(x703,x702,x704))
% 1.28/1.60 [71]~E(x711,x712)+E(f99(x713,x714,x711),f99(x713,x714,x712))
% 1.28/1.60 [72]~E(x721,x722)+E(f97(x721,x723),f97(x722,x723))
% 1.28/1.60 [73]~E(x731,x732)+E(f97(x733,x731),f97(x733,x732))
% 1.28/1.60 [74]~E(x741,x742)+E(f88(x741,x743),f88(x742,x743))
% 1.28/1.60 [75]~E(x751,x752)+E(f88(x753,x751),f88(x753,x752))
% 1.28/1.60 [76]~E(x761,x762)+E(f107(x761,x763,x764),f107(x762,x763,x764))
% 1.28/1.60 [77]~E(x771,x772)+E(f107(x773,x771,x774),f107(x773,x772,x774))
% 1.28/1.60 [78]~E(x781,x782)+E(f107(x783,x784,x781),f107(x783,x784,x782))
% 1.28/1.60 [79]~E(x791,x792)+E(f38(x791),f38(x792))
% 1.28/1.60 [80]~E(x801,x802)+E(f92(x801,x803),f92(x802,x803))
% 1.28/1.60 [81]~E(x811,x812)+E(f92(x813,x811),f92(x813,x812))
% 1.28/1.60 [82]~E(x821,x822)+E(f106(x821,x823,x824),f106(x822,x823,x824))
% 1.28/1.60 [83]~E(x831,x832)+E(f106(x833,x831,x834),f106(x833,x832,x834))
% 1.28/1.60 [84]~E(x841,x842)+E(f106(x843,x844,x841),f106(x843,x844,x842))
% 1.28/1.60 [85]~E(x851,x852)+E(f31(x851,x853,x854),f31(x852,x853,x854))
% 1.28/1.60 [86]~E(x861,x862)+E(f31(x863,x861,x864),f31(x863,x862,x864))
% 1.28/1.60 [87]~E(x871,x872)+E(f31(x873,x874,x871),f31(x873,x874,x872))
% 1.28/1.60 [88]~E(x881,x882)+E(f98(x881,x883,x884),f98(x882,x883,x884))
% 1.28/1.60 [89]~E(x891,x892)+E(f98(x893,x891,x894),f98(x893,x892,x894))
% 1.28/1.60 [90]~E(x901,x902)+E(f98(x903,x904,x901),f98(x903,x904,x902))
% 1.28/1.60 [91]~E(x911,x912)+E(f64(x911,x913),f64(x912,x913))
% 1.28/1.60 [92]~E(x921,x922)+E(f64(x923,x921),f64(x923,x922))
% 1.28/1.60 [93]~E(x931,x932)+E(f71(x931,x933,x934,x935),f71(x932,x933,x934,x935))
% 1.28/1.60 [94]~E(x941,x942)+E(f71(x943,x941,x944,x945),f71(x943,x942,x944,x945))
% 1.28/1.60 [95]~E(x951,x952)+E(f71(x953,x954,x951,x955),f71(x953,x954,x952,x955))
% 1.28/1.60 [96]~E(x961,x962)+E(f71(x963,x964,x965,x961),f71(x963,x964,x965,x962))
% 1.28/1.60 [97]~E(x971,x972)+E(f14(x971,x973),f14(x972,x973))
% 1.28/1.60 [98]~E(x981,x982)+E(f14(x983,x981),f14(x983,x982))
% 1.28/1.60 [99]~E(x991,x992)+E(f43(x991),f43(x992))
% 1.28/1.60 [100]~E(x1001,x1002)+E(f80(x1001),f80(x1002))
% 1.28/1.60 [101]~E(x1011,x1012)+E(f56(x1011),f56(x1012))
% 1.28/1.60 [102]~E(x1021,x1022)+E(f61(x1021,x1023),f61(x1022,x1023))
% 1.28/1.60 [103]~E(x1031,x1032)+E(f61(x1033,x1031),f61(x1033,x1032))
% 1.28/1.60 [104]~E(x1041,x1042)+E(f53(x1041,x1043),f53(x1042,x1043))
% 1.28/1.60 [105]~E(x1051,x1052)+E(f53(x1053,x1051),f53(x1053,x1052))
% 1.28/1.60 [106]~E(x1061,x1062)+E(f77(x1061,x1063,x1064),f77(x1062,x1063,x1064))
% 1.28/1.60 [107]~E(x1071,x1072)+E(f77(x1073,x1071,x1074),f77(x1073,x1072,x1074))
% 1.28/1.60 [108]~E(x1081,x1082)+E(f77(x1083,x1084,x1081),f77(x1083,x1084,x1082))
% 1.28/1.60 [109]~E(x1091,x1092)+E(f85(x1091,x1093),f85(x1092,x1093))
% 1.28/1.60 [110]~E(x1101,x1102)+E(f85(x1103,x1101),f85(x1103,x1102))
% 1.28/1.60 [111]~E(x1111,x1112)+E(f55(x1111,x1113),f55(x1112,x1113))
% 1.28/1.60 [112]~E(x1121,x1122)+E(f55(x1123,x1121),f55(x1123,x1122))
% 1.28/1.60 [113]~E(x1131,x1132)+E(f26(x1131,x1133),f26(x1132,x1133))
% 1.28/1.60 [114]~E(x1141,x1142)+E(f26(x1143,x1141),f26(x1143,x1142))
% 1.28/1.60 [115]~E(x1151,x1152)+E(f79(x1151,x1153,x1154),f79(x1152,x1153,x1154))
% 1.28/1.60 [116]~E(x1161,x1162)+E(f79(x1163,x1161,x1164),f79(x1163,x1162,x1164))
% 1.28/1.60 [117]~E(x1171,x1172)+E(f79(x1173,x1174,x1171),f79(x1173,x1174,x1172))
% 1.28/1.60 [118]~E(x1181,x1182)+E(f78(x1181,x1183,x1184),f78(x1182,x1183,x1184))
% 1.28/1.60 [119]~E(x1191,x1192)+E(f78(x1193,x1191,x1194),f78(x1193,x1192,x1194))
% 1.28/1.60 [120]~E(x1201,x1202)+E(f78(x1203,x1204,x1201),f78(x1203,x1204,x1202))
% 1.28/1.60 [121]~E(x1211,x1212)+E(f33(x1211,x1213,x1214),f33(x1212,x1213,x1214))
% 1.28/1.60 [122]~E(x1221,x1222)+E(f33(x1223,x1221,x1224),f33(x1223,x1222,x1224))
% 1.28/1.60 [123]~E(x1231,x1232)+E(f33(x1233,x1234,x1231),f33(x1233,x1234,x1232))
% 1.28/1.60 [124]~E(x1241,x1242)+E(f44(x1241,x1243),f44(x1242,x1243))
% 1.28/1.60 [125]~E(x1251,x1252)+E(f44(x1253,x1251),f44(x1253,x1252))
% 1.28/1.60 [126]~E(x1261,x1262)+E(f47(x1261,x1263,x1264,x1265),f47(x1262,x1263,x1264,x1265))
% 1.28/1.60 [127]~E(x1271,x1272)+E(f47(x1273,x1271,x1274,x1275),f47(x1273,x1272,x1274,x1275))
% 1.28/1.60 [128]~E(x1281,x1282)+E(f47(x1283,x1284,x1281,x1285),f47(x1283,x1284,x1282,x1285))
% 1.28/1.60 [129]~E(x1291,x1292)+E(f47(x1293,x1294,x1295,x1291),f47(x1293,x1294,x1295,x1292))
% 1.28/1.60 [130]~E(x1301,x1302)+E(f90(x1301,x1303),f90(x1302,x1303))
% 1.28/1.60 [131]~E(x1311,x1312)+E(f90(x1313,x1311),f90(x1313,x1312))
% 1.28/1.60 [132]~E(x1321,x1322)+E(f75(x1321,x1323,x1324),f75(x1322,x1323,x1324))
% 1.28/1.60 [133]~E(x1331,x1332)+E(f75(x1333,x1331,x1334),f75(x1333,x1332,x1334))
% 1.28/1.60 [134]~E(x1341,x1342)+E(f75(x1343,x1344,x1341),f75(x1343,x1344,x1342))
% 1.28/1.60 [135]~E(x1351,x1352)+E(f45(x1351,x1353),f45(x1352,x1353))
% 1.28/1.60 [136]~E(x1361,x1362)+E(f45(x1363,x1361),f45(x1363,x1362))
% 1.28/1.60 [137]~E(x1371,x1372)+E(f93(x1371,x1373,x1374),f93(x1372,x1373,x1374))
% 1.28/1.60 [138]~E(x1381,x1382)+E(f93(x1383,x1381,x1384),f93(x1383,x1382,x1384))
% 1.28/1.60 [139]~E(x1391,x1392)+E(f93(x1393,x1394,x1391),f93(x1393,x1394,x1392))
% 1.28/1.60 [140]~E(x1401,x1402)+E(f60(x1401,x1403,x1404),f60(x1402,x1403,x1404))
% 1.28/1.60 [141]~E(x1411,x1412)+E(f60(x1413,x1411,x1414),f60(x1413,x1412,x1414))
% 1.28/1.60 [142]~E(x1421,x1422)+E(f60(x1423,x1424,x1421),f60(x1423,x1424,x1422))
% 1.28/1.60 [143]~E(x1431,x1432)+E(f84(x1431,x1433),f84(x1432,x1433))
% 1.28/1.60 [144]~E(x1441,x1442)+E(f84(x1443,x1441),f84(x1443,x1442))
% 1.28/1.60 [145]~E(x1451,x1452)+E(f35(x1451,x1453,x1454),f35(x1452,x1453,x1454))
% 1.28/1.60 [146]~E(x1461,x1462)+E(f35(x1463,x1461,x1464),f35(x1463,x1462,x1464))
% 1.28/1.60 [147]~E(x1471,x1472)+E(f35(x1473,x1474,x1471),f35(x1473,x1474,x1472))
% 1.28/1.60 [148]~E(x1481,x1482)+E(f17(x1481,x1483,x1484),f17(x1482,x1483,x1484))
% 1.28/1.60 [149]~E(x1491,x1492)+E(f17(x1493,x1491,x1494),f17(x1493,x1492,x1494))
% 1.28/1.60 [150]~E(x1501,x1502)+E(f17(x1503,x1504,x1501),f17(x1503,x1504,x1502))
% 1.28/1.60 [151]~E(x1511,x1512)+E(f83(x1511,x1513),f83(x1512,x1513))
% 1.28/1.60 [152]~E(x1521,x1522)+E(f83(x1523,x1521),f83(x1523,x1522))
% 1.28/1.60 [153]~E(x1531,x1532)+E(f74(x1531,x1533,x1534,x1535),f74(x1532,x1533,x1534,x1535))
% 1.28/1.60 [154]~E(x1541,x1542)+E(f74(x1543,x1541,x1544,x1545),f74(x1543,x1542,x1544,x1545))
% 1.28/1.60 [155]~E(x1551,x1552)+E(f74(x1553,x1554,x1551,x1555),f74(x1553,x1554,x1552,x1555))
% 1.28/1.60 [156]~E(x1561,x1562)+E(f74(x1563,x1564,x1565,x1561),f74(x1563,x1564,x1565,x1562))
% 1.28/1.60 [157]~E(x1571,x1572)+E(f58(x1571,x1573),f58(x1572,x1573))
% 1.28/1.60 [158]~E(x1581,x1582)+E(f58(x1583,x1581),f58(x1583,x1582))
% 1.28/1.60 [159]~E(x1591,x1592)+E(f95(x1591,x1593,x1594),f95(x1592,x1593,x1594))
% 1.28/1.60 [160]~E(x1601,x1602)+E(f95(x1603,x1601,x1604),f95(x1603,x1602,x1604))
% 1.28/1.60 [161]~E(x1611,x1612)+E(f95(x1613,x1614,x1611),f95(x1613,x1614,x1612))
% 1.28/1.60 [162]~E(x1621,x1622)+E(f65(x1621,x1623),f65(x1622,x1623))
% 1.28/1.60 [163]~E(x1631,x1632)+E(f65(x1633,x1631),f65(x1633,x1632))
% 1.28/1.60 [164]~E(x1641,x1642)+E(f87(x1641,x1643),f87(x1642,x1643))
% 1.28/1.60 [165]~E(x1651,x1652)+E(f87(x1653,x1651),f87(x1653,x1652))
% 1.28/1.60 [166]~E(x1661,x1662)+E(f48(x1661,x1663),f48(x1662,x1663))
% 1.28/1.60 [167]~E(x1671,x1672)+E(f48(x1673,x1671),f48(x1673,x1672))
% 1.28/1.60 [168]~E(x1681,x1682)+E(f57(x1681,x1683),f57(x1682,x1683))
% 1.28/1.60 [169]~E(x1691,x1692)+E(f57(x1693,x1691),f57(x1693,x1692))
% 1.28/1.60 [170]~E(x1701,x1702)+E(f52(x1701,x1703),f52(x1702,x1703))
% 1.28/1.60 [171]~E(x1711,x1712)+E(f52(x1713,x1711),f52(x1713,x1712))
% 1.28/1.60 [172]~E(x1721,x1722)+E(f42(x1721,x1723),f42(x1722,x1723))
% 1.28/1.60 [173]~E(x1731,x1732)+E(f42(x1733,x1731),f42(x1733,x1732))
% 1.28/1.60 [174]~E(x1741,x1742)+E(f108(x1741,x1743,x1744),f108(x1742,x1743,x1744))
% 1.28/1.60 [175]~E(x1751,x1752)+E(f108(x1753,x1751,x1754),f108(x1753,x1752,x1754))
% 1.28/1.60 [176]~E(x1761,x1762)+E(f108(x1763,x1764,x1761),f108(x1763,x1764,x1762))
% 1.28/1.60 [177]~E(x1771,x1772)+E(f91(x1771),f91(x1772))
% 1.28/1.60 [178]~E(x1781,x1782)+E(f96(x1781,x1783,x1784),f96(x1782,x1783,x1784))
% 1.28/1.60 [179]~E(x1791,x1792)+E(f96(x1793,x1791,x1794),f96(x1793,x1792,x1794))
% 1.28/1.60 [180]~E(x1801,x1802)+E(f96(x1803,x1804,x1801),f96(x1803,x1804,x1802))
% 1.28/1.60 [181]~E(x1811,x1812)+E(f9(x1811,x1813),f9(x1812,x1813))
% 1.28/1.60 [182]~E(x1821,x1822)+E(f9(x1823,x1821),f9(x1823,x1822))
% 1.28/1.60 [183]~E(x1831,x1832)+E(f25(x1831,x1833),f25(x1832,x1833))
% 1.28/1.60 [184]~E(x1841,x1842)+E(f25(x1843,x1841),f25(x1843,x1842))
% 1.28/1.60 [185]~E(x1851,x1852)+E(f51(x1851),f51(x1852))
% 1.28/1.60 [186]~E(x1861,x1862)+E(f73(x1861,x1863),f73(x1862,x1863))
% 1.28/1.60 [187]~E(x1871,x1872)+E(f73(x1873,x1871),f73(x1873,x1872))
% 1.28/1.60 [188]~E(x1881,x1882)+E(f40(x1881,x1883),f40(x1882,x1883))
% 1.28/1.60 [189]~E(x1891,x1892)+E(f40(x1893,x1891),f40(x1893,x1892))
% 1.28/1.60 [190]~E(x1901,x1902)+E(f66(x1901,x1903),f66(x1902,x1903))
% 1.28/1.60 [191]~E(x1911,x1912)+E(f66(x1913,x1911),f66(x1913,x1912))
% 1.28/1.60 [192]~E(x1921,x1922)+E(f27(x1921,x1923),f27(x1922,x1923))
% 1.28/1.60 [193]~E(x1931,x1932)+E(f27(x1933,x1931),f27(x1933,x1932))
% 1.28/1.60 [194]~E(x1941,x1942)+E(f89(x1941,x1943,x1944),f89(x1942,x1943,x1944))
% 1.28/1.60 [195]~E(x1951,x1952)+E(f89(x1953,x1951,x1954),f89(x1953,x1952,x1954))
% 1.28/1.60 [196]~E(x1961,x1962)+E(f89(x1963,x1964,x1961),f89(x1963,x1964,x1962))
% 1.28/1.60 [197]~E(x1971,x1972)+E(f59(x1971,x1973,x1974),f59(x1972,x1973,x1974))
% 1.28/1.60 [198]~E(x1981,x1982)+E(f59(x1983,x1981,x1984),f59(x1983,x1982,x1984))
% 1.28/1.60 [199]~E(x1991,x1992)+E(f59(x1993,x1994,x1991),f59(x1993,x1994,x1992))
% 1.28/1.60 [200]~E(x2001,x2002)+E(f82(x2001),f82(x2002))
% 1.28/1.60 [201]~E(x2011,x2012)+E(f101(x2011),f101(x2012))
% 1.28/1.60 [202]~E(x2021,x2022)+E(f100(x2021),f100(x2022))
% 1.28/1.60 [203]~E(x2031,x2032)+E(f81(x2031),f81(x2032))
% 1.28/1.60 [204]~E(x2041,x2042)+E(f34(x2041,x2043),f34(x2042,x2043))
% 1.28/1.60 [205]~E(x2051,x2052)+E(f34(x2053,x2051),f34(x2053,x2052))
% 1.28/1.60 [206]~E(x2061,x2062)+E(f68(x2061,x2063),f68(x2062,x2063))
% 1.28/1.60 [207]~E(x2071,x2072)+E(f68(x2073,x2071),f68(x2073,x2072))
% 1.28/1.60 [208]~E(x2081,x2082)+E(f62(x2081,x2083),f62(x2082,x2083))
% 1.28/1.60 [209]~E(x2091,x2092)+E(f62(x2093,x2091),f62(x2093,x2092))
% 1.28/1.60 [210]~E(x2101,x2102)+E(f72(x2101,x2103,x2104),f72(x2102,x2103,x2104))
% 1.28/1.60 [211]~E(x2111,x2112)+E(f72(x2113,x2111,x2114),f72(x2113,x2112,x2114))
% 1.28/1.60 [212]~E(x2121,x2122)+E(f72(x2123,x2124,x2121),f72(x2123,x2124,x2122))
% 1.28/1.60 [213]~E(x2131,x2132)+E(f30(x2131,x2133),f30(x2132,x2133))
% 1.28/1.60 [214]~E(x2141,x2142)+E(f30(x2143,x2141),f30(x2143,x2142))
% 1.28/1.60 [215]~E(x2151,x2152)+E(f86(x2151,x2153),f86(x2152,x2153))
% 1.28/1.60 [216]~E(x2161,x2162)+E(f86(x2163,x2161),f86(x2163,x2162))
% 1.28/1.60 [217]~E(x2171,x2172)+E(f63(x2171,x2173,x2174),f63(x2172,x2173,x2174))
% 1.28/1.60 [218]~E(x2181,x2182)+E(f63(x2183,x2181,x2184),f63(x2183,x2182,x2184))
% 1.28/1.60 [219]~E(x2191,x2192)+E(f63(x2193,x2194,x2191),f63(x2193,x2194,x2192))
% 1.28/1.60 [220]~E(x2201,x2202)+E(f15(x2201,x2203,x2204),f15(x2202,x2203,x2204))
% 1.28/1.60 [221]~E(x2211,x2212)+E(f15(x2213,x2211,x2214),f15(x2213,x2212,x2214))
% 1.28/1.60 [222]~E(x2221,x2222)+E(f15(x2223,x2224,x2221),f15(x2223,x2224,x2222))
% 1.28/1.61 [223]~E(x2231,x2232)+E(f36(x2231,x2233),f36(x2232,x2233))
% 1.28/1.61 [224]~E(x2241,x2242)+E(f36(x2243,x2241),f36(x2243,x2242))
% 1.28/1.61 [225]~E(x2251,x2252)+E(f37(x2251,x2253,x2254),f37(x2252,x2253,x2254))
% 1.28/1.61 [226]~E(x2261,x2262)+E(f37(x2263,x2261,x2264),f37(x2263,x2262,x2264))
% 1.28/1.61 [227]~E(x2271,x2272)+E(f37(x2273,x2274,x2271),f37(x2273,x2274,x2272))
% 1.28/1.61 [228]~P1(x2281)+P1(x2282)+~E(x2281,x2282)
% 1.28/1.61 [229]P6(x2292,x2293,x2294)+~E(x2291,x2292)+~P6(x2291,x2293,x2294)
% 1.28/1.61 [230]P6(x2303,x2302,x2304)+~E(x2301,x2302)+~P6(x2303,x2301,x2304)
% 1.28/1.61 [231]P6(x2313,x2314,x2312)+~E(x2311,x2312)+~P6(x2313,x2314,x2311)
% 1.28/1.61 [232]~P2(x2321)+P2(x2322)+~E(x2321,x2322)
% 1.28/1.61 [233]~P12(x2331)+P12(x2332)+~E(x2331,x2332)
% 1.28/1.61 [234]P7(x2342,x2343,x2344)+~E(x2341,x2342)+~P7(x2341,x2343,x2344)
% 1.28/1.61 [235]P7(x2353,x2352,x2354)+~E(x2351,x2352)+~P7(x2353,x2351,x2354)
% 1.28/1.61 [236]P7(x2363,x2364,x2362)+~E(x2361,x2362)+~P7(x2363,x2364,x2361)
% 1.28/1.61 [237]~P13(x2371)+P13(x2372)+~E(x2371,x2372)
% 1.28/1.61 [238]~P14(x2381)+P14(x2382)+~E(x2381,x2382)
% 1.28/1.61 [239]~P77(x2391)+P77(x2392)+~E(x2391,x2392)
% 1.28/1.61 [240]~P48(x2401)+P48(x2402)+~E(x2401,x2402)
% 1.28/1.61 [241]~P3(x2411)+P3(x2412)+~E(x2411,x2412)
% 1.28/1.61 [242]~P42(x2421)+P42(x2422)+~E(x2421,x2422)
% 1.28/1.61 [243]~P23(x2431)+P23(x2432)+~E(x2431,x2432)
% 1.28/1.61 [244]~P62(x2441)+P62(x2442)+~E(x2441,x2442)
% 1.28/1.61 [245]~P45(x2451)+P45(x2452)+~E(x2451,x2452)
% 1.28/1.61 [246]~P27(x2461)+P27(x2462)+~E(x2461,x2462)
% 1.28/1.61 [247]~P24(x2471)+P24(x2472)+~E(x2471,x2472)
% 1.28/1.61 [248]~P35(x2481)+P35(x2482)+~E(x2481,x2482)
% 1.28/1.61 [249]~P41(x2491)+P41(x2492)+~E(x2491,x2492)
% 1.28/1.61 [250]P79(x2502,x2503,x2504)+~E(x2501,x2502)+~P79(x2501,x2503,x2504)
% 1.28/1.61 [251]P79(x2513,x2512,x2514)+~E(x2511,x2512)+~P79(x2513,x2511,x2514)
% 1.28/1.61 [252]P79(x2523,x2524,x2522)+~E(x2521,x2522)+~P79(x2523,x2524,x2521)
% 1.28/1.61 [253]~P46(x2531)+P46(x2532)+~E(x2531,x2532)
% 1.28/1.61 [254]~P39(x2541)+P39(x2542)+~E(x2541,x2542)
% 1.28/1.61 [255]~P33(x2551)+P33(x2552)+~E(x2551,x2552)
% 1.28/1.61 [256]P78(x2562,x2563,x2564)+~E(x2561,x2562)+~P78(x2561,x2563,x2564)
% 1.28/1.61 [257]P78(x2573,x2572,x2574)+~E(x2571,x2572)+~P78(x2573,x2571,x2574)
% 1.28/1.61 [258]P78(x2583,x2584,x2582)+~E(x2581,x2582)+~P78(x2583,x2584,x2581)
% 1.28/1.61 [259]P8(x2592,x2593)+~E(x2591,x2592)+~P8(x2591,x2593)
% 1.28/1.61 [260]P8(x2603,x2602)+~E(x2601,x2602)+~P8(x2603,x2601)
% 1.28/1.61 [261]~P4(x2611)+P4(x2612)+~E(x2611,x2612)
% 1.28/1.61 [262]~P52(x2621)+P52(x2622)+~E(x2621,x2622)
% 1.28/1.61 [263]~P57(x2631)+P57(x2632)+~E(x2631,x2632)
% 1.28/1.61 [264]~P15(x2641)+P15(x2642)+~E(x2641,x2642)
% 1.28/1.61 [265]~P21(x2651)+P21(x2652)+~E(x2651,x2652)
% 1.28/1.61 [266]~P74(x2661)+P74(x2662)+~E(x2661,x2662)
% 1.28/1.61 [267]~P43(x2671)+P43(x2672)+~E(x2671,x2672)
% 1.28/1.61 [268]~P17(x2681)+P17(x2682)+~E(x2681,x2682)
% 1.28/1.61 [269]~P11(x2691)+P11(x2692)+~E(x2691,x2692)
% 1.28/1.61 [270]~P61(x2701)+P61(x2702)+~E(x2701,x2702)
% 1.28/1.61 [271]~P5(x2711)+P5(x2712)+~E(x2711,x2712)
% 1.28/1.61 [272]~P18(x2721)+P18(x2722)+~E(x2721,x2722)
% 1.28/1.61 [273]~P56(x2731)+P56(x2732)+~E(x2731,x2732)
% 1.28/1.61 [274]~P44(x2741)+P44(x2742)+~E(x2741,x2742)
% 1.28/1.61 [275]~P30(x2751)+P30(x2752)+~E(x2751,x2752)
% 1.28/1.61 [276]~P25(x2761)+P25(x2762)+~E(x2761,x2762)
% 1.28/1.61 [277]~P19(x2771)+P19(x2772)+~E(x2771,x2772)
% 1.28/1.61 [278]~P54(x2781)+P54(x2782)+~E(x2781,x2782)
% 1.28/1.61 [279]~P31(x2791)+P31(x2792)+~E(x2791,x2792)
% 1.28/1.61 [280]~P26(x2801)+P26(x2802)+~E(x2801,x2802)
% 1.28/1.61 [281]~P68(x2811)+P68(x2812)+~E(x2811,x2812)
% 1.28/1.61 [282]~P60(x2821)+P60(x2822)+~E(x2821,x2822)
% 1.28/1.61 [283]~P69(x2831)+P69(x2832)+~E(x2831,x2832)
% 1.28/1.61 [284]~P32(x2841)+P32(x2842)+~E(x2841,x2842)
% 1.28/1.61 [285]~P72(x2851)+P72(x2852)+~E(x2851,x2852)
% 1.28/1.61 [286]~P28(x2861)+P28(x2862)+~E(x2861,x2862)
% 1.28/1.61 [287]~P49(x2871)+P49(x2872)+~E(x2871,x2872)
% 1.28/1.61 [288]~P67(x2881)+P67(x2882)+~E(x2881,x2882)
% 1.28/1.61 [289]~P16(x2891)+P16(x2892)+~E(x2891,x2892)
% 1.28/1.61 [290]~P29(x2901)+P29(x2902)+~E(x2901,x2902)
% 1.28/1.61 [291]~P63(x2911)+P63(x2912)+~E(x2911,x2912)
% 1.28/1.61 [292]~P51(x2921)+P51(x2922)+~E(x2921,x2922)
% 1.28/1.61 [293]~P73(x2931)+P73(x2932)+~E(x2931,x2932)
% 1.28/1.61 [294]~P75(x2941)+P75(x2942)+~E(x2941,x2942)
% 1.28/1.61 [295]~P65(x2951)+P65(x2952)+~E(x2951,x2952)
% 1.28/1.61 [296]~P55(x2961)+P55(x2962)+~E(x2961,x2962)
% 1.28/1.61 [297]~P34(x2971)+P34(x2972)+~E(x2971,x2972)
% 1.28/1.61 [298]~P47(x2981)+P47(x2982)+~E(x2981,x2982)
% 1.28/1.61 [299]~P58(x2991)+P58(x2992)+~E(x2991,x2992)
% 1.28/1.61 [300]~P66(x3001)+P66(x3002)+~E(x3001,x3002)
% 1.28/1.61 [301]~P50(x3011)+P50(x3012)+~E(x3011,x3012)
% 1.28/1.61 [302]~P36(x3021)+P36(x3022)+~E(x3021,x3022)
% 1.28/1.61 [303]~P37(x3031)+P37(x3032)+~E(x3031,x3032)
% 1.28/1.61 [304]~P64(x3041)+P64(x3042)+~E(x3041,x3042)
% 1.28/1.61 [305]~P53(x3051)+P53(x3052)+~E(x3051,x3052)
% 1.28/1.61 [306]P9(x3062,x3063)+~E(x3061,x3062)+~P9(x3061,x3063)
% 1.28/1.61 [307]P9(x3073,x3072)+~E(x3071,x3072)+~P9(x3073,x3071)
% 1.28/1.61 [308]~P20(x3081)+P20(x3082)+~E(x3081,x3082)
% 1.28/1.61 [309]~P76(x3091)+P76(x3092)+~E(x3091,x3092)
% 1.28/1.61 [310]~P71(x3101)+P71(x3102)+~E(x3101,x3102)
% 1.28/1.61 [311]~P59(x3111)+P59(x3112)+~E(x3111,x3112)
% 1.28/1.61 [312]P10(x3122,x3123)+~E(x3121,x3122)+~P10(x3121,x3123)
% 1.28/1.61 [313]P10(x3133,x3132)+~E(x3131,x3132)+~P10(x3133,x3131)
% 1.28/1.61 [314]~P40(x3141)+P40(x3142)+~E(x3141,x3142)
% 1.28/1.61 [315]~P70(x3151)+P70(x3152)+~E(x3151,x3152)
% 1.28/1.61 [316]~P38(x3161)+P38(x3162)+~E(x3161,x3162)
% 1.28/1.61 [317]~P22(x3171)+P22(x3172)+~E(x3171,x3172)
% 1.28/1.61
% 1.28/1.61 %-------------------------------------------
% 1.28/1.61 cnf(2115,plain,
% 1.28/1.61 ($false),
% 1.28/1.61 inference(scs_inference,[],[672,581,668,2109]),
% 1.28/1.61 ['proof']).
% 1.28/1.61 % SZS output end Proof
% 1.28/1.61 % Total time :0.190000s
%------------------------------------------------------------------------------