TSTP Solution File: SWW232+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW232+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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:15 EDT 2023
% Result : Theorem 12.04s 12.16s
% Output : CNFRefutation 12.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW232+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 18:08:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.55 start to proof:theBenchmark
% 11.88/12.09 %-------------------------------------------
% 11.88/12.09 % File :CSE---1.6
% 11.88/12.09 % Problem :theBenchmark
% 11.88/12.09 % Transform :cnf
% 11.88/12.09 % Format :tptp:raw
% 11.88/12.09 % Command :java -jar mcs_scs.jar %d %s
% 11.88/12.09
% 11.88/12.09 % Result :Theorem 10.920000s
% 11.88/12.09 % Output :CNFRefutation 10.920000s
% 11.88/12.09 %-------------------------------------------
% 11.88/12.10 %------------------------------------------------------------------------------
% 11.88/12.10 % File : SWW232+1 : TPTP v8.1.2. Released v5.2.0.
% 11.88/12.10 % Domain : Software Verification
% 11.88/12.10 % Problem : Fundamental Theorem of Algebra 437571, 1000 axioms selected
% 11.88/12.10 % Version : Especial.
% 11.88/12.10 % English :
% 11.88/12.10
% 11.88/12.10 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 11.88/12.10 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 11.88/12.10 % Source : [Bla11]
% 11.88/12.10 % Names : fta_437571.1000.p [Bla11]
% 11.88/12.10
% 11.88/12.10 % Status : Theorem
% 11.88/12.10 % Rating : 0.44 v8.1.0, 0.42 v7.5.0, 0.38 v7.4.0, 0.47 v7.3.0, 0.45 v7.2.0, 0.41 v7.1.0, 0.39 v7.0.0, 0.43 v6.4.0, 0.46 v6.3.0, 0.50 v6.2.0, 0.56 v6.1.0, 0.57 v6.0.0, 0.65 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.70 v5.2.0
% 11.88/12.10 % Syntax : Number of formulae : 1254 ( 340 unt; 0 def)
% 11.88/12.10 % Number of atoms : 2990 ( 729 equ)
% 11.88/12.10 % Maximal formula atoms : 7 ( 2 avg)
% 11.88/12.10 % Number of connectives : 1921 ( 185 ~; 66 |; 115 &)
% 11.88/12.10 % ( 250 <=>;1305 =>; 0 <=; 0 <~>)
% 11.88/12.10 % Maximal formula depth : 13 ( 5 avg)
% 11.88/12.10 % Maximal term depth : 8 ( 2 avg)
% 11.88/12.10 % Number of predicates : 69 ( 68 usr; 1 prp; 0-3 aty)
% 11.88/12.10 % Number of functors : 41 ( 41 usr; 11 con; 0-5 aty)
% 11.88/12.10 % Number of variables : 2837 (2807 !; 30 ?)
% 11.88/12.10 % SPC : FOF_THM_RFO_SEQ
% 11.88/12.10
% 11.88/12.10 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 11.88/12.10 % 2011-03-01 11:42:19
% 11.88/12.10 %------------------------------------------------------------------------------
% 11.88/12.10 %----Relevant facts (995)
% 11.88/12.10 fof(fact_ext,axiom,
% 11.88/12.10 ! [V_g_2,V_f_2] :
% 11.88/12.10 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 11.88/12.10 => V_f_2 = V_g_2 ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_H,axiom,
% 11.88/12.10 v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_pCons_Oprems,axiom,
% 11.88/12.10 c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_pCons_Ohyps,axiom,
% 11.88/12.10 ! [V_a,V_d] :
% 11.88/12.10 ( v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 11.88/12.10 => ? [B_r] :
% 11.88/12.10 ! [B_z] :
% 11.88/12.10 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z))
% 11.88/12.10 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_d,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,V_a,v_cs____)),B_z))) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_assms,axiom,
% 11.88/12.10 v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_norm__triangle__ineq,axiom,
% 11.88/12.10 ! [V_y,V_x,T_a] :
% 11.88/12.10 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.10 => 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))) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_order__refl,axiom,
% 11.88/12.10 ! [V_x,T_a] :
% 11.88/12.10 ( class_Orderings_Opreorder(T_a)
% 11.88/12.10 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_poly__add,axiom,
% 11.88/12.10 ! [V_x,V_q,V_p,T_a] :
% 11.88/12.10 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.10 => 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)) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add__pCons,axiom,
% 11.88/12.10 ! [V_q,V_b,V_p,V_a,T_a] :
% 11.88/12.10 ( class_Groups_Ocomm__monoid__add(T_a)
% 11.88/12.10 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_real__add__left__mono,axiom,
% 11.88/12.10 ! [V_z,V_y,V_x] :
% 11.88/12.10 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 11.88/12.10 => 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)) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add__le__cancel__right,axiom,
% 11.88/12.10 ! [V_b_2,V_ca_2,V_ab_2,T_a] :
% 11.88/12.10 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 11.88/12.10 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
% 11.88/12.10 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add__le__cancel__left,axiom,
% 11.88/12.10 ! [V_b_2,V_ab_2,V_ca_2,T_a] :
% 11.88/12.10 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 11.88/12.10 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
% 11.88/12.10 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add__right__mono,axiom,
% 11.88/12.10 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.10 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 11.88/12.10 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 11.88/12.10 => 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)) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add__left__mono,axiom,
% 11.88/12.10 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.10 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 11.88/12.10 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 11.88/12.10 => 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)) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add__mono,axiom,
% 11.88/12.10 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.88/12.10 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 11.88/12.10 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 11.88/12.10 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 11.88/12.10 => 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)) ) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_norm__zero,axiom,
% 11.88/12.10 ! [T_a] :
% 11.88/12.10 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.10 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_pCons__0__0,axiom,
% 11.88/12.10 ! [T_a] :
% 11.88/12.10 ( class_Groups_Ozero(T_a)
% 11.88/12.10 => c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_poly__0,axiom,
% 11.88/12.10 ! [V_x,T_a] :
% 11.88/12.10 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.10 => 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) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add__poly__code_I1_J,axiom,
% 11.88/12.10 ! [V_q,T_a] :
% 11.88/12.10 ( class_Groups_Ocomm__monoid__add(T_a)
% 11.88/12.10 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_zero__reorient,axiom,
% 11.88/12.10 ! [V_x_2,T_a] :
% 11.88/12.10 ( class_Groups_Ozero(T_a)
% 11.88/12.10 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 11.88/12.10 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add__poly__code_I2_J,axiom,
% 11.88/12.10 ! [V_p,T_a] :
% 11.88/12.10 ( class_Groups_Ocomm__monoid__add(T_a)
% 11.88/12.10 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_norm__eq__zero,axiom,
% 11.88/12.10 ! [V_x_2,T_a] :
% 11.88/12.10 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.10 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 11.88/12.10 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_pCons__eq__0__iff,axiom,
% 11.88/12.10 ! [V_pa_2,V_ab_2,T_a] :
% 11.88/12.10 ( class_Groups_Ozero(T_a)
% 11.88/12.10 => ( c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 11.88/12.10 <=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.10 & V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 11.88/12.10
% 11.88/12.10 fof(fact_add_Ocomm__neutral,axiom,
% 11.88/12.10 ! [V_a,T_a] :
% 11.88/12.11 ( class_Groups_Ocomm__monoid__add(T_a)
% 11.88/12.11 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__0__right,axiom,
% 11.88/12.11 ! [V_a,T_a] :
% 11.88/12.11 ( class_Groups_Omonoid__add(T_a)
% 11.88/12.11 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_double__zero__sym,axiom,
% 11.88/12.11 ! [V_ab_2,T_a] :
% 11.88/12.11 ( class_Groups_Olinordered__ab__group__add(T_a)
% 11.88/12.11 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2)
% 11.88/12.11 <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__0,axiom,
% 11.88/12.11 ! [V_a,T_a] :
% 11.88/12.11 ( class_Groups_Ocomm__monoid__add(T_a)
% 11.88/12.11 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__0__left,axiom,
% 11.88/12.11 ! [V_a,T_a] :
% 11.88/12.11 ( class_Groups_Omonoid__add(T_a)
% 11.88/12.11 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_norm__le__zero__iff,axiom,
% 11.88/12.11 ! [V_x_2,T_a] :
% 11.88/12.11 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.11 => ( 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))
% 11.88/12.11 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_poly__zero,axiom,
% 11.88/12.11 ! [V_pa_2,T_a] :
% 11.88/12.11 ( ( class_Int_Oring__char__0(T_a)
% 11.88/12.11 & class_Rings_Oidom(T_a) )
% 11.88/12.11 => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 11.88/12.11 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__nonpos__nonpos,axiom,
% 11.88/12.11 ! [V_b,V_a,T_a] :
% 11.88/12.11 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 11.88/12.11 => 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)) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__increasing2,axiom,
% 11.88/12.11 ! [V_a,V_b,V_c,T_a] :
% 11.88/12.11 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__increasing,axiom,
% 11.88/12.11 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.11 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__nonneg__eq__0__iff,axiom,
% 11.88/12.11 ! [V_y_2,V_x_2,T_a] :
% 11.88/12.11 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 11.88/12.11 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.11 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.11 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__nonneg__nonneg,axiom,
% 11.88/12.11 ! [V_b,V_a,T_a] :
% 11.88/12.11 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 11.88/12.11 => 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)) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 11.88/12.11 ! [V_ab_2,T_a] :
% 11.88/12.11 ( class_Groups_Olinordered__ab__group__add(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
% 11.88/12.11 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 11.88/12.11 ! [V_ab_2,T_a] :
% 11.88/12.11 ( class_Groups_Olinordered__ab__group__add(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2))
% 11.88/12.11 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_linorder__le__cases,axiom,
% 11.88/12.11 ! [V_y,V_x,T_a] :
% 11.88/12.11 ( class_Orderings_Olinorder(T_a)
% 11.88/12.11 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_le__funE,axiom,
% 11.88/12.11 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 11.88/12.11 ( class_Orderings_Oord(T_b)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_xt1_I6_J,axiom,
% 11.88/12.11 ! [V_z,V_x,V_y,T_a] :
% 11.88/12.11 ( class_Orderings_Oorder(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_xt1_I5_J,axiom,
% 11.88/12.11 ! [V_x,V_y,T_a] :
% 11.88/12.11 ( class_Orderings_Oorder(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 11.88/12.11 => V_x = V_y ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_order__trans,axiom,
% 11.88/12.11 ! [V_z,V_y,V_x,T_a] :
% 11.88/12.11 ( class_Orderings_Opreorder(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_order__antisym,axiom,
% 11.88/12.11 ! [V_y,V_x,T_a] :
% 11.88/12.11 ( class_Orderings_Oorder(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 11.88/12.11 => V_x = V_y ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_xt1_I4_J,axiom,
% 11.88/12.11 ! [V_c,V_a,V_b,T_a] :
% 11.88/12.11 ( class_Orderings_Oorder(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 11.88/12.11 => ( V_b = V_c
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_ord__le__eq__trans,axiom,
% 11.88/12.11 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.11 ( class_Orderings_Oord(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 11.88/12.11 => ( V_b = V_c
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_xt1_I3_J,axiom,
% 11.88/12.11 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.11 ( class_Orderings_Oorder(T_a)
% 11.88/12.11 => ( V_a = V_b
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_ord__eq__le__trans,axiom,
% 11.88/12.11 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.11 ( class_Orderings_Oord(T_a)
% 11.88/12.11 => ( V_a = V_b
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_order__antisym__conv,axiom,
% 11.88/12.11 ! [V_x_2,V_y_2,T_a] :
% 11.88/12.11 ( class_Orderings_Oorder(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 11.88/12.11 <=> V_x_2 = V_y_2 ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_le__funD,axiom,
% 11.88/12.11 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 11.88/12.11 ( class_Orderings_Oord(T_b)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_order__eq__refl,axiom,
% 11.88/12.11 ! [V_y,V_x,T_a] :
% 11.88/12.11 ( class_Orderings_Opreorder(T_a)
% 11.88/12.11 => ( V_x = V_y
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_order__eq__iff,axiom,
% 11.88/12.11 ! [V_y_2,V_x_2,T_a] :
% 11.88/12.11 ( class_Orderings_Oorder(T_a)
% 11.88/12.11 => ( V_x_2 = V_y_2
% 11.88/12.11 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 11.88/12.11 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_linorder__linear,axiom,
% 11.88/12.11 ! [V_y,V_x,T_a] :
% 11.88/12.11 ( class_Orderings_Olinorder(T_a)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 11.88/12.11 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_le__fun__def,axiom,
% 11.88/12.11 ! [V_g_2,V_f_2,T_a,T_b] :
% 11.88/12.11 ( class_Orderings_Oord(T_b)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 11.88/12.11 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_complex__mod__triangle__sub,axiom,
% 11.88/12.11 ! [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))) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__right__imp__eq,axiom,
% 11.88/12.11 ! [V_c,V_a,V_b,T_a] :
% 11.88/12.11 ( class_Groups_Ocancel__semigroup__add(T_a)
% 11.88/12.11 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 11.88/12.11 => V_b = V_c ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__imp__eq,axiom,
% 11.88/12.11 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.11 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 11.88/12.11 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 11.88/12.11 => V_b = V_c ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__left__imp__eq,axiom,
% 11.88/12.11 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.11 ( class_Groups_Ocancel__semigroup__add(T_a)
% 11.88/12.11 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 11.88/12.11 => V_b = V_c ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__right__cancel,axiom,
% 11.88/12.11 ! [V_ca_2,V_ab_2,V_b_2,T_a] :
% 11.88/12.11 ( class_Groups_Ocancel__semigroup__add(T_a)
% 11.88/12.11 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2)
% 11.88/12.11 <=> V_b_2 = V_ca_2 ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__left__cancel,axiom,
% 11.88/12.11 ! [V_ca_2,V_b_2,V_ab_2,T_a] :
% 11.88/12.11 ( class_Groups_Ocancel__semigroup__add(T_a)
% 11.88/12.11 => ( c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2)
% 11.88/12.11 <=> V_b_2 = V_ca_2 ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 11.88/12.11 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.11 ( class_Groups_Oab__semigroup__add(T_a)
% 11.88/12.11 => 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)) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_real__le__antisym,axiom,
% 11.88/12.11 ! [V_w,V_z] :
% 11.88/12.11 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 11.88/12.11 => V_z = V_w ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_real__le__trans,axiom,
% 11.88/12.11 ! [V_k,V_j,V_i] :
% 11.88/12.11 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 11.88/12.11 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_real__le__linear,axiom,
% 11.88/12.11 ! [V_w,V_z] :
% 11.88/12.11 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 11.88/12.11 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_real__le__refl,axiom,
% 11.88/12.11 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_pCons__eq__iff,axiom,
% 11.88/12.11 ! [V_q_2,V_b_2,V_pa_2,V_ab_2,T_a] :
% 11.88/12.11 ( class_Groups_Ozero(T_a)
% 11.88/12.11 => ( c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) = c_Polynomial_OpCons(T_a,V_b_2,V_q_2)
% 11.88/12.11 <=> ( V_ab_2 = V_b_2
% 11.88/12.11 & V_pa_2 = V_q_2 ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_poly__eq__iff,axiom,
% 11.88/12.11 ! [V_q_2,V_pa_2,T_a] :
% 11.88/12.11 ( ( class_Int_Oring__char__0(T_a)
% 11.88/12.11 & class_Rings_Oidom(T_a) )
% 11.88/12.11 => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
% 11.88/12.11 <=> V_pa_2 = V_q_2 ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__le__imp__le__left,axiom,
% 11.88/12.11 ! [V_b,V_a,V_c,T_a] :
% 11.88/12.11 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 11.88/12.11 => ( 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))
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_add__le__imp__le__right,axiom,
% 11.88/12.11 ! [V_b,V_c,V_a,T_a] :
% 11.88/12.11 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 11.88/12.11 => ( 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))
% 11.88/12.11 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_order__root,axiom,
% 11.88/12.11 ! [V_ab_2,V_pa_2,T_a] :
% 11.88/12.11 ( class_Rings_Oidom(T_a)
% 11.88/12.11 => ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.11 <=> ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 11.88/12.11 | c_Polynomial_Oorder(T_a,V_ab_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 11.88/12.11
% 11.88/12.11 fof(fact_double__eq__0__iff,axiom,
% 11.88/12.11 ! [V_ab_2,T_a] :
% 11.88/12.11 ( class_Groups_Olinordered__ab__group__add(T_a)
% 11.88/12.12 => ( c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.12 <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_add__0__iff,axiom,
% 11.88/12.12 ! [V_ab_2,V_b_2,T_a] :
% 11.88/12.12 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 11.88/12.12 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2)
% 11.88/12.12 <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 11.88/12.12 ! [V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 11.88/12.12 ! [V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_poly__rec__pCons,axiom,
% 11.88/12.12 ! [V_pa_2,V_ab_2,T_a,V_z_2,V_f_2,T_b] :
% 11.88/12.12 ( class_Groups_Ozero(T_b)
% 11.88/12.12 => ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
% 11.88/12.12 => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_ab_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_ab_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_poly__rec_Osimps,axiom,
% 11.88/12.12 ! [V_pa_2,V_ab_2,V_f_2,V_z_2,T_a,T_b] :
% 11.88/12.12 ( class_Groups_Ozero(T_b)
% 11.88/12.12 => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_ab_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_ab_2),V_pa_2),c_If(T_a,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_poly__minimum__modulus__disc,axiom,
% 11.88/12.12 ! [V_p,V_r] :
% 11.88/12.12 ? [B_z] :
% 11.88/12.12 ! [B_w] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_w),V_r)
% 11.88/12.12 => 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))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_offset__poly__single,axiom,
% 11.88/12.12 ! [V_h,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_poly__rec__0,axiom,
% 11.88/12.12 ! [T_a,V_z_2,V_f_2,T_b] :
% 11.88/12.12 ( class_Groups_Ozero(T_b)
% 11.88/12.12 => ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
% 11.88/12.12 => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2 ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_synthetic__div__pCons,axiom,
% 11.88/12.12 ! [V_c,V_p,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_poly__offset__poly,axiom,
% 11.88/12.12 ! [V_x,V_h,V_p,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_synthetic__div__0,axiom,
% 11.88/12.12 ! [V_c,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_norm__ge__zero,axiom,
% 11.88/12.12 ! [V_x,T_a] :
% 11.88/12.12 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_offset__poly__eq__0__iff,axiom,
% 11.88/12.12 ! [V_h_2,V_pa_2,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pa_2,V_h_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 11.88/12.12 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_offset__poly__0,axiom,
% 11.88/12.12 ! [V_h,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 11.88/12.12 ! [V_c,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 11.88/12.12 ! [V_d,V_c,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 11.88/12.12 ! [V_d,V_c,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 11.88/12.12 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 11.88/12.12 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 11.88/12.12 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_psize__eq__0__iff,axiom,
% 11.88/12.12 ! [V_pa_2,T_a] :
% 11.88/12.12 ( class_Groups_Ozero(T_a)
% 11.88/12.12 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.88/12.12 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le0,axiom,
% 11.88/12.12 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_synthetic__div__correct,axiom,
% 11.88/12.12 ! [V_c,V_p,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_synthetic__div__unique,axiom,
% 11.88/12.12 ! [V_r,V_q,V_c,V_p,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q)) = c_Polynomial_OpCons(T_a,V_r,V_q)
% 11.88/12.12 => ( V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)
% 11.88/12.12 & V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c) ) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_monom__0,axiom,
% 11.88/12.12 ! [V_a,T_a] :
% 11.88/12.12 ( class_Groups_Ozero(T_a)
% 11.88/12.12 => c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_norm__diff__triangle__ineq,axiom,
% 11.88/12.12 ! [V_d,V_c,V_b,V_a,T_a] :
% 11.88/12.12 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.12 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_offset__poly__pCons,axiom,
% 11.88/12.12 ! [V_h,V_p,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_offset__poly__eq__0__lemma,axiom,
% 11.88/12.12 ! [V_a,V_p,V_c,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 11.88/12.12 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_poly__pCons,axiom,
% 11.88/12.12 ! [V_x,V_p,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 11.88/12.12 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__refl,axiom,
% 11.88/12.12 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__square,axiom,
% 11.88/12.12 ! [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)) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__add2,axiom,
% 11.88/12.12 ! [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)) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__add1,axiom,
% 11.88/12.12 ! [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)) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__cube,axiom,
% 11.88/12.12 ! [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))) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__le__self,axiom,
% 11.88/12.12 ! [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) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__iff__add,axiom,
% 11.88/12.12 ! [V_n_2,V_m_2] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 11.88/12.12 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_nat__le__linear,axiom,
% 11.88/12.12 ! [V_n,V_m] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 11.88/12.12 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__diff__right,axiom,
% 11.88/12.12 ! [V_i,V_j,V_k] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__diff__conv,axiom,
% 11.88/12.12 ! [V_i_2,V_k_2,V_j_2] :
% 11.88/12.12 ( 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)
% 11.88/12.12 <=> 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_nat__add__left__cancel__le,axiom,
% 11.88/12.12 ! [V_n_2,V_m_2,V_k_2] :
% 11.88/12.12 ( 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))
% 11.88/12.12 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult__monom,axiom,
% 11.88/12.12 ! [V_n,V_b,V_m,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_eq__imp__le,axiom,
% 11.88/12.12 ! [V_n,V_m] :
% 11.88/12.12 ( V_m = V_n
% 11.88/12.12 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_trans__le__add1,axiom,
% 11.88/12.12 ! [V_m,V_j,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 11.88/12.12 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_trans__le__add2,axiom,
% 11.88/12.12 ! [V_m,V_j,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 11.88/12.12 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__add__diff,axiom,
% 11.88/12.12 ! [V_m,V_n,V_k] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_add__le__mono1,axiom,
% 11.88/12.12 ! [V_k,V_j,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult__le__mono1,axiom,
% 11.88/12.12 ! [V_k,V_j,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult__le__mono2,axiom,
% 11.88/12.12 ! [V_k,V_j,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__le__mono2,axiom,
% 11.88/12.12 ! [V_l,V_n,V_m] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__le__mono,axiom,
% 11.88/12.12 ! [V_l,V_n,V_m] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__diff__cancel,axiom,
% 11.88/12.12 ! [V_n,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 11.88/12.12 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__add__diff__inverse,axiom,
% 11.88/12.12 ! [V_m,V_n] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 11.88/12.12 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_add__diff__assoc,axiom,
% 11.88/12.12 ! [V_i,V_j,V_k] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__diff__conv2,axiom,
% 11.88/12.12 ! [V_i_2,V_j_2,V_k_2] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
% 11.88/12.12 => ( 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))
% 11.88/12.12 <=> 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) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__add__diff__inverse2,axiom,
% 11.88/12.12 ! [V_m,V_n] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 11.88/12.12 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__imp__diff__is__add,axiom,
% 11.88/12.12 ! [V_k_2,V_j_2,V_i_2] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 11.88/12.12 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 11.88/12.12 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__add__assoc,axiom,
% 11.88/12.12 ! [V_i,V_j,V_k] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_add__diff__assoc2,axiom,
% 11.88/12.12 ! [V_i,V_j,V_k] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__add__assoc2,axiom,
% 11.88/12.12 ! [V_i,V_j,V_k] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__trans,axiom,
% 11.88/12.12 ! [V_k,V_j,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 11.88/12.12 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 11.88/12.12 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__antisym,axiom,
% 11.88/12.12 ! [V_n,V_m] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 11.88/12.12 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 11.88/12.12 => V_m = V_n ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_add__le__mono,axiom,
% 11.88/12.12 ! [V_l,V_k,V_j,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 11.88/12.12 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 11.88/12.12 => 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)) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult__le__mono,axiom,
% 11.88/12.12 ! [V_l,V_k,V_j,V_i] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 11.88/12.12 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 11.88/12.12 => 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)) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_eq__diff__iff,axiom,
% 11.88/12.12 ! [V_n_2,V_m_2,V_k_2] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 11.88/12.12 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 11.88/12.12 => ( 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)
% 11.88/12.12 <=> V_m_2 = V_n_2 ) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_Nat_Odiff__diff__eq,axiom,
% 11.88/12.12 ! [V_n,V_m,V_k] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 11.88/12.12 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 11.88/12.12 => 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) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_le__diff__iff,axiom,
% 11.88/12.12 ! [V_n_2,V_m_2,V_k_2] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 11.88/12.12 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 11.88/12.12 => ( 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))
% 11.88/12.12 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_add__leD2,axiom,
% 11.88/12.12 ! [V_n,V_k,V_m] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 11.88/12.12 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_add__leD1,axiom,
% 11.88/12.12 ! [V_n,V_k,V_m] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 11.88/12.12 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_add__leE,axiom,
% 11.88/12.12 ! [V_n,V_k,V_m] :
% 11.88/12.12 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 11.88/12.12 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 11.88/12.12 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 11.88/12.12 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 11.88/12.12 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 11.88/12.12 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 11.88/12.12 ! [V_rx,V_ly,V_lx,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 11.88/12.12 ! [V_rx,V_ly,V_lx,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 11.88/12.12 ! [V_ry,V_rx,V_lx,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 11.88/12.12 ! [V_ry,V_rx,V_lx,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 11.88/12.12 ! [V_b,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.12 => 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) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult_Oprod__diff__prod,axiom,
% 11.88/12.12 ! [V_b,V_a,V_y,V_x,T_a] :
% 11.88/12.12 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.12 => 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))) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult__diff__mult,axiom,
% 11.88/12.12 ! [V_b,V_a,V_y,V_x,T_a] :
% 11.88/12.12 ( class_Rings_Oring(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__eq__diff__eq,axiom,
% 11.88/12.12 ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
% 11.88/12.12 ( class_Groups_Oab__group__add(T_a)
% 11.88/12.12 => ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
% 11.88/12.12 => ( V_ab_2 = V_b_2
% 11.88/12.12 <=> V_ca_2 = V_db_2 ) ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_diff__monom,axiom,
% 11.88/12.12 ! [V_b,V_n,V_a,T_a] :
% 11.88/12.12 ( class_Groups_Oab__group__add(T_a)
% 11.88/12.12 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_monom__eq__iff,axiom,
% 11.88/12.12 ! [V_b_2,V_n_2,V_ab_2,T_a] :
% 11.88/12.12 ( class_Groups_Ozero(T_a)
% 11.88/12.12 => ( c_Polynomial_Omonom(T_a,V_ab_2,V_n_2) = c_Polynomial_Omonom(T_a,V_b_2,V_n_2)
% 11.88/12.12 <=> V_ab_2 = V_b_2 ) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult__left_Odiff,axiom,
% 11.88/12.12 ! [V_ya,V_y,V_x,T_a] :
% 11.88/12.12 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.12 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult_Odiff__left,axiom,
% 11.88/12.12 ! [V_b,V_a_H,V_a,T_a] :
% 11.88/12.12 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.12 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_smult__diff__left,axiom,
% 11.88/12.12 ! [V_p,V_b,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__ring(T_a)
% 11.88/12.12 => c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 11.88/12.12 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.12 ( class_Groups_Oab__semigroup__mult(T_a)
% 11.88/12.12 => 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)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult__smult__left,axiom,
% 11.88/12.12 ! [V_q,V_p,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.12 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(T_a,V_a,V_p)),V_q) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult__right_Odiff,axiom,
% 11.88/12.12 ! [V_y,V_x,V_xa,T_a] :
% 11.88/12.12 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.12 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_mult_Odiff__right,axiom,
% 11.88/12.12 ! [V_b_H,V_b,V_a,T_a] :
% 11.88/12.12 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.12 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_smult__diff__right,axiom,
% 11.88/12.12 ! [V_q,V_p,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__ring(T_a)
% 11.88/12.12 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) ) ).
% 11.88/12.12
% 11.88/12.12 fof(fact_smult__smult,axiom,
% 11.88/12.12 ! [V_p,V_b,V_a,T_a] :
% 11.88/12.12 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p)) = c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_smult__monom,axiom,
% 11.88/12.13 ! [V_n,V_b,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__smult__right,axiom,
% 11.88/12.13 ! [V_q,V_a,V_p,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__pCons,axiom,
% 11.88/12.13 ! [V_q,V_b,V_p,V_a,T_a] :
% 11.88/12.13 ( class_Groups_Oab__group__add(T_a)
% 11.88/12.13 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_norm__mult,axiom,
% 11.88/12.13 ! [V_y,V_x,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_smult__pCons,axiom,
% 11.88/12.13 ! [V_p,V_b,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p)) = c_Polynomial_OpCons(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_poly__diff,axiom,
% 11.88/12.13 ! [V_x,V_q,V_p,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__ring(T_a)
% 11.88/12.13 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_poly__smult,axiom,
% 11.88/12.13 ! [V_x,V_p,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diffs0__imp__equal,axiom,
% 11.88/12.13 ! [V_n,V_m] :
% 11.88/12.13 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.88/12.13 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.88/12.13 => V_m = V_n ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__is__0__eq_H,axiom,
% 11.88/12.13 ! [V_n,V_m] :
% 11.88/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 11.88/12.13 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__is__0__eq,axiom,
% 11.88/12.13 ! [V_n_2,V_m_2] :
% 11.88/12.13 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.88/12.13 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__add__0,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__self__eq__0,axiom,
% 11.88/12.13 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_minus__nat_Odiff__0,axiom,
% 11.88/12.13 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__0__eq__0,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_poly__mult,axiom,
% 11.88/12.13 ! [V_x,V_q,V_p,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__cancel2,axiom,
% 11.88/12.13 ! [V_n_2,V_k_2,V_m_2] :
% 11.88/12.13 ( 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)
% 11.88/12.13 <=> ( V_m_2 = V_n_2
% 11.88/12.13 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__cancel1,axiom,
% 11.88/12.13 ! [V_n_2,V_m_2,V_k_2] :
% 11.88/12.13 ( 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)
% 11.88/12.13 <=> ( V_m_2 = V_n_2
% 11.88/12.13 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__is__0,axiom,
% 11.88/12.13 ! [V_n_2,V_m_2] :
% 11.88/12.13 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.88/12.13 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.88/12.13 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__0__right,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__0,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_norm__triangle__ineq2,axiom,
% 11.88/12.13 ! [V_b,V_a,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.13 => 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))) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_norm__mult__ineq,axiom,
% 11.88/12.13 ! [V_y,V_x,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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))) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__0__right,axiom,
% 11.88/12.13 ! [V_a,T_a] :
% 11.88/12.13 ( class_Groups_Ogroup__add(T_a)
% 11.88/12.13 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__self,axiom,
% 11.88/12.13 ! [V_a,T_a] :
% 11.88/12.13 ( class_Groups_Ogroup__add(T_a)
% 11.88/12.13 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_eq__iff__diff__eq__0,axiom,
% 11.88/12.13 ! [V_b_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Groups_Oab__group__add(T_a)
% 11.88/12.13 => ( V_ab_2 = V_b_2
% 11.88/12.13 <=> c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_right__minus__eq,axiom,
% 11.88/12.13 ! [V_b_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Groups_Ogroup__add(T_a)
% 11.88/12.13 => ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 <=> V_ab_2 = V_b_2 ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__eq__diff__less__eq,axiom,
% 11.88/12.13 ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Groups_Oordered__ab__group__add(T_a)
% 11.88/12.13 => ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
% 11.88/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
% 11.88/12.13 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_db_2) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_add__diff__cancel,axiom,
% 11.88/12.13 ! [V_b,V_a,T_a] :
% 11.88/12.13 ( class_Groups_Ogroup__add(T_a)
% 11.88/12.13 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__add__cancel,axiom,
% 11.88/12.13 ! [V_b,V_a,T_a] :
% 11.88/12.13 ( class_Groups_Ogroup__add(T_a)
% 11.88/12.13 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult_Ozero__left,axiom,
% 11.88/12.13 ! [V_b,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__left_Ozero,axiom,
% 11.88/12.13 ! [V_y,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult_Ozero__right,axiom,
% 11.88/12.13 ! [V_a,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__right_Ozero,axiom,
% 11.88/12.13 ! [V_x,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 11.88/12.13 ! [V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.13 => 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) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 11.88/12.13 ! [V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.13 => 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) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_norm__minus__commute,axiom,
% 11.88/12.13 ! [V_b,V_a,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.13 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__left_Oadd,axiom,
% 11.88/12.13 ! [V_ya,V_y,V_x,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult_Oadd__left,axiom,
% 11.88/12.13 ! [V_b,V_a_H,V_a,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__right_Oadd,axiom,
% 11.88/12.13 ! [V_y,V_x,V_xa,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult_Oadd__right,axiom,
% 11.88/12.13 ! [V_b_H,V_b,V_a,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_crossproduct__eq,axiom,
% 11.88/12.13 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 11.88/12.13 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 11.88/12.13 => ( 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))
% 11.88/12.13 <=> ( V_w_2 = V_x_2
% 11.88/12.13 | V_y_2 = V_z_2 ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 11.88/12.13 ! [V_b,V_m,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.13 => 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) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 11.88/12.13 ! [V_c,V_b,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_crossproduct__noteq,axiom,
% 11.88/12.13 ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 11.88/12.13 => ( ( V_ab_2 != V_b_2
% 11.88/12.13 & V_ca_2 != V_db_2 )
% 11.88/12.13 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_db_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 11.88/12.13 ! [V_z,V_y,V_x,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__1(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__poly__code_I2_J,axiom,
% 11.88/12.13 ! [V_p,T_a] :
% 11.88/12.13 ( class_Groups_Oab__group__add(T_a)
% 11.88/12.13 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_real__mult__left__cancel,axiom,
% 11.88/12.13 ! [V_b_2,V_ab_2,V_ca_2] :
% 11.88/12.13 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 11.88/12.13 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_ab_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)
% 11.88/12.13 <=> V_ab_2 = V_b_2 ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_real__mult__right__cancel,axiom,
% 11.88/12.13 ! [V_b_2,V_ab_2,V_ca_2] :
% 11.88/12.13 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 11.88/12.13 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ab_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)
% 11.88/12.13 <=> V_ab_2 = V_b_2 ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_smult__0__right,axiom,
% 11.88/12.13 ! [V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_real__add__mult__distrib,axiom,
% 11.88/12.13 ! [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)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__poly__0__left,axiom,
% 11.88/12.13 ! [V_q,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__poly__0__right,axiom,
% 11.88/12.13 ! [V_p,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_smult__add__right,axiom,
% 11.88/12.13 ! [V_q,V_p,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__poly__add__left,axiom,
% 11.88/12.13 ! [V_r,V_q,V_p,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__pCons__right,axiom,
% 11.88/12.13 ! [V_q,V_a,V_p,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__pCons__left,axiom,
% 11.88/12.13 ! [V_q,V_p,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,V_p)),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_le__iff__diff__le__0,axiom,
% 11.88/12.13 ! [V_b_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Groups_Oordered__ab__group__add(T_a)
% 11.88/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
% 11.88/12.13 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_add__scale__eq__noteq,axiom,
% 11.88/12.13 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 11.88/12.13 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 11.88/12.13 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 => ( ( V_a = V_b
% 11.88/12.13 & V_c != V_d )
% 11.88/12.13 => 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)) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_real__le__eq__diff,axiom,
% 11.88/12.13 ! [V_y_2,V_x_2] :
% 11.88/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 11.88/12.13 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_smult__0__left,axiom,
% 11.88/12.13 ! [V_p,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_smult__eq__0__iff,axiom,
% 11.88/12.13 ! [V_pa_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Rings_Oidom(T_a)
% 11.88/12.13 => ( c_Polynomial_Osmult(T_a,V_ab_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 11.88/12.13 <=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_real__two__squares__add__zero__iff,axiom,
% 11.88/12.13 ! [V_y_2,V_x_2] :
% 11.88/12.13 ( 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)
% 11.88/12.13 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 11.88/12.13 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_synthetic__div__unique__lemma,axiom,
% 11.88/12.13 ! [V_a,V_p,V_c,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => ( c_Polynomial_Osmult(T_a,V_c,V_p) = c_Polynomial_OpCons(T_a,V_a,V_p)
% 11.88/12.13 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_smult__add__left,axiom,
% 11.88/12.13 ! [V_p,V_b,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 11.88/12.13 => c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_monom__eq__0,axiom,
% 11.88/12.13 ! [V_n,T_a] :
% 11.88/12.13 ( class_Groups_Ozero(T_a)
% 11.88/12.13 => c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_monom__eq__0__iff,axiom,
% 11.88/12.13 ! [V_n_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Groups_Ozero(T_a)
% 11.88/12.13 => ( c_Polynomial_Omonom(T_a,V_ab_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 11.88/12.13 <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_add__monom,axiom,
% 11.88/12.13 ! [V_b,V_n,V_a,T_a] :
% 11.88/12.13 ( class_Groups_Ocomm__monoid__add(T_a)
% 11.88/12.13 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_norm__diff__ineq,axiom,
% 11.88/12.13 ! [V_b,V_a,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.13 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_norm__triangle__ineq4,axiom,
% 11.88/12.13 ! [V_b,V_a,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.13 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_add__eq__self__zero,axiom,
% 11.88/12.13 ! [V_n,V_m] :
% 11.88/12.13 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 11.88/12.13 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_add__is__0,axiom,
% 11.88/12.13 ! [V_n_2,V_m_2] :
% 11.88/12.13 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.88/12.13 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 11.88/12.13 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_le__0__eq,axiom,
% 11.88/12.13 ! [V_n_2] :
% 11.88/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 11.88/12.13 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_Nat_Oadd__0__right,axiom,
% 11.88/12.13 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 11.88/12.13
% 11.88/12.13 fof(fact_plus__nat_Oadd__0,axiom,
% 11.88/12.13 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 11.88/12.13
% 11.88/12.13 fof(fact_norm__ratiotest__lemma,axiom,
% 11.88/12.13 ! [V_y,V_x,V_c,T_a] :
% 11.88/12.13 ( class_RealVector_Oreal__normed__vector(T_a)
% 11.88/12.13 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 11.88/12.13 => ( 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)))
% 11.88/12.13 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_le__add__iff1,axiom,
% 11.88/12.13 ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Rings_Oordered__ring(T_a)
% 11.88/12.13 => ( 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_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
% 11.88/12.13 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_le__add__iff2,axiom,
% 11.88/12.13 ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Rings_Oordered__ring(T_a)
% 11.88/12.13 => ( 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_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
% 11.88/12.13 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2)) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_sum__squares__le__zero__iff,axiom,
% 11.88/12.13 ! [V_y_2,V_x_2,T_a] :
% 11.88/12.13 ( class_Rings_Olinordered__ring__strict(T_a)
% 11.88/12.13 => ( 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))
% 11.88/12.13 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_sum__squares__ge__zero,axiom,
% 11.88/12.13 ! [V_y,V_x,T_a] :
% 11.88/12.13 ( class_Rings_Olinordered__ring(T_a)
% 11.88/12.13 => 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))) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_complex__mod__triangle__ineq2,axiom,
% 11.88/12.13 ! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_eq__add__iff2,axiom,
% 11.88/12.13 ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Rings_Oring(T_a)
% 11.88/12.13 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)
% 11.88/12.13 <=> V_ca_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_eq__add__iff1,axiom,
% 11.88/12.13 ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Rings_Oring(T_a)
% 11.88/12.13 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)
% 11.88/12.13 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2) = V_db_2 ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_sum__squares__eq__zero__iff,axiom,
% 11.88/12.13 ! [V_y_2,V_x_2,T_a] :
% 11.88/12.13 ( class_Rings_Olinordered__ring__strict(T_a)
% 11.88/12.13 => ( 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)
% 11.88/12.13 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_zero__le__square,axiom,
% 11.88/12.13 ! [V_a,T_a] :
% 11.88/12.13 ( class_Rings_Olinordered__ring(T_a)
% 11.88/12.13 => 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)) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_nat__add__commute,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_nat__add__left__commute,axiom,
% 11.88/12.13 ! [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)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_add__mult__distrib2,axiom,
% 11.88/12.13 ! [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)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__add__inverse2,axiom,
% 11.88/12.13 ! [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 ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__add__inverse,axiom,
% 11.88/12.13 ! [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 ).
% 11.88/12.13
% 11.88/12.13 fof(fact_nat__add__assoc,axiom,
% 11.88/12.13 ! [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)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__diff__left,axiom,
% 11.88/12.13 ! [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)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_add__mult__distrib,axiom,
% 11.88/12.13 ! [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)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_nat__add__left__cancel,axiom,
% 11.88/12.13 ! [V_n_2,V_m_2,V_k_2] :
% 11.88/12.13 ( 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)
% 11.88/12.13 <=> V_m_2 = V_n_2 ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_nat__add__right__cancel,axiom,
% 11.88/12.13 ! [V_n_2,V_k_2,V_m_2] :
% 11.88/12.13 ( 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)
% 11.88/12.13 <=> V_m_2 = V_n_2 ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__cancel,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__cancel2,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_nat__mult__commute,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__mult__distrib2,axiom,
% 11.88/12.13 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_nat__mult__assoc,axiom,
% 11.88/12.13 ! [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)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__commute,axiom,
% 11.88/12.13 ! [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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_diff__mult__distrib,axiom,
% 11.88/12.13 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_real__mult__assoc,axiom,
% 11.88/12.13 ! [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)) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_real__mult__commute,axiom,
% 11.88/12.13 ! [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) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_le__Suc__ex__iff,axiom,
% 11.88/12.13 ! [V_l_2,V_k_2] :
% 11.88/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 11.88/12.13 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_divisors__zero,axiom,
% 11.88/12.13 ! [V_b,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ono__zero__divisors(T_a)
% 11.88/12.13 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_no__zero__divisors,axiom,
% 11.88/12.13 ! [V_b,V_a,T_a] :
% 11.88/12.13 ( class_Rings_Ono__zero__divisors(T_a)
% 11.88/12.13 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__eq__0__iff,axiom,
% 11.88/12.13 ! [V_b_2,V_ab_2,T_a] :
% 11.88/12.13 ( class_Rings_Oring__no__zero__divisors(T_a)
% 11.88/12.13 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 <=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
% 11.88/12.13 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 11.88/12.13
% 11.88/12.13 fof(fact_mult__zero__right,axiom,
% 11.88/12.13 ! [V_a,T_a] :
% 11.88/12.13 ( class_Rings_Omult__zero(T_a)
% 12.04/12.13 => 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) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__zero__left,axiom,
% 12.04/12.13 ! [V_a,T_a] :
% 12.04/12.13 ( class_Rings_Omult__zero(T_a)
% 12.04/12.13 => 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) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_comm__semiring__class_Odistrib,axiom,
% 12.04/12.13 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Ocomm__semiring(T_a)
% 12.04/12.13 => 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)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_combine__common__factor,axiom,
% 12.04/12.13 ! [V_c,V_b,V_e,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Osemiring(T_a)
% 12.04/12.13 => 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) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_split__mult__neg__le,axiom,
% 12.04/12.13 ! [V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__cancel__semiring(T_a)
% 12.04/12.13 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.13 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 12.04/12.13 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 12.04/12.13 => 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)) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_split__mult__pos__le,axiom,
% 12.04/12.13 ! [V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__ring(T_a)
% 12.04/12.13 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.13 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 12.04/12.13 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 12.04/12.13 => 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)) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__mono,axiom,
% 12.04/12.13 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.13 => 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)) ) ) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__mono_H,axiom,
% 12.04/12.13 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.13 => 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)) ) ) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__left__mono__neg,axiom,
% 12.04/12.13 ! [V_c,V_a,V_b,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__ring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__right__mono__neg,axiom,
% 12.04/12.13 ! [V_c,V_a,V_b,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__ring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_comm__mult__left__mono,axiom,
% 12.04/12.13 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__comm__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__left__mono,axiom,
% 12.04/12.13 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__right__mono,axiom,
% 12.04/12.13 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__nonpos__nonpos,axiom,
% 12.04/12.13 ! [V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__ring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__nonpos__nonneg,axiom,
% 12.04/12.13 ! [V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__cancel__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__nonneg__nonpos2,axiom,
% 12.04/12.13 ! [V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__cancel__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__nonneg__nonpos,axiom,
% 12.04/12.13 ! [V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__cancel__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__nonneg__nonneg,axiom,
% 12.04/12.13 ! [V_b,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Oordered__cancel__semiring(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__le__0__iff,axiom,
% 12.04/12.13 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.13 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
% 12.04/12.13 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 12.04/12.13 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_zero__le__mult__iff,axiom,
% 12.04/12.13 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.13 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.13 => ( 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_ab_2),V_b_2))
% 12.04/12.13 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
% 12.04/12.13 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 12.04/12.13 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.13 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__le__add__iff1,axiom,
% 12.04/12.13 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 12.04/12.13 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__diff__add__eq1,axiom,
% 12.04/12.13 ! [V_n,V_m,V_u,V_i,V_j] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
% 12.04/12.13 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__eq__add__iff1,axiom,
% 12.04/12.13 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 12.04/12.13 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
% 12.04/12.13 <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_n_2 ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__le__add__iff2,axiom,
% 12.04/12.13 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 12.04/12.13 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__diff__add__eq2,axiom,
% 12.04/12.13 ! [V_n,V_m,V_u,V_j,V_i] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 12.04/12.13 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__eq__add__iff2,axiom,
% 12.04/12.13 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 12.04/12.13 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
% 12.04/12.13 <=> V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_pcompose__pCons,axiom,
% 12.04/12.13 ! [V_q,V_p,V_a,T_a] :
% 12.04/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 12.04/12.13 => c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_pcompose__0,axiom,
% 12.04/12.13 ! [V_q,T_a] :
% 12.04/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 12.04/12.13 => c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_poly__pcompose,axiom,
% 12.04/12.13 ! [V_x,V_q,V_p,T_a] :
% 12.04/12.13 ( class_Rings_Ocomm__semiring__0(T_a)
% 12.04/12.13 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 12.04/12.13 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.13 ( 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)
% 12.04/12.13 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.13 | V_m_2 = V_n_2 ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_left__add__mult__distrib,axiom,
% 12.04/12.13 ! [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) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_termination__basic__simps_I3_J,axiom,
% 12.04/12.13 ! [V_z,V_y,V_x] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 12.04/12.13 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_termination__basic__simps_I4_J,axiom,
% 12.04/12.13 ! [V_y,V_z,V_x] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 12.04/12.13 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_Deriv_Oadd__diff__add,axiom,
% 12.04/12.13 ! [V_d,V_b,V_c,V_a,T_a] :
% 12.04/12.13 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.13 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult_Ononneg__bounded,axiom,
% 12.04/12.13 ! [T_a] :
% 12.04/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.13 => ? [B_K] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 12.04/12.13 & ! [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)) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__right_Ononneg__bounded,axiom,
% 12.04/12.13 ! [V_x,T_a] :
% 12.04/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.13 => ? [B_K] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 12.04/12.13 & ! [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)) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__left_Ononneg__bounded,axiom,
% 12.04/12.13 ! [V_y,T_a] :
% 12.04/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.13 => ? [B_K] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 12.04/12.13 & ! [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)) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult_Obounded,axiom,
% 12.04/12.13 ! [T_a] :
% 12.04/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.13 => ? [B_K] :
% 12.04/12.13 ! [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)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__right_Obounded,axiom,
% 12.04/12.13 ! [V_x,T_a] :
% 12.04/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.13 => ? [B_K] :
% 12.04/12.13 ! [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)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__left_Obounded,axiom,
% 12.04/12.13 ! [V_y,T_a] :
% 12.04/12.13 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.13 => ? [B_K] :
% 12.04/12.13 ! [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)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_mult__eq__if,axiom,
% 12.04/12.13 ! [V_n,V_m] :
% 12.04/12.13 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 12.04/12.13 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.13 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__less__add__iff1,axiom,
% 12.04/12.13 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 12.04/12.13 => ( 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_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 12.04/12.13 <=> 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_nat__less__add__iff2,axiom,
% 12.04/12.13 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 12.04/12.13 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 12.04/12.13 => ( 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_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 12.04/12.13 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_less__zeroE,axiom,
% 12.04/12.13 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_less__1__mult,axiom,
% 12.04/12.13 ! [V_n,V_m,T_a] :
% 12.04/12.13 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 12.04/12.13 => 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)) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_linorder__neqE__linordered__idom,axiom,
% 12.04/12.13 ! [V_y,V_x,T_a] :
% 12.04/12.13 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.13 => ( V_x != V_y
% 12.04/12.13 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_less__add__one,axiom,
% 12.04/12.13 ! [V_a,T_a] :
% 12.04/12.13 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.13 => 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))) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_zero__less__one,axiom,
% 12.04/12.13 ! [T_a] :
% 12.04/12.13 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_not__one__less__zero,axiom,
% 12.04/12.13 ! [T_a] :
% 12.04/12.13 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.13 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_poly__1,axiom,
% 12.04/12.13 ! [V_x,T_a] :
% 12.04/12.13 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.13 => 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) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_linorder__cases,axiom,
% 12.04/12.13 ! [V_y,V_x,T_a] :
% 12.04/12.13 ( class_Orderings_Olinorder(T_a)
% 12.04/12.13 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.13 => ( V_x != V_y
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_order__less__asym,axiom,
% 12.04/12.13 ! [V_y,V_x,T_a] :
% 12.04/12.13 ( class_Orderings_Opreorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.13 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_xt1_I10_J,axiom,
% 12.04/12.13 ! [V_z,V_x,V_y,T_a] :
% 12.04/12.13 ( class_Orderings_Oorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_order__less__trans,axiom,
% 12.04/12.13 ! [V_z,V_y,V_x,T_a] :
% 12.04/12.13 ( class_Orderings_Opreorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_xt1_I2_J,axiom,
% 12.04/12.13 ! [V_c,V_a,V_b,T_a] :
% 12.04/12.13 ( class_Orderings_Oorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 12.04/12.13 => ( V_b = V_c
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_ord__less__eq__trans,axiom,
% 12.04/12.13 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Orderings_Oord(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.13 => ( V_b = V_c
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_xt1_I1_J,axiom,
% 12.04/12.13 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Orderings_Oorder(T_a)
% 12.04/12.13 => ( V_a = V_b
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_ord__eq__less__trans,axiom,
% 12.04/12.13 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.13 ( class_Orderings_Oord(T_a)
% 12.04/12.13 => ( V_a = V_b
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 12.04/12.13 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_xt1_I9_J,axiom,
% 12.04/12.13 ! [V_a,V_b,T_a] :
% 12.04/12.13 ( class_Orderings_Oorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 12.04/12.13 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_order__less__asym_H,axiom,
% 12.04/12.13 ! [V_b,V_a,T_a] :
% 12.04/12.13 ( class_Orderings_Opreorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.13 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_order__less__imp__not__eq2,axiom,
% 12.04/12.13 ! [V_y,V_x,T_a] :
% 12.04/12.13 ( class_Orderings_Oorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.13 => V_y != V_x ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_order__less__imp__not__eq,axiom,
% 12.04/12.13 ! [V_y,V_x,T_a] :
% 12.04/12.13 ( class_Orderings_Oorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.13 => V_x != V_y ) ) ).
% 12.04/12.13
% 12.04/12.13 fof(fact_order__less__imp__not__less,axiom,
% 12.04/12.13 ! [V_y,V_x,T_a] :
% 12.04/12.13 ( class_Orderings_Opreorder(T_a)
% 12.04/12.13 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__less__not__sym,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Opreorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__imp__neq,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 => V_x != V_y ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__neqE,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( V_x != V_y
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__antisym__conv3,axiom,
% 12.04/12.14 ! [V_x_2,V_y_2,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> V_x_2 = V_y_2 ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__less__linear,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 | V_x = V_y
% 12.04/12.14 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_one__reorient,axiom,
% 12.04/12.14 ! [V_x_2,T_a] :
% 12.04/12.14 ( class_Groups_Oone(T_a)
% 12.04/12.14 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 12.04/12.14 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__less__iff__gr__or__eq,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 12.04/12.14 | V_x_2 = V_y_2 ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__neq__iff,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( V_x_2 != V_y_2
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__less__irrefl,axiom,
% 12.04/12.14 ! [V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Opreorder(T_a)
% 12.04/12.14 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_norm__one,axiom,
% 12.04/12.14 ! [T_a] :
% 12.04/12.14 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 12.04/12.14 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__less__cases,axiom,
% 12.04/12.14 ! [V_P_2,V_n_2,V_m_2] :
% 12.04/12.14 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.14 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 12.04/12.14 => ( ( V_m_2 = V_n_2
% 12.04/12.14 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 12.04/12.14 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 12.04/12.14 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 12.04/12.14 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__not__refl3,axiom,
% 12.04/12.14 ! [V_t,V_s] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 12.04/12.14 => V_s != V_t ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__not__refl2,axiom,
% 12.04/12.14 ! [V_m,V_n] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 12.04/12.14 => V_m != V_n ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__irrefl__nat,axiom,
% 12.04/12.14 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__neqE__nat,axiom,
% 12.04/12.14 ! [V_y,V_x] :
% 12.04/12.14 ( V_x != V_y
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__neq__iff,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( V_m_2 != V_n_2
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__not__refl,axiom,
% 12.04/12.14 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zero__less__two,axiom,
% 12.04/12.14 ! [T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.14 => 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))) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_one__poly__def,axiom,
% 12.04/12.14 ! [T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_xt1_I8_J,axiom,
% 12.04/12.14 ! [V_z,V_x,V_y,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__le__less__trans,axiom,
% 12.04/12.14 ! [V_z,V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Opreorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_xt1_I7_J,axiom,
% 12.04/12.14 ! [V_z,V_x,V_y,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__less__le__trans,axiom,
% 12.04/12.14 ! [V_z,V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Opreorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_xt1_I11_J,axiom,
% 12.04/12.14 ! [V_a,V_b,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 12.04/12.14 => ( V_a != V_b
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__le__neq__trans,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.14 => ( V_a != V_b
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__le__imp__less__or__eq,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 | V_x = V_y ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__antisym__conv2,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> V_x_2 = V_y_2 ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__less__imp__le,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Opreorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_leD,axiom,
% 12.04/12.14 ! [V_x,V_y,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 12.04/12.14 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_xt1_I12_J,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( V_a != V_b
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__neq__le__trans,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( V_a != V_b
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__antisym__conv1,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> V_x_2 = V_y_2 ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__leE,axiom,
% 12.04/12.14 ! [V_x,V_y,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_leI,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__le__less,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 | V_x_2 = V_y_2 ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__le__not__le,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Opreorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 12.04/12.14 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_order__less__le,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Oorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 12.04/12.14 & V_x_2 != V_y_2 ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__le__less__linear,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 12.04/12.14 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__not__le,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_linorder__not__less,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Orderings_Olinorder(T_a)
% 12.04/12.14 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_one__neq__zero,axiom,
% 12.04/12.14 ! [T_a] :
% 12.04/12.14 ( class_Rings_Ozero__neq__one(T_a)
% 12.04/12.14 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zero__neq__one,axiom,
% 12.04/12.14 ! [T_a] :
% 12.04/12.14 ( class_Rings_Ozero__neq__one(T_a)
% 12.04/12.14 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__less__imp__less__left,axiom,
% 12.04/12.14 ! [V_b,V_a,V_c,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__less__imp__less__right,axiom,
% 12.04/12.14 ! [V_b,V_c,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__strict__mono,axiom,
% 12.04/12.14 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__strict__left__mono,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => 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)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__strict__right__mono,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => 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)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__less__cancel__left,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,V_ca_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__less__cancel__right,axiom,
% 12.04/12.14 ! [V_b_2,V_ca_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_diff__eq__diff__less,axiom,
% 12.04/12.14 ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_db_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 12.04/12.14 ! [V_a,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 12.04/12.14 ! [V_a,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult_Ocomm__neutral,axiom,
% 12.04/12.14 ! [V_a,T_a] :
% 12.04/12.14 ( class_Groups_Ocomm__monoid__mult(T_a)
% 12.04/12.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__1__right,axiom,
% 12.04/12.14 ! [V_a,T_a] :
% 12.04/12.14 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__1,axiom,
% 12.04/12.14 ! [V_a,T_a] :
% 12.04/12.14 ( class_Groups_Ocomm__monoid__mult(T_a)
% 12.04/12.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__1__left,axiom,
% 12.04/12.14 ! [V_a,T_a] :
% 12.04/12.14 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_gr0I,axiom,
% 12.04/12.14 ! [V_n] :
% 12.04/12.14 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_gr__implies__not0,axiom,
% 12.04/12.14 ! [V_n,V_m] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.14 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__nat__zero__code,axiom,
% 12.04/12.14 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_neq0__conv,axiom,
% 12.04/12.14 ! [V_n_2] :
% 12.04/12.14 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__less0,axiom,
% 12.04/12.14 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__lessD1,axiom,
% 12.04/12.14 ! [V_k,V_j,V_i] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__add__eq__less,axiom,
% 12.04/12.14 ! [V_n,V_m,V_l,V_k] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 12.04/12.14 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__less__mono,axiom,
% 12.04/12.14 ! [V_l,V_k,V_j,V_i] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 12.04/12.14 => 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)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__less__mono1,axiom,
% 12.04/12.14 ! [V_k,V_j,V_i] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_trans__less__add2,axiom,
% 12.04/12.14 ! [V_m,V_j,V_i] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_trans__less__add1,axiom,
% 12.04/12.14 ! [V_m,V_j,V_i] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__add__left__cancel__less,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__add__less2,axiom,
% 12.04/12.14 ! [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) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__add__less1,axiom,
% 12.04/12.14 ! [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) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_termination__basic__simps_I2_J,axiom,
% 12.04/12.14 ! [V_y,V_z,V_x] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_termination__basic__simps_I1_J,axiom,
% 12.04/12.14 ! [V_z,V_y,V_x] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__less__le,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.14 & V_m_2 != V_n_2 ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_le__eq__less__or__eq,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.14 | V_m_2 = V_n_2 ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__imp__le__nat,axiom,
% 12.04/12.14 ! [V_n,V_m] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_le__neq__implies__less,axiom,
% 12.04/12.14 ! [V_n,V_m] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 12.04/12.14 => ( V_m != V_n
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__or__eq__imp__le,axiom,
% 12.04/12.14 ! [V_n,V_m] :
% 12.04/12.14 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.14 | V_m = V_n )
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_termination__basic__simps_I5_J,axiom,
% 12.04/12.14 ! [V_y,V_x] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_diff__less__mono2,axiom,
% 12.04/12.14 ! [V_l,V_n,V_m] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 12.04/12.14 => 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)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__imp__diff__less,axiom,
% 12.04/12.14 ! [V_n,V_k,V_j] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__mult__eq__1__iff,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 12.04/12.14 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 12.04/12.14 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__mult__1__right,axiom,
% 12.04/12.14 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__1__eq__mult__iff,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 12.04/12.14 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 12.04/12.14 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__mult__1,axiom,
% 12.04/12.14 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 12.04/12.14
% 12.04/12.14 fof(fact_smult__1__left,axiom,
% 12.04/12.14 ! [V_p,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p) = V_p ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_convex__bound__lt,axiom,
% 12.04/12.14 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 12.04/12.14 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 12.04/12.14 => 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) ) ) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__square__less__zero,axiom,
% 12.04/12.14 ! [V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring(T_a)
% 12.04/12.14 => ~ 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__cancel__right__disj,axiom,
% 12.04/12.14 ! [V_b_2,V_ca_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
% 12.04/12.14 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 12.04/12.14 & c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) )
% 12.04/12.14 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__cancel__left__disj,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,V_ca_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 12.04/12.14 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 12.04/12.14 & c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) )
% 12.04/12.14 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__cancel__left__pos,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,V_ca_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__pos__pos,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__pos__neg,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__pos__neg2,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zero__less__mult__pos,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zero__less__mult__pos2,axiom,
% 12.04/12.14 ! [V_a,V_b,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__cancel__left__neg,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,V_ca_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__neg__pos,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__neg__neg,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__strict__right__mono,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__strict__left__mono,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__mult__strict__left__mono,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__strict__right__mono__neg,axiom,
% 12.04/12.14 ! [V_c,V_a,V_b,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__strict__left__mono__neg,axiom,
% 12.04/12.14 ! [V_c,V_a,V_b,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 12.04/12.14 ! [V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Olinordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 12.04/12.14 ! [V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Olinordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__pos__pos,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__neg__neg,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_even__less__0__iff,axiom,
% 12.04/12.14 ! [V_ab_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_pos__add__strict,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__le__less__mono,axiom,
% 12.04/12.14 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__less__le__mono,axiom,
% 12.04/12.14 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__iff__diff__less__0,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__one__le__zero,axiom,
% 12.04/12.14 ! [T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.14 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zero__le__one,axiom,
% 12.04/12.14 ! [T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 12.04/12.14 ! [V_m,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 12.04/12.14 ! [V_a,V_m,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 12.04/12.14 ! [V_m,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__gr__0,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 12.04/12.14 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__mult__eq__cancel1,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 12.04/12.14 => ( 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)
% 12.04/12.14 <=> V_m_2 = V_n_2 ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__mult__less__cancel1,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 12.04/12.14 => ( 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))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__0__less__mult__iff,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 12.04/12.14 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__cancel1,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 12.04/12.14 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__cancel2,axiom,
% 12.04/12.14 ! [V_n_2,V_k_2,V_m_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 12.04/12.14 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__mono1,axiom,
% 12.04/12.14 ! [V_k,V_j,V_i] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 12.04/12.14 => 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)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__mono2,axiom,
% 12.04/12.14 ! [V_k,V_j,V_i] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 12.04/12.14 => 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)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zero__less__diff,axiom,
% 12.04/12.14 ! [V_m_2,V_n_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_diff__less,axiom,
% 12.04/12.14 ! [V_m,V_n] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__diff__inverse,axiom,
% 12.04/12.14 ! [V_n,V_m] :
% 12.04/12.14 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.14 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__diff__conv,axiom,
% 12.04/12.14 ! [V_k_2,V_j_2,V_i_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_diff__less__mono,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 12.04/12.14 => 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)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__diff__iff,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 12.04/12.14 => ( 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))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__eq__self__implies__10,axiom,
% 12.04/12.14 ! [V_n,V_m] :
% 12.04/12.14 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 12.04/12.14 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 12.04/12.14 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__le__cancel__left__pos,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,V_ca_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__le__cancel__left__neg,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,V_ca_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_ab_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__strict__mono,axiom,
% 12.04/12.14 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => 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)) ) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__strict__mono_H,axiom,
% 12.04/12.14 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => 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)) ) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__le__imp__less,axiom,
% 12.04/12.14 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => 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)) ) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__le__less__imp__less,axiom,
% 12.04/12.14 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => 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)) ) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__right__less__imp__less,axiom,
% 12.04/12.14 ! [V_b,V_c,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__imp__less__right,axiom,
% 12.04/12.14 ! [V_b,V_c,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__left__less__imp__less,axiom,
% 12.04/12.14 ! [V_b,V_a,V_c,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__less__imp__less__left,axiom,
% 12.04/12.14 ! [V_b,V_a,V_c,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__right__le__imp__le,axiom,
% 12.04/12.14 ! [V_b,V_c,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__left__le__imp__le,axiom,
% 12.04/12.14 ! [V_b,V_a,V_c,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__strict(T_a)
% 12.04/12.14 => ( 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))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__nonpos__neg,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__neg__nonpos,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__strict__increasing2,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__strict__increasing,axiom,
% 12.04/12.14 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__nonneg__pos,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__pos__nonneg,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.14 => 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)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__sum__squares__lt__zero,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring(T_a)
% 12.04/12.14 => ~ 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_sum__squares__gt__zero__iff,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__ring__strict(T_a)
% 12.04/12.14 => ( 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)))
% 12.04/12.14 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.14 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__right__le__one__le,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__left__le__one__le,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__add__iff2,axiom,
% 12.04/12.14 ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Rings_Oordered__ring(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__add__iff1,axiom,
% 12.04/12.14 ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Rings_Oordered__ring(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_real__squared__diff__one__factored,axiom,
% 12.04/12.14 ! [V_x,T_a] :
% 12.04/12.14 ( class_Rings_Oring__1(T_a)
% 12.04/12.14 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__mult__le__cancel1,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 12.04/12.14 => ( 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))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__le__cancel1,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__le__cancel2,axiom,
% 12.04/12.14 ! [V_n_2,V_k_2,V_m_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 12.04/12.14 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__diff__split__asm,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,V_P_2] :
% 12.04/12.14 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ab_2,V_b_2)))
% 12.04/12.14 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ab_2,V_b_2)
% 12.04/12.14 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 12.04/12.14 | ? [B_d] :
% 12.04/12.14 ( V_ab_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 12.04/12.14 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat__diff__split,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,V_P_2] :
% 12.04/12.14 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ab_2,V_b_2)))
% 12.04/12.14 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ab_2,V_b_2)
% 12.04/12.14 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 12.04/12.14 & ! [B_d] :
% 12.04/12.14 ( V_ab_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 12.04/12.14 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_convex__bound__le,axiom,
% 12.04/12.14 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__semiring__1(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 12.04/12.14 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 12.04/12.14 => 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) ) ) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_synthetic__div__correct_H,axiom,
% 12.04/12.14 ! [V_p,V_c,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__ring__1(T_a)
% 12.04/12.14 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_pos__poly__pCons,axiom,
% 12.04/12.14 ! [V_pa_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.14 => ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2))
% 12.04/12.14 <=> ( c_Polynomial_Opos__poly(T_a,V_pa_2)
% 12.04/12.14 | ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 12.04/12.14 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_ex__least__nat__less,axiom,
% 12.04/12.14 ! [V_n_2,V_P_2] :
% 12.04/12.14 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 12.04/12.14 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 12.04/12.14 => ? [B_k] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)
% 12.04/12.14 & ! [B_i] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
% 12.04/12.14 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 12.04/12.14 & hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_realpow__minus__mult,axiom,
% 12.04/12.14 ! [V_x,V_n,T_a] :
% 12.04/12.14 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.14 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_le__mult__natfloor,axiom,
% 12.04/12.14 ! [V_b,V_a] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
% 12.04/12.14 => 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))) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__eq__if,axiom,
% 12.04/12.14 ! [V_n,V_m] :
% 12.04/12.14 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.14 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n )
% 12.04/12.14 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.14 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_lessI,axiom,
% 12.04/12.14 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_Suc__mono,axiom,
% 12.04/12.14 ! [V_n,V_m] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.14 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zero__less__Suc,axiom,
% 12.04/12.14 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__poly__def,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 12.04/12.14 <=> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_natfloor__one,axiom,
% 12.04/12.14 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_n__not__Suc__n,axiom,
% 12.04/12.14 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_Suc__n__not__n,axiom,
% 12.04/12.14 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat_Oinject,axiom,
% 12.04/12.14 ! [V_nat_H_2,V_nat_2] :
% 12.04/12.14 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 12.04/12.14 <=> V_nat_2 = V_nat_H_2 ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_Suc__inject,axiom,
% 12.04/12.14 ! [V_y,V_x] :
% 12.04/12.14 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 12.04/12.14 => V_x = V_y ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_smult__minus__left,axiom,
% 12.04/12.14 ! [V_p,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__ring(T_a)
% 12.04/12.14 => c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__pCons,axiom,
% 12.04/12.14 ! [V_p,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.14 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__poly__code_I2_J,axiom,
% 12.04/12.14 ! [V_p,V_a,T_b] :
% 12.04/12.14 ( class_Groups_Oab__group__add(T_b)
% 12.04/12.14 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__minus,axiom,
% 12.04/12.14 ! [V_a,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_equation__minus__iff,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 12.04/12.14 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__equation__iff,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = V_b_2
% 12.04/12.14 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_ab_2 ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_neg__equal__iff__equal,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 12.04/12.14 <=> V_ab_2 = V_b_2 ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_norm__power,axiom,
% 12.04/12.14 ! [V_n,V_x,T_a] :
% 12.04/12.14 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_realpow__two__disj,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.14 ( class_Rings_Oidom(T_a)
% 12.04/12.14 => ( 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))))
% 12.04/12.14 <=> ( V_x_2 = V_y_2
% 12.04/12.14 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_pos__poly__total,axiom,
% 12.04/12.14 ! [V_p,T_a] :
% 12.04/12.14 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.14 => ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 12.04/12.14 | c_Polynomial_Opos__poly(T_a,V_p)
% 12.04/12.14 | c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__monom,axiom,
% 12.04/12.14 ! [V_n,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.14 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_poly__power,axiom,
% 12.04/12.14 ! [V_x,V_n,V_p,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_poly__minus,axiom,
% 12.04/12.14 ! [V_x,V_p,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__ring(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 12.04/12.14 ! [V_q,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 12.04/12.14 ! [V_q,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 12.04/12.14 ! [V_q,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_norm__power__ineq,axiom,
% 12.04/12.14 ! [V_n,V_x,T_a] :
% 12.04/12.14 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_real__0__less__add__iff,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_real__add__less__0__iff,axiom,
% 12.04/12.14 ! [V_y_2,V_x_2] :
% 12.04/12.14 ( 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))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_neg__equal__zero,axiom,
% 12.04/12.14 ! [V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Olinordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = V_ab_2
% 12.04/12.14 <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_neg__equal__0__iff__equal,axiom,
% 12.04/12.14 ! [V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.14 <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_equal__neg__zero,axiom,
% 12.04/12.14 ! [V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Olinordered__ab__group__add(T_a)
% 12.04/12.14 => ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)
% 12.04/12.14 <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_neg__0__equal__iff__equal,axiom,
% 12.04/12.14 ! [V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)
% 12.04/12.14 <=> c_Groups_Ozero__class_Ozero(T_a) = V_ab_2 ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__zero,axiom,
% 12.04/12.14 ! [T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_le__minus__iff,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__le__iff,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_b_2)
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_ab_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_neg__le__iff__le,axiom,
% 12.04/12.14 ! [V_ab_2,V_b_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( 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_ab_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_le__imp__neg__le,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.14 => 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)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__minus__iff,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__less__iff,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_b_2)
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_ab_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_neg__less__iff__less,axiom,
% 12.04/12.14 ! [V_ab_2,V_b_2,T_a] :
% 12.04/12.14 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.14 => ( 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_ab_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__mult__right,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Oring(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__mult__left,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Oring(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__mult__commute,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Oring(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__mult__minus,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Rings_Oring(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_square__eq__iff,axiom,
% 12.04/12.14 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.14 ( class_Rings_Oidom(T_a)
% 12.04/12.14 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ab_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
% 12.04/12.14 <=> ( V_ab_2 = V_b_2
% 12.04/12.14 | V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult_Ominus__right,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__right_Ominus,axiom,
% 12.04/12.14 ! [V_x,V_xa,T_a] :
% 12.04/12.14 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult_Ominus__left,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_mult__left_Ominus,axiom,
% 12.04/12.14 ! [V_y,V_x,T_a] :
% 12.04/12.14 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 12.04/12.14 ! [V_q,V_y,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__add__distrib,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__add,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_add__minus__cancel,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => 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 ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__add__cancel,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.14 => 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 ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_minus__diff__eq,axiom,
% 12.04/12.14 ! [V_b,V_a,T_a] :
% 12.04/12.14 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__fun__def,axiom,
% 12.04/12.14 ! [V_g_2,V_f_2,T_a,T_b] :
% 12.04/12.14 ( class_Orderings_Oord(T_b)
% 12.04/12.14 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 12.04/12.14 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zpower__zadd__distrib,axiom,
% 12.04/12.14 ! [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)) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_norm__minus__cancel,axiom,
% 12.04/12.14 ! [V_x,T_a] :
% 12.04/12.14 ( class_RealVector_Oreal__normed__vector(T_a)
% 12.04/12.14 => 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) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_Zero__not__Suc,axiom,
% 12.04/12.14 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat_Osimps_I2_J,axiom,
% 12.04/12.14 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_Suc__not__Zero,axiom,
% 12.04/12.14 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_nat_Osimps_I3_J,axiom,
% 12.04/12.14 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_Zero__neq__Suc,axiom,
% 12.04/12.14 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_Suc__neq__Zero,axiom,
% 12.04/12.14 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 12.04/12.14 ! [V_q,V_p,V_x,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => 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)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_zpower__zpower,axiom,
% 12.04/12.14 ! [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)) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 12.04/12.14 ! [V_x,T_a] :
% 12.04/12.14 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.14 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__less__eq,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_less__Suc__eq,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 12.04/12.14 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.14 | V_m_2 = V_n_2 ) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_Suc__less__eq,axiom,
% 12.04/12.14 ! [V_n_2,V_m_2] :
% 12.04/12.14 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
% 12.04/12.14 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 12.04/12.14
% 12.04/12.14 fof(fact_not__less__less__Suc__eq,axiom,
% 12.04/12.14 ! [V_m_2,V_n_2] :
% 12.04/12.15 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 12.04/12.15 <=> V_n_2 = V_m_2 ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__antisym,axiom,
% 12.04/12.15 ! [V_m,V_n] :
% 12.04/12.15 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 12.04/12.15 => V_m = V_n ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__SucI,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__lessI,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => ( c_Nat_OSuc(V_m) != V_n
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__trans__Suc,axiom,
% 12.04/12.15 ! [V_k,V_j,V_i] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__SucE,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 12.04/12.15 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => V_m = V_n ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__lessD,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__less__SucD,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_add__Suc__right,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_add__Suc,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_add__Suc__shift,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__leD,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__SucE,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 12.04/12.15 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__SucI,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__le__mono,axiom,
% 12.04/12.15 ! [V_m_2,V_n_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__Suc__eq,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 12.04/12.15 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.15 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_not__less__eq__eq,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__n__not__le__n,axiom,
% 12.04/12.15 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__mult__cancel1,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.15 ( 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)
% 12.04/12.15 <=> V_m_2 = V_n_2 ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_minus__poly__code_I1_J,axiom,
% 12.04/12.15 ! [T_a] :
% 12.04/12.15 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__less__def,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 12.04/12.15 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 12.04/12.15 & V_x_2 != V_y_2 ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__eq__real__def,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 12.04/12.15 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 12.04/12.15 | V_x_2 = V_y_2 ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__Suc__Suc,axiom,
% 12.04/12.15 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__diff__diff,axiom,
% 12.04/12.15 ! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__zero__not__eq__one,axiom,
% 12.04/12.15 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__mult__1,axiom,
% 12.04/12.15 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 12.04/12.15
% 12.04/12.15 fof(fact_smult__minus__right,axiom,
% 12.04/12.15 ! [V_p,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__ring(T_a)
% 12.04/12.15 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__natfloor__eq__one,axiom,
% 12.04/12.15 ! [V_x_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_realpow__Suc__le__self,axiom,
% 12.04/12.15 ! [V_n,V_r,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
% 12.04/12.15 => 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) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_complex__diff__def,axiom,
% 12.04/12.15 ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natfloor__zero,axiom,
% 12.04/12.15 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zero__le__natfloor,axiom,
% 12.04/12.15 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natfloor__mono,axiom,
% 12.04/12.15 ! [V_y,V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_realpow__two__diff,axiom,
% 12.04/12.15 ! [V_y,V_x,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__ring__1(T_a)
% 12.04/12.15 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_minus__le__self__iff,axiom,
% 12.04/12.15 ! [V_ab_2,T_a] :
% 12.04/12.15 ( class_Groups_Olinordered__ab__group__add(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_ab_2)
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_neg__le__0__iff__le,axiom,
% 12.04/12.15 ! [V_ab_2,T_a] :
% 12.04/12.15 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__minus__self__iff,axiom,
% 12.04/12.15 ! [V_ab_2,T_a] :
% 12.04/12.15 ( class_Groups_Olinordered__ab__group__add(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_neg__0__le__iff__le,axiom,
% 12.04/12.15 ! [V_ab_2,T_a] :
% 12.04/12.15 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_neg__0__less__iff__less,axiom,
% 12.04/12.15 ! [V_ab_2,T_a] :
% 12.04/12.15 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_neg__less__0__iff__less,axiom,
% 12.04/12.15 ! [V_ab_2,T_a] :
% 12.04/12.15 ( class_Groups_Oordered__ab__group__add(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_neg__less__nonneg,axiom,
% 12.04/12.15 ! [V_ab_2,T_a] :
% 12.04/12.15 ( class_Groups_Olinordered__ab__group__add(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_ab_2)
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__minus__self__iff,axiom,
% 12.04/12.15 ! [V_ab_2,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_minus__unique,axiom,
% 12.04/12.15 ! [V_b,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.15 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_add__eq__0__iff,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.15 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.15 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_ab__left__minus,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_left__minus,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 12.04/12.15 ! [V_b_2,V_ab_2,T_a] :
% 12.04/12.15 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.15 => ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 12.04/12.15 <=> c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_right__minus,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__0,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.15 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_square__eq__1__iff,axiom,
% 12.04/12.15 ! [V_x_2,T_a] :
% 12.04/12.15 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 12.04/12.15 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 12.04/12.15 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 12.04/12.15 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 12.04/12.15 ! [V_x,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__ring__1(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__def,axiom,
% 12.04/12.15 ! [V_b,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.15 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_ab__diff__minus,axiom,
% 12.04/12.15 ! [V_b,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.15 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__minus__eq__add,axiom,
% 12.04/12.15 ! [V_b,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Ogroup__add(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 12.04/12.15 ! [V_y,V_x,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__ring__1(T_a)
% 12.04/12.15 => c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 12.04/12.15 ! [V_x,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 12.04/12.15 ! [V_q,V_p,V_x,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__minus__mult__self__le,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_not__pos__poly__0,axiom,
% 12.04/12.15 ! [T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.15 => ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_gr0__conv__Suc,axiom,
% 12.04/12.15 ! [V_n_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 12.04/12.15 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__Suc0,axiom,
% 12.04/12.15 ! [V_n_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 12.04/12.15 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__Suc__eq__0__disj,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 12.04/12.15 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 | ? [B_j] :
% 12.04/12.15 ( V_m_2 = c_Nat_OSuc(B_j)
% 12.04/12.15 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_one__is__add,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( 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)
% 12.04/12.15 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 12.04/12.15 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 12.04/12.15 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_add__is__1,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 12.04/12.15 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 12.04/12.15 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__add__minus__iff,axiom,
% 12.04/12.15 ! [V_ab_2,V_x_2] :
% 12.04/12.15 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ab_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 12.04/12.15 <=> V_x_2 = V_ab_2 ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__add__eq__0__iff,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2] :
% 12.04/12.15 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 12.04/12.15 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_mult__eq__1__iff,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 12.04/12.15 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__iff__Suc__add,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.15 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__add__Suc2,axiom,
% 12.04/12.15 ! [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))) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__add__Suc1,axiom,
% 12.04/12.15 ! [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))) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__eq__Suc__le,axiom,
% 12.04/12.15 ! [V_m_2,V_n_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__Suc__eq__le,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__le__eq,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__imp__less__Suc,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__leI,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__less__Suc__eq,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 12.04/12.15 <=> V_n_2 = V_m_2 ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__le__lessD,axiom,
% 12.04/12.15 ! [V_n,V_m] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_One__nat__def,axiom,
% 12.04/12.15 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__mult__less__cancel1,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__less__Suc,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_mult__Suc__right,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_mult__Suc,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__mult__le__cancel1,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__diff__le,axiom,
% 12.04/12.15 ! [V_m,V_n] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__eq__plus1__left,axiom,
% 12.04/12.15 ! [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) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__eq__plus1,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natfloor__add__one,axiom,
% 12.04/12.15 ! [V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__Suc__1,axiom,
% 12.04/12.15 ! [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 ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 12.04/12.15 ! [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) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__diff__def,axiom,
% 12.04/12.15 ! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_minus__real__def,axiom,
% 12.04/12.15 ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__mult__less__mono2,axiom,
% 12.04/12.15 ! [V_y,V_x,V_z] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__mult__order,axiom,
% 12.04/12.15 ! [V_y,V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__mult__less__iff1,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,V_z_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 12.04/12.15 => ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_norm__not__less__zero,axiom,
% 12.04/12.15 ! [V_x,T_a] :
% 12.04/12.15 ( class_RealVector_Oreal__normed__vector(T_a)
% 12.04/12.15 => ~ 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_complex__mod__minus__le__complex__mod,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_pos__poly__add,axiom,
% 12.04/12.15 ! [V_q,V_p,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.15 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 12.04/12.15 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 12.04/12.15 => c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_pos__poly__mult,axiom,
% 12.04/12.15 ! [V_q,V_p,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.15 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 12.04/12.15 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 12.04/12.15 => c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__poly__code_I1_J,axiom,
% 12.04/12.15 ! [V_q,T_a] :
% 12.04/12.15 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.15 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natfloor__neg,axiom,
% 12.04/12.15 ! [V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 12.04/12.15 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__eq__poly__def,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__idom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 12.04/12.15 <=> ( V_x_2 = V_y_2
% 12.04/12.15 | c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__0__le__add__iff,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__add__le__0__iff,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_n__less__m__mult__n,axiom,
% 12.04/12.15 ! [V_m,V_n] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_n__less__n__mult__m,axiom,
% 12.04/12.15 ! [V_m,V_n] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_one__less__mult,axiom,
% 12.04/12.15 ! [V_m,V_n] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__pred,axiom,
% 12.04/12.15 ! [V_n] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.15 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__Suc__less,axiom,
% 12.04/12.15 ! [V_i,V_n] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_one__le__mult__iff,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
% 12.04/12.15 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zero__less__norm__iff,axiom,
% 12.04/12.15 ! [V_x_2,T_a] :
% 12.04/12.15 ( class_RealVector_Oreal__normed__vector(T_a)
% 12.04/12.15 => ( 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))
% 12.04/12.15 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__Suc__diff__eq2,axiom,
% 12.04/12.15 ! [V_m,V_j,V_k] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 12.04/12.15 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__Suc__diff__eq1,axiom,
% 12.04/12.15 ! [V_m,V_j,V_k] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 12.04/12.15 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(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_m,V_k),c_Nat_OSuc(V_j)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_norm__mult__less,axiom,
% 12.04/12.15 ! [V_s,V_y,V_r,V_x,T_a] :
% 12.04/12.15 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 12.04/12.15 => 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)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__mult__le__cancel__iff1,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,V_z_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 12.04/12.15 => ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_real__mult__le__cancel__iff2,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,V_z_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 12.04/12.15 => ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_norm__add__less,axiom,
% 12.04/12.15 ! [V_s,V_y,V_r,V_x,T_a] :
% 12.04/12.15 ( class_RealVector_Oreal__normed__vector(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 12.04/12.15 => 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)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_poly__monom,axiom,
% 12.04/12.15 ! [V_x,V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_monom__Suc,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Ozero(T_a)
% 12.04/12.15 => c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n)) = c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__eq__if,axiom,
% 12.04/12.15 ! [V_p,V_m] :
% 12.04/12.15 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 12.04/12.15 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__diff__1,axiom,
% 12.04/12.15 ! [V_n] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.15 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Suc__pred_H,axiom,
% 12.04/12.15 ! [V_n] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.15 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_realpow__num__eq__if,axiom,
% 12.04/12.15 ! [V_m,V_n,T_a] :
% 12.04/12.15 ( class_Power_Opower(T_a)
% 12.04/12.15 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 12.04/12.15 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__strict__mono,axiom,
% 12.04/12.15 ! [V_n,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.15 => 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)) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_lemma__realpow__diff,axiom,
% 12.04/12.15 ! [V_y,V_n,V_p,T_a] :
% 12.04/12.15 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
% 12.04/12.15 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_one__less__power,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.15 => 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)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_pos__zmult__eq__1__iff,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)
% 12.04/12.15 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 12.04/12.15 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 12.04/12.15 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zmult__zless__mono2,axiom,
% 12.04/12.15 ! [V_k,V_j,V_i] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zmult__1__right,axiom,
% 12.04/12.15 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zmult__1,axiom,
% 12.04/12.15 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zmult__zminus,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__zmult__distrib2,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__zmult__distrib,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zdiff__zmult__distrib,axiom,
% 12.04/12.15 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zmult__assoc,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zdiff__zmult__distrib2,axiom,
% 12.04/12.15 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zmult__commute,axiom,
% 12.04/12.15 ! [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) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_field__power__not__zero,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 12.04/12.15 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__commutes,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__mult__distrib,axiom,
% 12.04/12.15 ! [V_n,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Ocomm__monoid__mult(T_a)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__one,axiom,
% 12.04/12.15 ! [V_n,T_a] :
% 12.04/12.15 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__Suc__0,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 12.04/12.15 ! [V_m_2,V_x_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_nat__zero__less__power__iff,axiom,
% 12.04/12.15 ! [V_n_2,V_x_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 12.04/12.15 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_nat__power__less__imp__less,axiom,
% 12.04/12.15 ! [V_n,V_m,V_i] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__mult,axiom,
% 12.04/12.15 ! [V_n,V_m,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__one__right,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.15 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zero__le__power,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__mono,axiom,
% 12.04/12.15 ! [V_n,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => 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)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zero__less__power,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_one__le__power,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__eq__0__iff,axiom,
% 12.04/12.15 ! [V_n_2,V_ab_2,T_a] :
% 12.04/12.15 ( ( class_Power_Opower(T_a)
% 12.04/12.15 & class_Rings_Omult__zero(T_a)
% 12.04/12.15 & class_Rings_Ono__zero__divisors(T_a)
% 12.04/12.15 & class_Rings_Ozero__neq__one(T_a) )
% 12.04/12.15 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 <=> ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__inject__exp,axiom,
% 12.04/12.15 ! [V_n_2,V_m_2,V_ab_2,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_ab_2)
% 12.04/12.15 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2)
% 12.04/12.15 <=> V_m_2 = V_n_2 ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__0__Suc,axiom,
% 12.04/12.15 ! [V_n,T_a] :
% 12.04/12.15 ( ( class_Power_Opower(T_a)
% 12.04/12.15 & class_Rings_Osemiring__0(T_a) )
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__Suc,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Power_Opower(T_a)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__Suc2,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__0,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Power_Opower(T_a)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__add,axiom,
% 12.04/12.15 ! [V_n,V_m,V_a,T_a] :
% 12.04/12.15 ( class_Groups_Omonoid__mult(T_a)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_nat__one__le__power,axiom,
% 12.04/12.15 ! [V_n,V_i] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__less__imp__less__base,axiom,
% 12.04/12.15 ! [V_b,V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.15 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__inject__base,axiom,
% 12.04/12.15 ! [V_b,V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.15 => V_a = V_b ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__le__imp__le__base,axiom,
% 12.04/12.15 ! [V_b,V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( 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)))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__gt1__lemma,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => 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))) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__less__power__Suc,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => 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))) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__0__left,axiom,
% 12.04/12.15 ! [V_n,T_a] :
% 12.04/12.15 ( ( class_Power_Opower(T_a)
% 12.04/12.15 & class_Rings_Osemiring__0(T_a) )
% 12.04/12.15 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 => 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) )
% 12.04/12.15 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 => 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) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__gt1,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => 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))) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__minus,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Oring__1(T_a)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__strict__increasing__iff,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 12.04/12.15 => ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__less__imp__less__exp,axiom,
% 12.04/12.15 ! [V_n,V_m,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__strict__increasing,axiom,
% 12.04/12.15 ! [V_a,V_N,V_n,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => 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)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__increasing,axiom,
% 12.04/12.15 ! [V_a,V_N,V_n,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => 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)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__Suc__less,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 12.04/12.15 => 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)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__Suc__less__one,axiom,
% 12.04/12.15 ! [V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 12.04/12.15 => 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)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__strict__decreasing,axiom,
% 12.04/12.15 ! [V_a,V_N,V_n,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 12.04/12.15 => 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)) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__eq__imp__eq__base,axiom,
% 12.04/12.15 ! [V_b,V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( 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)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.15 => V_a = V_b ) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__decreasing,axiom,
% 12.04/12.15 ! [V_a,V_N,V_n,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 12.04/12.15 => 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)) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__le__imp__le__exp,axiom,
% 12.04/12.15 ! [V_n,V_m,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__increasing__iff,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 12.04/12.15 ( class_Rings_Olinordered__semidom(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 12.04/12.15 => ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zero__less__power__nat__eq,axiom,
% 12.04/12.15 ! [V_n_2,V_x_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_not__real__square__gt__zero,axiom,
% 12.04/12.15 ! [V_x_2] :
% 12.04/12.15 ( ~ 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))
% 12.04/12.15 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 12.04/12.15 ! [V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 12.04/12.15 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.15 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_less__bin__lemma,axiom,
% 12.04/12.15 ! [V_l_2,V_k_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zle__add1__eq__le,axiom,
% 12.04/12.15 ! [V_z_2,V_w_2] :
% 12.04/12.15 ( 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)))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zle__diff1__eq,axiom,
% 12.04/12.15 ! [V_z_2,V_w_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_add1__zle__eq,axiom,
% 12.04/12.15 ! [V_z_2,V_w_2] :
% 12.04/12.15 ( 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)
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__imp__0__less,axiom,
% 12.04/12.15 ! [V_z] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zless__imp__add1__zle,axiom,
% 12.04/12.15 ! [V_z,V_w] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 12.04/12.15 => 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) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__zless__mono,axiom,
% 12.04/12.15 ! [V_z,V_z_H,V_w,V_w_H] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__strict__right__mono,axiom,
% 12.04/12.15 ! [V_k,V_j,V_i] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_odd__less__0,axiom,
% 12.04/12.15 ! [V_z_2] :
% 12.04/12.15 ( 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))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zless__add1__eq,axiom,
% 12.04/12.15 ! [V_z_2,V_w_2] :
% 12.04/12.15 ( 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)))
% 12.04/12.15 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
% 12.04/12.15 | V_w_2 = V_z_2 ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_int__0__less__1,axiom,
% 12.04/12.15 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zless__linear,axiom,
% 12.04/12.15 ! [V_y,V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 12.04/12.15 | V_x = V_y
% 12.04/12.15 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zless__le,axiom,
% 12.04/12.15 ! [V_w_2,V_z_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
% 12.04/12.15 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2)
% 12.04/12.15 & V_z_2 != V_w_2 ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_int__one__le__iff__zero__less,axiom,
% 12.04/12.15 ! [V_z_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zminus__zminus,axiom,
% 12.04/12.15 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zminus__0,axiom,
% 12.04/12.15 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zminus__zadd__distrib,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__zminus__inverse2,axiom,
% 12.04/12.15 ! [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) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__int__def__symmetric,axiom,
% 12.04/12.15 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_diff__int__def,axiom,
% 12.04/12.15 ! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__left__mono,axiom,
% 12.04/12.15 ! [V_k,V_j,V_i] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__0,axiom,
% 12.04/12.15 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__0__right,axiom,
% 12.04/12.15 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__commute,axiom,
% 12.04/12.15 ! [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) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__left__commute,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zadd__assoc,axiom,
% 12.04/12.15 ! [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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_int__0__neq__1,axiom,
% 12.04/12.15 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_odd__nonzero,axiom,
% 12.04/12.15 ! [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) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_self__quotient__aux1,axiom,
% 12.04/12.15 ! [V_q,V_r,V_a] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_self__quotient__aux2,axiom,
% 12.04/12.15 ! [V_q,V_r,V_a] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zle__refl,axiom,
% 12.04/12.15 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zle__linear,axiom,
% 12.04/12.15 ! [V_w,V_z] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 12.04/12.15 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zle__trans,axiom,
% 12.04/12.15 ! [V_k,V_j,V_i] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zle__antisym,axiom,
% 12.04/12.15 ! [V_w,V_z] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 12.04/12.15 => V_z = V_w ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_q__pos__lemma,axiom,
% 12.04/12.15 ! [V_r_H,V_q_H,V_b_H] :
% 12.04/12.15 ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_q__neg__lemma,axiom,
% 12.04/12.15 ! [V_r_H,V_q_H,V_b_H] :
% 12.04/12.15 ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_unique__quotient__lemma,axiom,
% 12.04/12.15 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 12.04/12.15 ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zdiv__mono2__lemma,axiom,
% 12.04/12.15 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 12.04/12.15 ( 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)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_unique__quotient__lemma__neg,axiom,
% 12.04/12.15 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 12.04/12.15 ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 12.04/12.15 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 12.04/12.15 ( 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)
% 12.04/12.15 => ( 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))
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 12.04/12.15 ! [V_n,V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 12.04/12.15 ! [V_y,V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 12.04/12.15 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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 12.04/12.15 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)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 12.04/12.15 ! [V_y,V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 12.04/12.15 => 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)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natceiling__add__one,axiom,
% 12.04/12.15 ! [V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__power__power,axiom,
% 12.04/12.15 ! [T_a] :
% 12.04/12.15 ( class_Power_Opower(T_a)
% 12.04/12.15 => 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)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natceiling__zero,axiom,
% 12.04/12.15 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_zero__le__natceiling,axiom,
% 12.04/12.15 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natceiling__mono,axiom,
% 12.04/12.15 ! [V_y,V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 12.04/12.15 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natceiling__one,axiom,
% 12.04/12.15 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power_Opower_Opower__0,axiom,
% 12.04/12.15 ! [V_ab_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power_Opower_Opower__Suc,axiom,
% 12.04/12.15 ! [V_n_2,V_ab_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_ab_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),V_n_2)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natceiling__neg,axiom,
% 12.04/12.15 ! [V_x] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 12.04/12.15 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_natceiling__le__eq__one,axiom,
% 12.04/12.15 ! [V_x_2] :
% 12.04/12.15 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 12.04/12.15 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_unimodular__reduce__norm,axiom,
% 12.04/12.15 ! [V_z] :
% 12.04/12.15 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 12.04/12.15 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 12.04/12.15 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 12.04/12.15 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_order__2,axiom,
% 12.04/12.15 ! [V_a,V_p,T_a] :
% 12.04/12.15 ( class_Rings_Oidom(T_a)
% 12.04/12.15 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 12.04/12.15 => ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__0__right,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_power__le__dvd,axiom,
% 12.04/12.15 ! [V_m,V_b,V_n,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__power__le,axiom,
% 12.04/12.15 ! [V_m,V_n,V_y,V_x,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_le__imp__power__dvd,axiom,
% 12.04/12.15 ! [V_a,V_n,V_m,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__power__same,axiom,
% 12.04/12.15 ! [V_n,V_y,V_x,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__triv__left,axiom,
% 12.04/12.15 ! [V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__triv__right,axiom,
% 12.04/12.15 ! [V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__mult2,axiom,
% 12.04/12.15 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__mult,axiom,
% 12.04/12.15 ! [V_b,V_c,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_mult__dvd__mono,axiom,
% 12.04/12.15 ! [V_d,V_c,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvdI,axiom,
% 12.04/12.15 ! [V_k,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Odvd(T_a)
% 12.04/12.15 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_a) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__mult__left,axiom,
% 12.04/12.15 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__mult__right,axiom,
% 12.04/12.15 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__refl,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_a) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__trans,axiom,
% 12.04/12.15 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_smult__dvd__cancel,axiom,
% 12.04/12.15 ! [V_q,V_p,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__smult,axiom,
% 12.04/12.15 ! [V_a,V_q,V_p,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_complex__i__not__one,axiom,
% 12.04/12.15 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__0__left,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 12.04/12.15 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__add,axiom,
% 12.04/12.15 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_one__dvd,axiom,
% 12.04/12.15 ! [V_a,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_complex__i__not__zero,axiom,
% 12.04/12.15 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__smult__iff,axiom,
% 12.04/12.15 ! [V_q_2,V_pa_2,V_ab_2,T_a] :
% 12.04/12.15 ( class_Fields_Ofield(T_a)
% 12.04/12.15 => ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_ab_2,V_q_2))
% 12.04/12.15 <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_smult__dvd,axiom,
% 12.04/12.15 ! [V_a,V_q,V_p,T_a] :
% 12.04/12.15 ( class_Fields_Ofield(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
% 12.04/12.15 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__smult__cancel,axiom,
% 12.04/12.15 ! [V_q,V_a,V_p,T_a] :
% 12.04/12.15 ( class_Fields_Ofield(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))
% 12.04/12.15 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__mult__cancel__left,axiom,
% 12.04/12.15 ! [V_b_2,V_ab_2,V_ca_2,T_a] :
% 12.04/12.15 ( class_Rings_Oidom(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 12.04/12.15 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 | c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__mult__cancel__right,axiom,
% 12.04/12.15 ! [V_b_2,V_ca_2,V_ab_2,T_a] :
% 12.04/12.15 ( class_Rings_Oidom(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
% 12.04/12.15 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 | c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__diff,axiom,
% 12.04/12.15 ! [V_z,V_y,V_x,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__ring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_complex__i__mult__minus,axiom,
% 12.04/12.15 ! [V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),V_x)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_x) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_minus__dvd__iff,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__ring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
% 12.04/12.15 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__minus__iff,axiom,
% 12.04/12.15 ! [V_y_2,V_x_2,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__ring__1(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 12.04/12.15 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_i__mult__eq2,axiom,
% 12.04/12.15 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_smult__dvd__iff,axiom,
% 12.04/12.15 ! [V_q_2,V_pa_2,V_ab_2,T_a] :
% 12.04/12.15 ( class_Fields_Ofield(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_ab_2,V_pa_2),V_q_2)
% 12.04/12.15 <=> ( ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 => V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 12.04/12.15 & ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2) ) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__power,axiom,
% 12.04/12.15 ! [V_x,V_n,T_a] :
% 12.04/12.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 12.04/12.15 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.15 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_dvd__iff__poly__eq__0,axiom,
% 12.04/12.15 ! [V_pa_2,V_ca_2,T_a] :
% 12.04/12.15 ( class_Rings_Oidom(T_a)
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)
% 12.04/12.15 <=> hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_poly__eq__0__iff__dvd,axiom,
% 12.04/12.15 ! [V_ca_2,V_pa_2,T_a] :
% 12.04/12.15 ( class_Rings_Oidom(T_a)
% 12.04/12.15 => ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2) = c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.15 <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_order__1,axiom,
% 12.04/12.15 ! [V_p,V_a,T_a] :
% 12.04/12.15 ( class_Rings_Oidom(T_a)
% 12.04/12.15 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_order,axiom,
% 12.04/12.15 ! [V_a,V_p,T_a] :
% 12.04/12.15 ( class_Rings_Oidom(T_a)
% 12.04/12.15 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p)
% 12.04/12.15 & ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_inf__period_I3_J,axiom,
% 12.04/12.15 ! [V_t_2,V_D_2,V_db_2,T_a] :
% 12.04/12.15 ( ( class_Rings_Ocomm__ring(T_a)
% 12.04/12.15 & class_Rings_Odvd(T_a) )
% 12.04/12.15 => ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,V_D_2)
% 12.04/12.15 => ! [B_x,B_k] :
% 12.04/12.15 ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
% 12.04/12.15 <=> c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) ) ) ) ).
% 12.04/12.15
% 12.04/12.15 fof(fact_inf__period_I4_J,axiom,
% 12.04/12.15 ! [V_t_2,V_D_2,V_db_2,T_a] :
% 12.04/12.16 ( ( class_Rings_Ocomm__ring(T_a)
% 12.04/12.16 & class_Rings_Odvd(T_a) )
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,V_D_2)
% 12.04/12.16 => ! [B_x,B_k] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__1__left,axiom,
% 12.04/12.16 ! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__antisym__nonneg,axiom,
% 12.04/12.16 ! [V_n,V_m] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
% 12.04/12.16 => V_m = V_n ) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__diffD1,axiom,
% 12.04/12.16 ! [V_n,V_m,V_k] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__diffD,axiom,
% 12.04/12.16 ! [V_n,V_m,V_k] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__reduce,axiom,
% 12.04/12.16 ! [V_n_2,V_k_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_nat__dvd__1__iff__1,axiom,
% 12.04/12.16 ! [V_m_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 12.04/12.16 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 12.04/12.16 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 12.04/12.16 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.16 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_nat__dvd__not__less,axiom,
% 12.04/12.16 ! [V_n,V_m] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 12.04/12.16 => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__1__iff__1,axiom,
% 12.04/12.16 ! [V_m_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 12.04/12.16 <=> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__zdiffD,axiom,
% 12.04/12.16 ! [V_n,V_m,V_k] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__mult__cancel,axiom,
% 12.04/12.16 ! [V_n,V_m,V_k] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))
% 12.04/12.16 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__period,axiom,
% 12.04/12.16 ! [V_ca_2,V_t_2,V_x_2,V_db_2,V_ab_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_db_2)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_db_2)),V_t_2)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__mono,axiom,
% 12.04/12.16 ! [V_t_2,V_m_2,V_k_2] :
% 12.04/12.16 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2)
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__reduce,axiom,
% 12.04/12.16 ! [V_m_2,V_n_2,V_k_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__diff__nat,axiom,
% 12.04/12.16 ! [V_n,V_m,V_k] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 12.04/12.16 ! [V_t_2,V_db_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,V_t_2)
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 12.04/12.16 ! [V_t_2,V_db_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,V_t_2)
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_db_2),V_t_2) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__not__zless,axiom,
% 12.04/12.16 ! [V_n,V_m] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
% 12.04/12.16 => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__imp__le,axiom,
% 12.04/12.16 ! [V_n,V_z] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
% 12.04/12.16 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__imp__le,axiom,
% 12.04/12.16 ! [V_n,V_k] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.16 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_nat__mult__dvd__cancel1,axiom,
% 12.04/12.16 ! [V_n_2,V_m_2,V_k_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__mult__cancel,axiom,
% 12.04/12.16 ! [V_n,V_m,V_k] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__mult__cancel1,axiom,
% 12.04/12.16 ! [V_n_2,V_m_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2),V_m_2)
% 12.04/12.16 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__mult__cancel2,axiom,
% 12.04/12.16 ! [V_n_2,V_m_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2),V_m_2)
% 12.04/12.16 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_power__dvd__imp__le,axiom,
% 12.04/12.16 ! [V_n,V_m,V_i] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
% 12.04/12.16 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_unity__coeff__ex,axiom,
% 12.04/12.16 ! [V_l_2,V_P_2,T_a] :
% 12.04/12.16 ( ( class_Rings_Odvd(T_a)
% 12.04/12.16 & class_Rings_Osemiring__0(T_a) )
% 12.04/12.16 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
% 12.04/12.16 <=> ? [B_x] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))
% 12.04/12.16 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_reduce__poly__simple,axiom,
% 12.04/12.16 ! [V_n,V_b] :
% 12.04/12.16 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 12.04/12.16 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.16 => ? [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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_pow__divides__eq__nat,axiom,
% 12.04/12.16 ! [V_b_2,V_ab_2,V_n_2] :
% 12.04/12.16 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ab_2,V_b_2) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oorder__refl,axiom,
% 12.04/12.16 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oeq__iff,axiom,
% 12.04/12.16 ! [V_y_2,V_x_2] :
% 12.04/12.16 ( V_x_2 = V_y_2
% 12.04/12.16 <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 12.04/12.16 & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Ole__less,axiom,
% 12.04/12.16 ! [V_y_2,V_x_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 12.04/12.16 <=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) )
% 12.04/12.16 | V_x_2 = V_y_2 ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__le,axiom,
% 12.04/12.16 ! [V_y_2,V_x_2] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) )
% 12.04/12.16 <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 12.04/12.16 & V_x_2 != V_y_2 ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oneq__le__trans,axiom,
% 12.04/12.16 ! [V_b,V_a] :
% 12.04/12.16 ( V_a != V_b
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oeq__refl,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( V_x = V_y
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oantisym__conv,axiom,
% 12.04/12.16 ! [V_x_2,V_y_2] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 12.04/12.16 <=> V_x_2 = V_y_2 ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 | V_x = V_y ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Ole__neq__trans,axiom,
% 12.04/12.16 ! [V_b,V_a] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 12.04/12.16 => ( V_a != V_b
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 12.04/12.16 ! [V_c,V_b,V_a] :
% 12.04/12.16 ( V_a = V_b
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 12.04/12.16 ! [V_c,V_b,V_a] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 12.04/12.16 => ( V_b = V_c
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__antisym,axiom,
% 12.04/12.16 ! [V_n,V_m] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)
% 12.04/12.16 => V_m = V_n ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oantisym,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 12.04/12.16 => V_x = V_y ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oorder__trans,axiom,
% 12.04/12.16 ! [V_z,V_y,V_x] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 12.04/12.16 ! [V_c,V_b,V_a] :
% 12.04/12.16 ( V_a = V_b
% 12.04/12.16 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b) )
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Ole__less__trans,axiom,
% 12.04/12.16 ! [V_z,V_y,V_x] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) )
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__imp__neq,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => V_x != V_y ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__not__sym,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__imp__le,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__imp__not__less,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => V_x != V_y ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => V_y != V_x ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 12.04/12.16 ! [V_c,V_b,V_a] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) )
% 12.04/12.16 => ( V_b = V_c
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__le__trans,axiom,
% 12.04/12.16 ! [V_z,V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__asym_H,axiom,
% 12.04/12.16 ! [V_b,V_a] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) )
% 12.04/12.16 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__trans,axiom,
% 12.04/12.16 ! [V_z,V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) )
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd_Oless__asym,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 12.04/12.16 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 12.04/12.16 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
% 12.04/12.16 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
% 12.04/12.16 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__pos__nat,axiom,
% 12.04/12.16 ! [V_m,V_n] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
% 12.04/12.16 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_pow__divides__pow__int,axiom,
% 12.04/12.16 ! [V_b,V_n,V_a] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))
% 12.04/12.16 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_pow__divides__eq__int,axiom,
% 12.04/12.16 ! [V_b_2,V_ab_2,V_n_2] :
% 12.04/12.16 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_b_2) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_pow__divides__pow__nat,axiom,
% 12.04/12.16 ! [V_b,V_n,V_a] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))
% 12.04/12.16 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 12.04/12.16 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_mult_Opos__bounded,axiom,
% 12.04/12.16 ! [T_a] :
% 12.04/12.16 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.16 => ? [B_K] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 12.04/12.16 & ! [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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_mult__right_Opos__bounded,axiom,
% 12.04/12.16 ! [V_x,T_a] :
% 12.04/12.16 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.16 => ? [B_K] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 12.04/12.16 & ! [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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_mult__left_Opos__bounded,axiom,
% 12.04/12.16 ! [V_y,T_a] :
% 12.04/12.16 ( class_RealVector_Oreal__normed__algebra(T_a)
% 12.04/12.16 => ? [B_K] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 12.04/12.16 & ! [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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_poly__cont,axiom,
% 12.04/12.16 ! [V_p,V_z,V_e] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)
% 12.04/12.16 => ? [B_d] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 12.04/12.16 & ! [B_w] :
% 12.04/12.16 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)))
% 12.04/12.16 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)),B_d) )
% 12.04/12.16 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),V_z))),V_e) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_tsub__def,axiom,
% 12.04/12.16 ! [V_x,V_y] :
% 12.04/12.16 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 12.04/12.16 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 12.04/12.16 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 12.04/12.16 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natceiling__eq,axiom,
% 12.04/12.16 ! [V_x,V_n] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 12.04/12.16 => ( 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)))
% 12.04/12.16 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__ge__zero,axiom,
% 12.04/12.16 ! [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)) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__power,axiom,
% 12.04/12.16 ! [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) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_power__real__of__nat,axiom,
% 12.04/12.16 ! [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)) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 12.04/12.16 ! [V_n_2] :
% 12.04/12.16 ( 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))
% 12.04/12.16 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__Suc__gt__zero,axiom,
% 12.04/12.16 ! [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))) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__one,axiom,
% 12.04/12.16 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) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__1,axiom,
% 12.04/12.16 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__less__iff,axiom,
% 12.04/12.16 ! [V_m_2,V_n_2] :
% 12.04/12.16 ( 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))
% 12.04/12.16 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__add,axiom,
% 12.04/12.16 ! [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)) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natfloor__real__of__nat,axiom,
% 12.04/12.16 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__inject,axiom,
% 12.04/12.16 ! [V_m_2,V_n_2] :
% 12.04/12.16 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
% 12.04/12.16 <=> V_n_2 = V_m_2 ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__le__iff,axiom,
% 12.04/12.16 ! [V_m_2,V_n_2] :
% 12.04/12.16 ( 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))
% 12.04/12.16 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__natceiling__ge,axiom,
% 12.04/12.16 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natceiling__real__of__nat,axiom,
% 12.04/12.16 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__mult,axiom,
% 12.04/12.16 ! [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)) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__zero,axiom,
% 12.04/12.16 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__zero__iff,axiom,
% 12.04/12.16 ! [V_n_2] :
% 12.04/12.16 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 12.04/12.16 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_not__real__of__nat__less__zero,axiom,
% 12.04/12.16 ! [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)) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natceiling__le,axiom,
% 12.04/12.16 ! [V_a,V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
% 12.04/12.16 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_le__natfloor,axiom,
% 12.04/12.16 ! [V_a,V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
% 12.04/12.16 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__natfloor__le,axiom,
% 12.04/12.16 ! [V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.16 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__diff,axiom,
% 12.04/12.16 ! [V_m,V_n] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 12.04/12.16 => c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__Suc,axiom,
% 12.04/12.16 ! [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)) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natfloor__power,axiom,
% 12.04/12.16 ! [V_n,V_x] :
% 12.04/12.16 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
% 12.04/12.16 => 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) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 12.04/12.16 ! [V_n_2] :
% 12.04/12.16 ( 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))
% 12.04/12.16 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_nat__less__real__le,axiom,
% 12.04/12.16 ! [V_m_2,V_n_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 12.04/12.16 <=> 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)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_nat__le__real__less,axiom,
% 12.04/12.16 ! [V_m_2,V_n_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
% 12.04/12.16 <=> 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))) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_le__natfloor__eq,axiom,
% 12.04/12.16 ! [V_ab_2,V_x_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ab_2,c_RComplete_Onatfloor(V_x_2))
% 12.04/12.16 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2),V_x_2) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natceiling__le__eq,axiom,
% 12.04/12.16 ! [V_ab_2,V_x_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_ab_2)
% 12.04/12.16 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__natfloor__add__one__gt,axiom,
% 12.04/12.16 ! [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))) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natfloor__subtract,axiom,
% 12.04/12.16 ! [V_x,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 12.04/12.16 => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_real__natfloor__gt__diff__one,axiom,
% 12.04/12.16 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natceiling__subtract,axiom,
% 12.04/12.16 ! [V_x,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 12.04/12.16 => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 12.04/12.16 ! [V_y,V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 12.04/12.16 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_less__natfloor,axiom,
% 12.04/12.16 ! [V_n,V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
% 12.04/12.16 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_tsub__eq,axiom,
% 12.04/12.16 ! [V_x,V_y] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 12.04/12.16 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natfloor__add,axiom,
% 12.04/12.16 ! [V_a,V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.16 => 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) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 12.04/12.16 ! [V_n,V_z] :
% 12.04/12.16 ( 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)
% 12.04/12.16 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natfloor__eq,axiom,
% 12.04/12.16 ! [V_x,V_n] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 12.04/12.16 => ( 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)))
% 12.04/12.16 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_natceiling__add,axiom,
% 12.04/12.16 ! [V_a,V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.16 => 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) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 12.04/12.16 ! [V_n,V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.16 => 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)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_lemma__NBseq__def,axiom,
% 12.04/12.16 ! [V_X_2,T_b] :
% 12.04/12.16 ( class_RealVector_Oreal__normed__vector(T_b)
% 12.04/12.16 => ( ? [B_K] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 12.04/12.16 & ! [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) )
% 12.04/12.16 <=> ? [B_N] :
% 12.04/12.16 ! [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))) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_lemma__NBseq__def2,axiom,
% 12.04/12.16 ! [V_X_2,T_b] :
% 12.04/12.16 ( class_RealVector_Oreal__normed__vector(T_b)
% 12.04/12.16 => ( ? [B_K] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 12.04/12.16 & ! [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) )
% 12.04/12.16 <=> ? [B_N] :
% 12.04/12.16 ! [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))) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_reals__Archimedean6,axiom,
% 12.04/12.16 ! [V_r] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 12.04/12.16 => ? [B_n] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r)
% 12.04/12.16 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_reals__Archimedean4,axiom,
% 12.04/12.16 ! [V_x,V_y] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 12.04/12.16 => ? [B_n] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y),V_x)
% 12.04/12.16 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y)) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_lemmaCauchy,axiom,
% 12.04/12.16 ! [V_X_2,V_M_2,T_a,T_b] :
% 12.04/12.16 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 12.04/12.16 & class_Orderings_Oord(T_a) )
% 12.04/12.16 => ( ! [B_n] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 12.04/12.16 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
% 12.04/12.16 => ! [B_n] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 12.04/12.16 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_poly__bound__exists,axiom,
% 12.04/12.16 ! [V_p,V_r] :
% 12.04/12.16 ? [B_m] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 12.04/12.16 & ! [B_z] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),V_r)
% 12.04/12.16 => 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) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_Limits_Ominus__diff__minus,axiom,
% 12.04/12.16 ! [V_b,V_a,T_a] :
% 12.04/12.16 ( class_Groups_Oab__group__add(T_a)
% 12.04/12.16 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_int__power__div__base,axiom,
% 12.04/12.16 ! [V_k,V_m] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 12.04/12.16 => 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)))) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__mult__self1,axiom,
% 12.04/12.16 ! [V_c,V_a,V_b,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.16 => 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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__mult__self2,axiom,
% 12.04/12.16 ! [V_c,V_a,V_b,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.16 => 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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__add__self2,axiom,
% 12.04/12.16 ! [V_a,V_b,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.16 => 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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__add__self1,axiom,
% 12.04/12.16 ! [V_a,V_b,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.16 => 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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__div__eq__mult,axiom,
% 12.04/12.16 ! [V_ca_2,V_b_2,V_ab_2,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
% 12.04/12.16 => ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) = V_ca_2
% 12.04/12.16 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2) ) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__div__div__eq__mult,axiom,
% 12.04/12.16 ! [V_db_2,V_b_2,V_ca_2,V_ab_2,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.16 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_ca_2,V_db_2)
% 12.04/12.16 => ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) = c_Divides_Odiv__class_Odiv(T_a,V_db_2,V_ca_2)
% 12.04/12.16 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2) ) ) ) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__neg__div,axiom,
% 12.04/12.16 ! [V_x,V_y,T_a] :
% 12.04/12.16 ( class_Divides_Oring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
% 12.04/12.16 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__div__neg,axiom,
% 12.04/12.16 ! [V_x,V_y,T_a] :
% 12.04/12.16 ( class_Divides_Oring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
% 12.04/12.16 => c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__add,axiom,
% 12.04/12.16 ! [V_y,V_x,V_z,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_x)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_y)
% 12.04/12.16 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__dvd__div,axiom,
% 12.04/12.16 ! [V_ca_2,V_b_2,V_ab_2,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_ca_2)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2),c_Divides_Odiv__class_Odiv(T_a,V_ca_2,V_ab_2))
% 12.04/12.16 <=> c_Rings_Odvd__class_Odvd(T_a,V_b_2,V_ca_2) ) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__mult__div__if__dvd,axiom,
% 12.04/12.16 ! [V_w,V_z,V_x,V_y,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_w)
% 12.04/12.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__div__mult,axiom,
% 12.04/12.16 ! [V_c,V_b,V_a,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 12.04/12.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__div__mult__self,axiom,
% 12.04/12.16 ! [V_b,V_a,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 12.04/12.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a) = V_b ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__mult__swap,axiom,
% 12.04/12.16 ! [V_a,V_b,V_c,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_b)
% 12.04/12.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdvd__mult__div__cancel,axiom,
% 12.04/12.16 ! [V_m,V_n] :
% 12.04/12.16 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
% 12.04/12.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = V_m ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_dvd__mult__div__cancel,axiom,
% 12.04/12.16 ! [V_b,V_a,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 12.04/12.16 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__power,axiom,
% 12.04/12.16 ! [V_n,V_x,V_y,T_a] :
% 12.04/12.16 ( class_Divides_Osemiring__div(T_a)
% 12.04/12.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
% 12.04/12.16 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdiv__eq__0__iff,axiom,
% 12.04/12.16 ! [V_k_2,V_i_2] :
% 12.04/12.16 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 12.04/12.16 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 12.04/12.16 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)
% 12.04/12.16 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) )
% 12.04/12.16 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 12.04/12.16 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 12.04/12.16 ! [V_ab_2,V_b_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 12.04/12.16 => ( 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_ab_2,V_b_2))
% 12.04/12.16 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 12.04/12.16 ! [V_i_2,V_k_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 12.04/12.16 => ( 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))
% 12.04/12.16 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 12.04/12.16 ! [V_b_2,V_ab_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2)
% 12.04/12.16 => ( 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_ab_2,V_b_2))
% 12.04/12.16 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_ab_2)
% 12.04/12.16 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdiv__mono2,axiom,
% 12.04/12.16 ! [V_b,V_b_H,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 12.04/12.16 => 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)) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__nonneg__neg__le0,axiom,
% 12.04/12.16 ! [V_b,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 12.04/12.16 => 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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__pos__pos__trivial,axiom,
% 12.04/12.16 ! [V_b,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 12.04/12.16 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 12.04/12.16 ! [V_ab_2,V_b_2] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 12.04/12.16 => ( 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_ab_2,V_b_2))
% 12.04/12.16 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_ab_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__nonpos__pos__le0,axiom,
% 12.04/12.16 ! [V_b,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 12.04/12.16 => 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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdiv__mono2__neg,axiom,
% 12.04/12.16 ! [V_b,V_b_H,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 12.04/12.16 => 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)) ) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_div__neg__neg__trivial,axiom,
% 12.04/12.16 ! [V_b,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 12.04/12.16 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdiv__mono1,axiom,
% 12.04/12.16 ! [V_b,V_a_H,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 12.04/12.16 => 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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_zdiv__mono1__neg,axiom,
% 12.04/12.16 ! [V_b,V_a_H,V_a] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 12.04/12.16 => 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)) ) ) ).
% 12.04/12.16
% 12.04/12.16 fof(fact_int__div__less__self,axiom,
% 12.04/12.16 ! [V_k,V_x] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 12.04/12.16 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
% 12.04/12.16 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ) ).
% 12.04/12.16
% 12.04/12.16 %----Arity declarations (255)
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 12.04/12.16 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_fun__Orderings_Opreorder,axiom,
% 12.04/12.16 ! [T_2,T_1] :
% 12.04/12.16 ( class_Orderings_Opreorder(T_1)
% 12.04/12.16 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_fun__Orderings_Oorder,axiom,
% 12.04/12.16 ! [T_2,T_1] :
% 12.04/12.16 ( class_Orderings_Oorder(T_1)
% 12.04/12.16 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_fun__Orderings_Oord,axiom,
% 12.04/12.16 ! [T_2,T_1] :
% 12.04/12.16 ( class_Orderings_Oord(T_1)
% 12.04/12.16 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 12.04/12.16 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 12.04/12.16 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 12.04/12.16 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 12.04/12.16 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 12.04/12.16 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 12.04/12.16 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 12.04/12.16 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 12.04/12.16 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 12.04/12.16 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 12.04/12.16 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 12.04/12.16 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 12.04/12.16 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 12.04/12.16 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 12.04/12.16 class_Orderings_Opreorder(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 12.04/12.16 class_Orderings_Olinorder(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 12.04/12.16 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 12.04/12.16 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 12.04/12.16 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 12.04/12.16 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 12.04/12.16 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 12.04/12.16 class_Divides_Oring__div(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 12.04/12.16 class_Rings_Omult__zero(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 12.04/12.16 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 12.04/12.16 class_Orderings_Oorder(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 12.04/12.16 class_Int_Oring__char__0(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 12.04/12.16 class_Rings_Osemiring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 12.04/12.16 class_Orderings_Oord(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 12.04/12.16 class_Rings_Oring__1(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Power_Opower,axiom,
% 12.04/12.16 class_Power_Opower(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 12.04/12.16 class_Groups_Ozero(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oring,axiom,
% 12.04/12.16 class_Rings_Oring(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 12.04/12.16 class_Rings_Oidom(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Groups_Oone,axiom,
% 12.04/12.16 class_Groups_Oone(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 12.04/12.16 class_Rings_Odvd(tc_Int_Oint) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 12.04/12.16 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 12.04/12.16 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 12.04/12.16 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 12.04/12.16 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 12.04/12.16 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 12.04/12.16 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 12.04/12.16 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 12.04/12.16 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 12.04/12.16 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 12.04/12.16 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 12.04/12.16 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 12.04/12.16 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 12.04/12.16 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 12.04/12.16 class_Orderings_Oorder(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 12.04/12.16 class_Rings_Osemiring(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 12.04/12.16 class_Orderings_Oord(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Power_Opower,axiom,
% 12.04/12.16 class_Power_Opower(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 12.04/12.16 class_Groups_Ozero(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 12.04/12.16 class_Groups_Oone(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 12.04/12.16 class_Rings_Odvd(tc_Nat_Onat) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 12.04/12.16 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 12.04/12.16 class_Orderings_Oorder(tc_HOL_Obool) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 12.04/12.16 class_Orderings_Oord(tc_HOL_Obool) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 12.04/12.16 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 12.04/12.16 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 12.04/12.16 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 12.04/12.16 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 12.04/12.16 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 12.04/12.16 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 12.04/12.16 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 12.04/12.16 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 12.04/12.16 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 12.04/12.16 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 12.04/12.16 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 12.04/12.16 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 12.04/12.16 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 12.04/12.16 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 12.04/12.16 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 12.04/12.16 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 12.04/12.16 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 12.04/12.16 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 12.04/12.16 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 12.04/12.16 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 12.04/12.16 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 12.04/12.16 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 12.04/12.16 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 12.04/12.16 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 12.04/12.16 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 12.04/12.16 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 12.04/12.16 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 12.04/12.16 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 12.04/12.16 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 12.04/12.16 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 12.04/12.16 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 12.04/12.16 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 12.04/12.16 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 12.04/12.16 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 12.04/12.16 class_Power_Opower(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 12.04/12.16 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 12.04/12.16 class_Rings_Oring(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 12.04/12.16 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 12.04/12.16 class_Groups_Oone(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
% 12.04/12.16 class_Rings_Odvd(tc_RealDef_Oreal) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 12.04/12.16 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 12.04/12.16 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 12.04/12.16 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 12.04/12.16 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 12.04/12.16 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 12.04/12.16 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 12.04/12.16 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 12.04/12.16 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 12.04/12.16 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 12.04/12.16 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 12.04/12.16 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 12.04/12.16 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 12.04/12.16 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 12.04/12.16 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 12.04/12.16 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 12.04/12.16 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 12.04/12.16 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 12.04/12.16 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 12.04/12.16 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 12.04/12.16 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 12.04/12.16 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 12.04/12.16 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 12.04/12.16 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 12.04/12.16 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 12.04/12.16 class_Power_Opower(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 12.04/12.16 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 12.04/12.16 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 12.04/12.16 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 12.04/12.16 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
% 12.04/12.16 class_Rings_Odvd(tc_Complex_Ocomplex) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Oidom(T_1)
% 12.04/12.16 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 12.04/12.16 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Oidom(T_1)
% 12.04/12.16 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Oidom(T_1)
% 12.04/12.16 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 12.04/12.16 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__0(T_1)
% 12.04/12.16 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__1(T_1)
% 12.04/12.16 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Ocomm__monoid__add(T_1)
% 12.04/12.16 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Oidom(T_1)
% 12.04/12.16 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Ocomm__monoid__add(T_1)
% 12.04/12.16 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__1(T_1)
% 12.04/12.16 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__0(T_1)
% 12.04/12.16 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Fields_Ofield(T_1)
% 12.04/12.16 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__0(T_1)
% 12.04/12.16 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Oab__group__add(T_1)
% 12.04/12.16 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__1(T_1)
% 12.04/12.16 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__1(T_1)
% 12.04/12.16 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__ring__1(T_1)
% 12.04/12.16 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Ocomm__monoid__add(T_1)
% 12.04/12.16 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__0(T_1)
% 12.04/12.16 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Oab__group__add(T_1)
% 12.04/12.16 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Divides_Oring__div,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Fields_Ofield(T_1)
% 12.04/12.16 => class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__0(T_1)
% 12.04/12.16 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__ring(T_1)
% 12.04/12.16 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__0(T_1)
% 12.04/12.16 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Olinordered__idom(T_1)
% 12.04/12.16 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__ring__1(T_1)
% 12.04/12.16 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__1(T_1)
% 12.04/12.16 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Groups_Ozero(T_1)
% 12.04/12.16 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__ring(T_1)
% 12.04/12.16 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Oidom(T_1)
% 12.04/12.16 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__1(T_1)
% 12.04/12.16 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
% 12.04/12.16 ! [T_1] :
% 12.04/12.16 ( class_Rings_Ocomm__semiring__1(T_1)
% 12.04/12.16 => class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ) ).
% 12.04/12.16
% 12.04/12.16 %----Helper facts (2)
% 12.04/12.16 fof(help_c__fequal__1,axiom,
% 12.04/12.16 ! [V_y_2,V_x_2] :
% 12.04/12.16 ( ~ hBOOL(c_fequal(V_x_2,V_y_2))
% 12.04/12.16 | V_x_2 = V_y_2 ) ).
% 12.04/12.16
% 12.04/12.16 fof(help_c__fequal__2,axiom,
% 12.04/12.16 ! [V_y_2,V_x_2] :
% 12.04/12.16 ( V_x_2 != V_y_2
% 12.04/12.16 | hBOOL(c_fequal(V_x_2,V_y_2)) ) ).
% 12.04/12.16
% 12.04/12.16 %----Conjectures (2)
% 12.04/12.16 fof(conj_0,hypothesis,
% 12.04/12.16 ( ? [B_r] :
% 12.04/12.16 ! [B_z] :
% 12.04/12.16 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z))
% 12.04/12.16 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),B_z))) )
% 12.04/12.16 => v_thesis____ ) ).
% 12.04/12.16
% 12.04/12.16 fof(conj_1,conjecture,
% 12.04/12.16 v_thesis____ ).
% 12.04/12.16
% 12.04/12.16 %------------------------------------------------------------------------------
% 12.04/12.16 %-------------------------------------------
% 12.04/12.16 % Proof found
% 12.04/12.16 % SZS status Theorem for theBenchmark
% 12.04/12.16 % SZS output start Proof
% 12.04/12.17 %ClaNum:1813(EqnAxiom:228)
% 12.04/12.17 %VarNum:8698(SingletonVarNum:3110)
% 12.04/12.17 %MaxLitNum:7
% 12.04/12.17 %MaxfuncDepth:6
% 12.04/12.17 %SharedTerms:266
% 12.04/12.17 %goalClause: 543
% 12.04/12.17 %singleGoalClaCount:1
% 12.04/12.17 [229]P1(a1)
% 12.04/12.17 [230]P1(a68)
% 12.04/12.17 [231]P2(a68)
% 12.04/12.17 [232]P2(a69)
% 12.04/12.17 [233]P2(a70)
% 12.04/12.17 [234]P2(a71)
% 12.04/12.17 [235]P37(a1)
% 12.04/12.17 [236]P37(a68)
% 12.04/12.17 [237]P37(a69)
% 12.04/12.17 [238]P37(a70)
% 12.04/12.17 [239]P3(a1)
% 12.04/12.17 [240]P3(a68)
% 12.04/12.17 [241]P3(a69)
% 12.04/12.17 [242]P3(a70)
% 12.04/12.17 [243]P17(a68)
% 12.04/12.17 [244]P17(a69)
% 12.04/12.17 [245]P17(a70)
% 12.04/12.17 [246]P18(a68)
% 12.04/12.17 [247]P18(a69)
% 12.04/12.17 [248]P18(a70)
% 12.04/12.17 [249]P26(a1)
% 12.04/12.17 [250]P26(a68)
% 12.04/12.17 [251]P26(a69)
% 12.04/12.17 [252]P26(a70)
% 12.04/12.17 [253]P19(a1)
% 12.04/12.17 [254]P19(a68)
% 12.04/12.17 [255]P19(a69)
% 12.04/12.17 [256]P19(a70)
% 12.04/12.17 [257]P20(a68)
% 12.04/12.17 [258]P20(a70)
% 12.04/12.17 [259]P29(a1)
% 12.04/12.17 [260]P29(a68)
% 12.04/12.17 [261]P29(a70)
% 12.04/12.17 [262]P41(a1)
% 12.04/12.17 [263]P41(a68)
% 12.04/12.17 [264]P41(a70)
% 12.04/12.17 [265]P27(a68)
% 12.04/12.17 [266]P27(a69)
% 12.04/12.17 [267]P27(a70)
% 12.04/12.17 [268]P30(a68)
% 12.04/12.17 [269]P30(a69)
% 12.04/12.17 [270]P30(a70)
% 12.04/12.17 [271]P31(a68)
% 12.04/12.17 [272]P31(a69)
% 12.04/12.17 [273]P31(a70)
% 12.04/12.17 [274]P31(a71)
% 12.04/12.17 [275]P32(a68)
% 12.04/12.17 [276]P32(a69)
% 12.04/12.17 [277]P32(a70)
% 12.04/12.17 [278]P32(a71)
% 12.04/12.17 [279]P4(a1)
% 12.04/12.17 [280]P4(a68)
% 12.04/12.17 [281]P4(a69)
% 12.04/12.17 [282]P4(a70)
% 12.04/12.17 [283]P5(a1)
% 12.04/12.17 [284]P5(a68)
% 12.04/12.17 [285]P5(a69)
% 12.04/12.17 [286]P5(a70)
% 12.04/12.17 [287]P6(a1)
% 12.04/12.17 [288]P6(a68)
% 12.04/12.17 [289]P6(a69)
% 12.04/12.17 [290]P6(a70)
% 12.04/12.17 [291]P44(a1)
% 12.04/12.17 [292]P44(a68)
% 12.04/12.17 [293]P44(a69)
% 12.04/12.17 [294]P44(a70)
% 12.04/12.17 [295]P42(a1)
% 12.04/12.17 [296]P42(a68)
% 12.04/12.17 [297]P42(a69)
% 12.04/12.17 [298]P42(a70)
% 12.04/12.17 [299]P33(a1)
% 12.04/12.17 [300]P33(a68)
% 12.04/12.17 [301]P45(a1)
% 12.04/12.17 [302]P45(a68)
% 12.04/12.17 [303]P45(a70)
% 12.04/12.17 [304]P7(a1)
% 12.04/12.17 [305]P7(a68)
% 12.04/12.17 [306]P7(a70)
% 12.04/12.17 [307]P38(a1)
% 12.04/12.17 [308]P38(a68)
% 12.04/12.17 [309]P38(a70)
% 12.04/12.17 [310]P15(a1)
% 12.04/12.17 [311]P15(a68)
% 12.04/12.17 [312]P15(a69)
% 12.04/12.17 [313]P15(a70)
% 12.04/12.17 [314]P35(a1)
% 12.04/12.17 [315]P35(a68)
% 12.04/12.17 [316]P21(a1)
% 12.04/12.17 [317]P21(a68)
% 12.04/12.17 [318]P21(a70)
% 12.04/12.17 [319]P23(a68)
% 12.04/12.17 [320]P23(a70)
% 12.04/12.17 [321]P46(a68)
% 12.04/12.17 [322]P46(a70)
% 12.04/12.17 [323]P47(a68)
% 12.04/12.17 [324]P47(a70)
% 12.04/12.17 [325]P48(a68)
% 12.04/12.17 [326]P48(a70)
% 12.04/12.17 [327]P51(a1)
% 12.04/12.17 [328]P51(a68)
% 12.04/12.17 [329]P51(a69)
% 12.04/12.17 [330]P51(a70)
% 12.04/12.17 [331]P61(a1)
% 12.04/12.17 [332]P61(a68)
% 12.04/12.17 [333]P61(a70)
% 12.04/12.17 [334]P52(a1)
% 12.04/12.17 [335]P52(a68)
% 12.04/12.17 [336]P52(a69)
% 12.04/12.17 [337]P52(a70)
% 12.04/12.17 [338]P39(a1)
% 12.04/12.17 [339]P39(a68)
% 12.04/12.17 [340]P39(a69)
% 12.04/12.17 [341]P39(a70)
% 12.04/12.17 [342]P64(a1)
% 12.04/12.17 [343]P64(a68)
% 12.04/12.17 [344]P64(a69)
% 12.04/12.17 [345]P64(a70)
% 12.04/12.17 [346]P58(a68)
% 12.04/12.17 [347]P58(a69)
% 12.04/12.17 [348]P58(a70)
% 12.04/12.17 [349]P60(a68)
% 12.04/12.17 [350]P60(a69)
% 12.04/12.17 [351]P60(a70)
% 12.04/12.17 [352]P59(a68)
% 12.04/12.17 [353]P59(a69)
% 12.04/12.17 [354]P59(a70)
% 12.04/12.17 [355]P53(a68)
% 12.04/12.17 [356]P53(a69)
% 12.04/12.17 [357]P53(a70)
% 12.04/12.17 [358]P49(a68)
% 12.04/12.17 [359]P49(a70)
% 12.04/12.17 [360]P24(a1)
% 12.04/12.17 [361]P24(a68)
% 12.04/12.17 [362]P24(a69)
% 12.04/12.17 [363]P24(a70)
% 12.04/12.17 [364]P36(a1)
% 12.04/12.17 [365]P36(a68)
% 12.04/12.17 [366]P65(a1)
% 12.04/12.17 [367]P65(a68)
% 12.04/12.17 [368]P65(a69)
% 12.04/12.17 [369]P65(a70)
% 12.04/12.17 [370]P28(a68)
% 12.04/12.17 [371]P28(a69)
% 12.04/12.17 [372]P28(a70)
% 12.04/12.17 [373]P22(a1)
% 12.04/12.17 [374]P22(a68)
% 12.04/12.17 [375]P22(a69)
% 12.04/12.17 [376]P22(a70)
% 12.04/12.17 [377]P25(a1)
% 12.04/12.17 [378]P25(a68)
% 12.04/12.17 [379]P25(a69)
% 12.04/12.17 [380]P25(a70)
% 12.04/12.17 [381]P54(a68)
% 12.04/12.17 [382]P54(a70)
% 12.04/12.17 [383]P57(a68)
% 12.04/12.17 [384]P57(a69)
% 12.04/12.17 [385]P57(a70)
% 12.04/12.17 [386]P50(a68)
% 12.04/12.17 [387]P50(a69)
% 12.04/12.17 [388]P50(a70)
% 12.04/12.17 [389]P55(a68)
% 12.04/12.17 [390]P55(a69)
% 12.04/12.17 [391]P55(a70)
% 12.04/12.17 [392]P62(a1)
% 12.04/12.17 [393]P62(a68)
% 12.04/12.17 [394]P62(a70)
% 12.04/12.17 [395]P56(a68)
% 12.04/12.17 [396]P56(a70)
% 12.04/12.17 [397]P40(a1)
% 12.04/12.17 [398]P40(a68)
% 12.04/12.17 [399]P40(a70)
% 12.04/12.17 [400]P63(a1)
% 12.04/12.17 [401]P63(a68)
% 12.04/12.17 [402]P63(a70)
% 12.04/12.17 [403]P34(a1)
% 12.04/12.17 [404]P34(a68)
% 12.04/12.17 [405]P34(a69)
% 12.04/12.17 [406]P34(a70)
% 12.04/12.17 [407]P66(a1)
% 12.04/12.17 [408]P66(a68)
% 12.04/12.17 [409]P66(a69)
% 12.04/12.17 [410]P66(a70)
% 12.04/12.17 [411]P43(a1)
% 12.04/12.17 [412]P43(a68)
% 12.04/12.17 [413]P43(a69)
% 12.04/12.17 [414]P43(a70)
% 12.04/12.17 [415]P8(a1)
% 12.04/12.17 [416]P8(a68)
% 12.04/12.17 [417]P9(a69)
% 12.04/12.17 [418]P9(a70)
% 12.04/12.17 [419]P10(a70)
% 12.04/12.17 [420]P16(a1)
% 12.04/12.17 [421]P16(a68)
% 12.04/12.17 [422]P16(a69)
% 12.04/12.17 [423]P16(a70)
% 12.04/12.17 [543]~P67(a500)
% 12.04/12.17 [458]P11(a70,f2(a70),f3(a70))
% 12.04/12.17 [459]P12(a70,f2(a70),f3(a70))
% 12.04/12.17 [544]~E(f2(a1),a5)
% 12.04/12.17 [545]~E(f3(a1),a5)
% 12.04/12.17 [546]~E(f3(a68),f2(a68))
% 12.04/12.17 [547]~E(f3(a70),f2(a70))
% 12.04/12.17 [424]E(f12(f2(a68)),f2(a69))
% 12.04/12.17 [425]E(f12(f3(a68)),f3(a69))
% 12.04/12.17 [426]E(f13(f2(a68)),f2(a69))
% 12.04/12.17 [427]E(f13(f3(a68)),f3(a69))
% 12.04/12.17 [428]E(f9(a70,f2(a70)),f2(a70))
% 12.04/12.17 [429]E(f26(a69,f2(a69)),f2(a68))
% 12.04/12.17 [430]E(f26(a69,f3(a69)),f3(a68))
% 12.04/12.17 [548]~E(f2(f72(a1)),a73)
% 12.04/12.17 [549]~E(f2(f72(a1)),a77)
% 12.04/12.17 [557]~E(f16(a1,a74,a73),f2(f72(a1)))
% 12.04/12.17 [455]E(f27(f27(f10(a1),a5),a5),f9(a1,f3(a1)))
% 12.04/12.17 [478]E(f26(a69,f11(a69,f2(a69),f3(a69))),f3(a68))
% 12.04/12.17 [437]P11(a68,x4371,x4371)
% 12.04/12.17 [438]P11(a69,x4381,x4381)
% 12.04/12.17 [439]P11(a70,x4391,x4391)
% 12.04/12.17 [440]P13(a69,x4401,x4401)
% 12.04/12.17 [551]~P12(a69,x5511,x5511)
% 12.04/12.17 [445]E(f4(a69,x4451,x4451),f2(a69))
% 12.04/12.17 [446]P13(a69,x4461,f2(a69))
% 12.04/12.17 [448]P11(a69,f2(a69),x4481)
% 12.04/12.17 [449]P13(a69,f3(a69),x4491)
% 12.04/12.17 [464]P11(a68,f2(a68),f26(a69,x4641))
% 12.04/12.17 [554]~P12(a69,x5541,f2(a69))
% 12.04/12.17 [564]~P12(a68,f26(a69,x5641),f2(a68))
% 12.04/12.17 [431]E(f12(f26(a69,x4311)),x4311)
% 12.04/12.17 [432]E(f13(f26(a69,x4321)),x4321)
% 12.04/12.17 [433]E(f9(a70,f9(a70,x4331)),x4331)
% 12.04/12.17 [434]E(f27(f27(f10(a69),x4341),f3(a69)),x4341)
% 12.04/12.17 [435]E(f27(f27(f10(a70),x4351),f3(a70)),x4351)
% 12.04/12.17 [436]E(f27(f27(f10(a69),x4361),f2(a69)),f2(a69))
% 12.04/12.17 [450]E(f11(a69,x4501,f2(a69)),x4501)
% 12.04/12.17 [451]E(f11(a70,x4511,f2(a70)),x4511)
% 12.04/12.17 [452]E(f4(a69,x4521,f2(a69)),x4521)
% 12.04/12.17 [453]E(f11(a69,f2(a69),x4531),x4531)
% 12.04/12.17 [454]E(f11(a70,f2(a70),x4541),x4541)
% 12.04/12.17 [456]E(f4(a69,f2(a69),x4561),f2(a69))
% 12.04/12.17 [463]E(f11(a70,f9(a70,x4631),x4631),f2(a70))
% 12.04/12.17 [466]P11(a68,x4661,f26(a69,f13(x4661)))
% 12.04/12.17 [481]P11(a68,f9(a68,f29(a1,x4811)),f29(a1,x4811))
% 12.04/12.17 [488]P12(a69,x4881,f11(a69,x4881,f3(a69)))
% 12.04/12.17 [489]P12(a69,f2(a69),f11(a69,x4891,f3(a69)))
% 12.04/12.17 [491]P13(a69,f11(a69,f2(a69),f3(a69)),x4911)
% 12.04/12.17 [495]P12(a68,f4(a68,x4951,f3(a68)),f26(a69,f12(x4951)))
% 12.04/12.17 [500]P12(a68,x5001,f11(a68,f26(a69,f12(x5001)),f3(a68)))
% 12.04/12.17 [556]~E(f11(a69,x5561,f3(a69)),x5561)
% 12.04/12.17 [563]~E(f11(a69,x5631,f3(a69)),f2(a69))
% 12.04/12.17 [567]~P11(a69,f11(a69,x5671,f3(a69)),x5671)
% 12.04/12.17 [441]E(f27(f27(f10(a68),f3(a68)),x4411),x4411)
% 12.04/12.17 [442]E(f27(f27(f10(a69),f3(a69)),x4421),x4421)
% 12.04/12.17 [443]E(f27(f27(f10(a70),f3(a70)),x4431),x4431)
% 12.04/12.17 [444]E(f27(f27(f10(a69),f2(a69)),x4441),f2(a69))
% 12.04/12.17 [480]P11(a69,x4801,f27(f27(f10(a69),x4801),x4801))
% 12.04/12.17 [496]E(f11(a68,f26(a69,x4961),f3(a68)),f26(a69,f11(a69,x4961,f3(a69))))
% 12.04/12.17 [503]P12(a68,f2(a68),f26(a69,f11(a69,x5031,f3(a69))))
% 12.04/12.17 [568]~E(f11(a70,f11(a70,f3(a70),x5681),x5681),f2(a70))
% 12.04/12.17 [479]E(f27(f27(f10(a1),a5),f27(f27(f10(a1),a5),x4791)),f9(a1,x4791))
% 12.04/12.17 [515]P11(a69,x5151,f27(f27(f10(a69),x5151),f27(f27(f10(a69),x5151),x5151)))
% 12.04/12.17 [519]E(f27(f27(f14(a69),f11(a69,f2(a69),f3(a69))),x5191),f11(a69,f2(a69),f3(a69)))
% 12.04/12.17 [465]P12(a68,f2(a68),f28(x4651,x4652))
% 12.04/12.17 [470]E(f11(a69,x4701,x4702),f11(a69,x4702,x4701))
% 12.04/12.17 [471]E(f11(a70,x4711,x4712),f11(a70,x4712,x4711))
% 12.04/12.17 [482]P11(a69,x4821,f11(a69,x4822,x4821))
% 12.04/12.17 [483]P11(a69,x4831,f11(a69,x4831,x4832))
% 12.04/12.17 [484]P11(a69,f4(a69,x4841,x4842),x4841)
% 12.04/12.17 [565]~P12(a69,f11(a69,x5651,x5652),x5652)
% 12.04/12.17 [566]~P12(a69,f11(a69,x5661,x5662),x5661)
% 12.04/12.17 [473]E(f11(a1,x4731,f9(a1,x4732)),f4(a1,x4731,x4732))
% 12.04/12.17 [475]E(f11(a68,x4751,f9(a68,x4752)),f4(a68,x4751,x4752))
% 12.04/12.17 [477]E(f11(a70,x4771,f9(a70,x4772)),f4(a70,x4771,x4772))
% 12.04/12.17 [485]E(f4(a69,f11(a69,x4851,x4852),x4852),x4851)
% 12.04/12.17 [486]E(f4(a69,f11(a69,x4861,x4862),x4861),x4862)
% 12.04/12.17 [487]E(f4(a69,x4871,f11(a69,x4871,x4872)),f2(a69))
% 12.04/12.17 [497]E(f11(a70,f9(a70,x4971),f9(a70,x4972)),f9(a70,f11(a70,x4971,x4972)))
% 12.04/12.17 [498]E(f11(a68,f26(a69,x4981),f26(a69,x4982)),f26(a69,f11(a69,x4981,x4982)))
% 12.04/12.17 [502]P12(a69,f4(a69,x5021,x5022),f11(a69,x5021,f3(a69)))
% 12.04/12.17 [525]P12(a69,x5251,f11(a69,f11(a69,x5252,x5251),f3(a69)))
% 12.04/12.17 [526]P12(a69,x5261,f11(a69,f11(a69,x5261,x5262),f3(a69)))
% 12.04/12.17 [539]P11(a68,f29(a1,x5391),f11(a68,f29(a1,f11(a1,x5391,x5392)),f29(a1,x5392)))
% 12.04/12.17 [540]P11(a68,f4(a68,f29(a1,f11(a1,x5401,x5402)),f29(a1,x5401)),f29(a1,x5402))
% 12.04/12.17 [467]E(f27(f27(f10(a68),x4671),x4672),f27(f27(f10(a68),x4672),x4671))
% 12.04/12.17 [468]E(f27(f27(f10(a69),x4681),x4682),f27(f27(f10(a69),x4682),x4681))
% 12.04/12.17 [469]E(f27(f27(f10(a70),x4691),x4692),f27(f27(f10(a70),x4692),x4691))
% 12.04/12.17 [514]E(f11(a69,f11(a69,x5141,f3(a69)),x5142),f11(a69,f11(a69,x5141,x5142),f3(a69)))
% 12.04/12.17 [516]E(f4(a69,f4(a69,x5161,f3(a69)),x5162),f4(a69,x5161,f11(a69,x5162,f3(a69))))
% 12.04/12.17 [517]E(f11(a69,f11(a69,x5171,f3(a69)),x5172),f11(a69,x5171,f11(a69,x5172,f3(a69))))
% 12.04/12.17 [493]E(f27(f27(f10(a70),f9(a70,x4931)),x4932),f9(a70,f27(f27(f10(a70),x4931),x4932)))
% 12.04/12.17 [494]E(f27(f27(f14(a68),f26(a69,x4941)),x4942),f26(a69,f27(f27(f14(a69),x4941),x4942)))
% 12.04/12.17 [499]E(f27(f27(f10(a68),f26(a69,x4991)),f26(a69,x4992)),f26(a69,f27(f27(f10(a69),x4991),x4992)))
% 12.04/12.17 [504]E(f27(f27(f10(a69),x5041),f11(a69,x5042,f3(a69))),f11(a69,x5041,f27(f27(f10(a69),x5041),x5042)))
% 12.04/12.17 [520]P11(a68,f9(a68,f27(f27(f10(a68),x5201),x5201)),f27(f27(f10(a68),x5202),x5202))
% 12.04/12.17 [531]E(f27(f27(f10(a69),f11(a69,x5311,f3(a69))),x5312),f11(a69,x5312,f27(f27(f10(a69),x5311),x5312)))
% 12.04/12.17 [505]E(f11(a69,x5051,f11(a69,x5052,x5053)),f11(a69,x5052,f11(a69,x5051,x5053)))
% 12.04/12.17 [506]E(f11(a70,x5061,f11(a70,x5062,x5063)),f11(a70,x5062,f11(a70,x5061,x5063)))
% 12.04/12.17 [507]E(f11(a69,f11(a69,x5071,x5072),x5073),f11(a69,x5071,f11(a69,x5072,x5073)))
% 12.04/12.17 [508]E(f11(a70,f11(a70,x5081,x5082),x5083),f11(a70,x5081,f11(a70,x5082,x5083)))
% 12.04/12.17 [509]E(f4(a69,f4(a69,x5091,x5092),x5093),f4(a69,x5091,f11(a69,x5092,x5093)))
% 12.04/12.17 [510]E(f4(a69,f4(a69,x5101,x5102),x5103),f4(a69,f4(a69,x5101,x5103),x5102))
% 12.04/12.17 [511]E(f4(a69,f11(a69,x5111,x5112),f11(a69,x5113,x5112)),f4(a69,x5111,x5113))
% 12.04/12.17 [512]E(f4(a69,f11(a69,x5121,x5122),f11(a69,x5121,x5123)),f4(a69,x5122,x5123))
% 12.04/12.17 [538]E(f4(a69,f4(a69,f11(a69,x5381,f3(a69)),x5382),f11(a69,x5383,f3(a69))),f4(a69,f4(a69,x5381,x5382),x5383))
% 12.04/12.17 [527]E(f11(a69,f27(f27(f10(a69),x5271),x5272),f27(f27(f10(a69),x5271),x5273)),f27(f27(f10(a69),x5271),f11(a69,x5272,x5273)))
% 12.04/12.17 [528]E(f4(a69,f27(f27(f10(a69),x5281),x5282),f27(f27(f10(a69),x5281),x5283)),f27(f27(f10(a69),x5281),f4(a69,x5282,x5283)))
% 12.04/12.17 [529]E(f11(a70,f27(f27(f10(a70),x5291),x5292),f27(f27(f10(a70),x5291),x5293)),f27(f27(f10(a70),x5291),f11(a70,x5292,x5293)))
% 12.04/12.17 [530]E(f4(a70,f27(f27(f10(a70),x5301),x5302),f27(f27(f10(a70),x5301),x5303)),f27(f27(f10(a70),x5301),f4(a70,x5302,x5303)))
% 12.04/12.17 [532]E(f27(f27(f10(a70),f27(f27(f14(a70),x5321),x5322)),f27(f27(f14(a70),x5321),x5323)),f27(f27(f14(a70),x5321),f11(a69,x5322,x5323)))
% 12.04/12.17 [533]E(f11(a68,f27(f27(f10(a68),x5331),x5332),f27(f27(f10(a68),x5333),x5332)),f27(f27(f10(a68),f11(a68,x5331,x5333)),x5332))
% 12.04/12.17 [534]E(f11(a69,f27(f27(f10(a69),x5341),x5342),f27(f27(f10(a69),x5343),x5342)),f27(f27(f10(a69),f11(a69,x5341,x5343)),x5342))
% 12.04/12.17 [535]E(f4(a69,f27(f27(f10(a69),x5351),x5352),f27(f27(f10(a69),x5353),x5352)),f27(f27(f10(a69),f4(a69,x5351,x5353)),x5352))
% 12.04/12.17 [536]E(f11(a70,f27(f27(f10(a70),x5361),x5362),f27(f27(f10(a70),x5363),x5362)),f27(f27(f10(a70),f11(a70,x5361,x5363)),x5362))
% 12.04/12.17 [537]E(f4(a70,f27(f27(f10(a70),x5371),x5372),f27(f27(f10(a70),x5373),x5372)),f27(f27(f10(a70),f4(a70,x5371,x5373)),x5372))
% 12.04/12.17 [521]E(f27(f27(f10(a68),f27(f27(f10(a68),x5211),x5212)),x5213),f27(f27(f10(a68),x5211),f27(f27(f10(a68),x5212),x5213)))
% 12.04/12.17 [522]E(f27(f27(f10(a69),f27(f27(f10(a69),x5221),x5222)),x5223),f27(f27(f10(a69),x5221),f27(f27(f10(a69),x5222),x5223)))
% 12.04/12.17 [523]E(f27(f27(f10(a70),f27(f27(f10(a70),x5231),x5232)),x5233),f27(f27(f10(a70),x5231),f27(f27(f10(a70),x5232),x5233)))
% 12.04/12.17 [524]E(f27(f27(f14(a70),f27(f27(f14(a70),x5241),x5242)),x5243),f27(f27(f14(a70),x5241),f27(f27(f10(a69),x5242),x5243)))
% 12.04/12.17 [501]E(f27(f27(f15(x5011,x5012,x5013),x5014),f2(a69)),x5012)
% 12.04/12.17 [542]E(f11(a69,f27(f27(f10(a69),x5421),x5422),f11(a69,f27(f27(f10(a69),x5423),x5422),x5424)),f11(a69,f27(f27(f10(a69),f11(a69,x5421,x5423)),x5422),x5424))
% 12.04/12.17 [541]E(f27(f27(f15(x5411,x5412,x5413),x5414),f11(a69,x5415,f3(a69))),f27(f27(x5413,x5414),f27(f27(f15(x5411,x5412,x5413),x5414),x5415)))
% 12.04/12.17 [569]~P49(x5691)+P2(f72(x5691))
% 12.04/12.17 [570]~P37(x5701)+P37(f72(x5701))
% 12.04/12.17 [571]~P3(x5711)+P3(f72(x5711))
% 12.04/12.17 [572]~P49(x5721)+P17(f72(x5721))
% 12.04/12.17 [573]~P49(x5731)+P18(f72(x5731))
% 12.04/12.17 [574]~P26(x5741)+P26(f72(x5741))
% 12.04/12.17 [575]~P3(x5751)+P19(f72(x5751))
% 12.04/12.17 [576]~P49(x5761)+P20(f72(x5761))
% 12.04/12.17 [577]~P49(x5771)+P29(f72(x5771))
% 12.04/12.17 [578]~P41(x5781)+P41(f72(x5781))
% 12.04/12.17 [579]~P49(x5791)+P27(f72(x5791))
% 12.04/12.17 [580]~P49(x5801)+P30(f72(x5801))
% 12.04/12.17 [581]~P49(x5811)+P31(f72(x5811))
% 12.04/12.17 [582]~P49(x5821)+P32(f72(x5821))
% 12.04/12.17 [583]~P16(x5831)+P4(f72(x5831))
% 12.04/12.17 [584]~P16(x5841)+P5(f72(x5841))
% 12.04/12.17 [585]~P3(x5851)+P6(f72(x5851))
% 12.04/12.17 [586]~P41(x5861)+P44(f72(x5861))
% 12.04/12.17 [587]~P42(x5871)+P42(f72(x5871))
% 12.04/12.17 [588]~P38(x5881)+P45(f72(x5881))
% 12.04/12.17 [589]~P7(x5891)+P7(f72(x5891))
% 12.04/12.17 [590]~P38(x5901)+P38(f72(x5901))
% 12.04/12.17 [591]~P37(x5911)+P15(f72(x5911))
% 12.04/12.17 [592]~P7(x5921)+P21(f72(x5921))
% 12.04/12.17 [593]~P49(x5931)+P23(f72(x5931))
% 12.04/12.17 [594]~P49(x5941)+P46(f72(x5941))
% 12.04/12.17 [595]~P49(x5951)+P47(f72(x5951))
% 12.04/12.17 [596]~P49(x5961)+P48(f72(x5961))
% 12.04/12.17 [597]~P41(x5971)+P51(f72(x5971))
% 12.04/12.17 [598]~P41(x5981)+P61(f72(x5981))
% 12.04/12.17 [599]~P37(x5991)+P52(f72(x5991))
% 12.04/12.17 [600]~P37(x6001)+P39(f72(x6001))
% 12.04/12.17 [601]~P37(x6011)+P64(f72(x6011))
% 12.04/12.17 [602]~P49(x6021)+P58(f72(x6021))
% 12.04/12.17 [603]~P49(x6031)+P60(f72(x6031))
% 12.04/12.17 [604]~P49(x6041)+P59(f72(x6041))
% 12.04/12.17 [605]~P49(x6051)+P53(f72(x6051))
% 12.04/12.17 [606]~P49(x6061)+P49(f72(x6061))
% 12.04/12.17 [607]~P42(x6071)+P24(f72(x6071))
% 12.04/12.17 [608]~P42(x6081)+P65(f72(x6081))
% 12.04/12.17 [609]~P49(x6091)+P28(f72(x6091))
% 12.04/12.17 [610]~P42(x6101)+P22(f72(x6101))
% 12.04/12.17 [611]~P42(x6111)+P25(f72(x6111))
% 12.04/12.17 [612]~P49(x6121)+P54(f72(x6121))
% 12.04/12.17 [613]~P49(x6131)+P57(f72(x6131))
% 12.04/12.17 [614]~P49(x6141)+P50(f72(x6141))
% 12.04/12.17 [615]~P49(x6151)+P55(f72(x6151))
% 12.04/12.17 [616]~P40(x6161)+P62(f72(x6161))
% 12.04/12.17 [617]~P49(x6171)+P56(f72(x6171))
% 12.04/12.17 [618]~P40(x6181)+P40(f72(x6181))
% 12.04/12.17 [619]~P41(x6191)+P63(f72(x6191))
% 12.04/12.17 [620]~P42(x6201)+P34(f72(x6201))
% 12.04/12.17 [621]~P37(x6211)+P66(f72(x6211))
% 12.04/12.17 [622]~P42(x6221)+P43(f72(x6221))
% 12.04/12.17 [623]~P8(x6231)+P9(f72(x6231))
% 12.04/12.17 [624]~P8(x6241)+P10(f72(x6241))
% 12.04/12.17 [625]~P16(x6251)+P16(f72(x6251))
% 12.04/12.17 [627]~P65(x6271)+~E(f3(x6271),f2(x6271))
% 12.04/12.17 [628]~E(x6281,f2(a69))+E(f26(a69,x6281),f2(a68))
% 12.04/12.17 [629]E(x6291,f2(a69))+~E(f26(a69,x6291),f2(a68))
% 12.04/12.17 [673]E(x6731,f2(a69))+P12(a69,f2(a69),x6731)
% 12.04/12.17 [710]~P33(x7101)+P11(a68,f2(a68),f60(x7101))
% 12.04/12.17 [711]~P33(x7111)+P12(a68,f2(a68),f31(x7111))
% 12.04/12.17 [725]~P53(x7251)+P11(x7251,f2(x7251),f3(x7251))
% 12.04/12.17 [726]~P53(x7261)+P12(x7261,f2(x7261),f3(x7261))
% 12.04/12.17 [748]~E(x7481,f2(a69))+P11(a68,f26(a69,x7481),f2(a68))
% 12.04/12.17 [785]E(x7851,f2(a69))+~P11(a69,x7851,f2(a69))
% 12.04/12.17 [786]E(x7861,f3(a69))+~P13(a69,x7861,f3(a69))
% 12.04/12.17 [790]E(f12(x7901),f2(a69))+~P11(a68,x7901,f2(a68))
% 12.04/12.17 [791]E(f13(x7911),f2(a69))+~P11(a68,x7911,f2(a68))
% 12.04/12.17 [831]~P53(x8311)+~P11(x8311,f3(x8311),f2(x8311))
% 12.04/12.17 [832]~P53(x8321)+~P12(x8321,f3(x8321),f2(x8321))
% 12.04/12.17 [862]E(x8621,f2(a69))+~P11(a68,f26(a69,x8621),f2(a68))
% 12.04/12.17 [892]~P12(a70,f2(a70),x8921)+P11(a70,f3(a70),x8921)
% 12.04/12.17 [893]~P11(a70,f3(a70),x8931)+P12(a70,f2(a70),x8931)
% 12.04/12.17 [921]~P11(a68,x9211,f3(a68))+P11(a69,f13(x9211),f3(a69))
% 12.04/12.17 [922]~P11(a68,f3(a68),x9221)+P11(a69,f3(a69),f12(x9221))
% 12.04/12.17 [927]~P11(a69,f13(x9271),f3(a69))+P11(a68,x9271,f3(a68))
% 12.04/12.17 [928]~P11(a69,f3(a69),f12(x9281))+P11(a68,f3(a68),x9281)
% 12.04/12.17 [938]~P12(a69,f2(a69),x9381)+P12(a68,f2(a68),f26(a69,x9381))
% 12.04/12.17 [992]P12(a69,f2(a69),x9921)+~P12(a68,f2(a68),f26(a69,x9921))
% 12.04/12.17 [630]~P1(x6301)+E(f29(x6301,f2(x6301)),f2(a68))
% 12.04/12.17 [631]~P36(x6311)+E(f29(x6311,f3(x6311)),f3(a68))
% 12.04/12.17 [634]~P21(x6341)+E(f9(x6341,f2(x6341)),f2(x6341))
% 12.04/12.17 [670]~P49(x6701)+~P14(x6701,f2(f72(x6701)))
% 12.04/12.17 [735]~P34(x7351)+E(f15(x7351,f3(x7351),f10(x7351)),f14(x7351))
% 12.04/12.17 [765]P67(a500)+P11(a68,x7651,f29(a1,f61(x7651)))
% 12.04/12.17 [924]~P12(a69,f2(a69),x9241)+E(f11(a69,f33(x9241),f3(a69)),x9241)
% 12.04/12.17 [965]~P11(a68,f2(a68),x9651)+P12(a68,x9651,f26(a69,f47(x9651)))
% 12.04/12.17 [966]~P11(a68,f2(a68),x9661)+P11(a68,f26(a69,f12(x9661)),x9661)
% 12.04/12.17 [1029]~P53(x10291)+P12(x10291,f2(x10291),f11(x10291,f3(x10291),f3(x10291)))
% 12.04/12.17 [1171]~P11(a70,f2(a70),x11711)+P12(a70,f2(a70),f11(a70,f3(a70),x11711))
% 12.04/12.17 [1173]~P12(a69,f2(a69),x11731)+E(f11(a69,f4(a69,x11731,f3(a69)),f3(a69)),x11731)
% 12.04/12.17 [1194]E(x11941,f2(a69))+~P12(a69,x11941,f11(a69,f2(a69),f3(a69)))
% 12.04/12.17 [1296]~P13(a69,x12961,f11(a69,f2(a69),f3(a69)))+E(x12961,f11(a69,f2(a69),f3(a69)))
% 12.04/12.17 [1560]~P12(a69,f2(a69),x15601)+E(f11(a69,f4(a69,x15601,f11(a69,f2(a69),f3(a69))),f3(a69)),x15601)
% 12.04/12.17 [661]~P7(x6611)+E(f9(f72(x6611),f2(f72(x6611))),f2(f72(x6611)))
% 12.04/12.17 [792]~P42(x7921)+E(f16(x7921,f3(x7921),f2(f72(x7921))),f3(f72(x7921)))
% 12.04/12.17 [793]~P26(x7931)+E(f16(x7931,f2(x7931),f2(f72(x7931))),f2(f72(x7931)))
% 12.04/12.17 [904]E(x9041,f2(a68))+P12(a68,f2(a68),f27(f27(f10(a68),x9041),x9041))
% 12.04/12.17 [1111]~E(x11111,f2(a68))+~P12(a68,f2(a68),f27(f27(f10(a68),x11111),x11111))
% 12.04/12.17 [1185]~P11(a68,f2(a68),x11851)+E(f12(f11(a68,x11851,f3(a68))),f11(a69,f12(x11851),f3(a69)))
% 12.04/12.17 [1186]~P11(a68,f2(a68),x11861)+E(f13(f11(a68,x11861,f3(a68))),f11(a69,f13(x11861),f3(a69)))
% 12.04/12.17 [1453]~P11(a68,f2(a68),x14531)+P11(a68,f26(a69,f4(a69,f47(x14531),f3(a69))),x14531)
% 12.04/12.17 [1555]~P12(a70,x15551,f2(a70))+P12(a70,f11(a70,f11(a70,f3(a70),x15551),x15551),f2(a70))
% 12.04/12.17 [1695]P12(a70,x16951,f2(a70))+~P12(a70,f11(a70,f11(a70,f3(a70),x16951),x16951),f2(a70))
% 12.04/12.17 [1781]P67(a500)+~P11(a68,f11(a68,a78,f29(a1,a76)),f29(a1,f27(f21(a1,f16(a1,a74,a73)),f61(x17811))))
% 12.04/12.17 [662]~E(x6621,x6622)+P11(a68,x6621,x6622)
% 12.04/12.17 [665]~E(x6651,x6652)+P11(a69,x6651,x6652)
% 12.04/12.17 [669]~E(x6691,x6692)+P13(a69,x6691,x6692)
% 12.04/12.17 [679]~P2(x6791)+P11(x6791,x6792,x6792)
% 12.04/12.17 [680]~P42(x6801)+P13(x6801,x6802,x6802)
% 12.04/12.17 [754]~E(x7541,x7542)+~P12(a68,x7541,x7542)
% 12.04/12.17 [759]~E(x7591,x7592)+~P12(a69,x7591,x7592)
% 12.04/12.17 [760]~E(x7601,x7602)+~P12(a70,x7601,x7602)
% 12.04/12.17 [787]~P12(x7871,x7872,x7872)+~P2(x7871)
% 12.04/12.17 [820]P11(a68,x8202,x8201)+P11(a68,x8201,x8202)
% 12.04/12.17 [821]P11(a69,x8212,x8211)+P11(a69,x8211,x8212)
% 12.04/12.17 [822]P11(a70,x8222,x8221)+P11(a70,x8221,x8222)
% 12.04/12.17 [867]~P12(a68,x8671,x8672)+P11(a68,x8671,x8672)
% 12.04/12.17 [872]~P12(a69,x8721,x8722)+P11(a69,x8721,x8722)
% 12.04/12.17 [873]~P12(a70,x8731,x8732)+P11(a70,x8731,x8732)
% 12.04/12.17 [638]~E(x6381,x6382)+P68(f30(x6381,x6382))
% 12.04/12.17 [641]~P2(x6412)+P2(f75(x6411,x6412))
% 12.04/12.17 [642]~P31(x6422)+P31(f75(x6421,x6422))
% 12.04/12.17 [643]~P32(x6432)+P32(f75(x6431,x6432))
% 12.04/12.17 [647]E(x6471,x6472)+~E(f26(a69,x6471),f26(a69,x6472))
% 12.04/12.17 [655]E(x6551,x6552)+~P68(f30(x6551,x6552))
% 12.04/12.17 [671]E(f11(a69,x6711,x6712),x6712)+~E(x6711,f2(a69))
% 12.04/12.17 [678]~E(x6782,f2(a70))+E(f7(a70,x6781,x6782),f2(a70))
% 12.04/12.17 [689]~P21(x6891)+E(f4(x6891,x6892,x6892),f2(x6891))
% 12.04/12.17 [696]~P42(x6961)+P13(x6961,x6962,f2(x6961))
% 12.04/12.17 [697]~P42(x6971)+P13(x6971,f3(x6971),x6972)
% 12.04/12.17 [716]P11(a70,x7162,x7161)+E(f17(x7161,x7162),f2(a70))
% 12.04/12.17 [734]~E(x7342,f9(a68,x7341))+E(f11(a68,x7341,x7342),f2(a68))
% 12.04/12.17 [763]~E(f11(a69,x7632,x7631),x7632)+E(x7631,f2(a69))
% 12.04/12.17 [766]~P1(x7661)+P11(a68,f2(a68),f29(x7661,x7662))
% 12.04/12.17 [767]~P33(x7672)+P11(a68,f2(a68),f66(x7671,x7672))
% 12.04/12.17 [768]~P33(x7682)+P11(a68,f2(a68),f67(x7681,x7682))
% 12.04/12.17 [769]~P33(x7692)+P12(a68,f2(a68),f45(x7691,x7692))
% 12.04/12.17 [770]~P33(x7702)+P12(a68,f2(a68),f46(x7701,x7702))
% 12.04/12.17 [773]~P12(a69,x7732,x7731)+~E(x7731,f2(a69))
% 12.04/12.17 [780]E(x7801,f2(a69))+~E(f11(a69,x7802,x7801),f2(a69))
% 12.04/12.17 [781]E(x7811,f2(a69))+~E(f11(a69,x7811,x7812),f2(a69))
% 12.04/12.17 [810]E(x8101,f9(a68,x8102))+~E(f11(a68,x8102,x8101),f2(a68))
% 12.04/12.17 [865]~P1(x8651)+~P12(a68,f29(x8651,x8652),f2(a68))
% 12.04/12.17 [878]~P11(a69,x8781,x8782)+E(f4(a69,x8781,x8782),f2(a69))
% 12.04/12.17 [885]P11(a69,x8851,x8852)+~E(f4(a69,x8851,x8852),f2(a69))
% 12.04/12.17 [900]~P11(a68,x9001,x9002)+P11(a69,f12(x9001),f12(x9002))
% 12.04/12.17 [901]~P11(a68,x9011,x9012)+P11(a69,f13(x9011),f13(x9012))
% 12.04/12.17 [915]~P11(a70,x9152,x9151)+E(f4(a70,x9151,x9152),f17(x9151,x9152))
% 12.04/12.17 [929]~P13(a70,x9291,x9292)+P13(a70,x9291,f9(a70,x9292))
% 12.04/12.17 [930]~P13(a70,x9301,x9302)+P13(a70,f9(a70,x9301),x9302)
% 12.04/12.17 [960]P13(a70,x9601,x9602)+~P13(a70,x9601,f9(a70,x9602))
% 12.04/12.17 [961]P13(a70,x9611,x9612)+~P13(a70,f9(a70,x9611),x9612)
% 12.04/12.17 [971]P11(a69,x9711,f12(x9712))+~P11(a68,f26(a69,x9711),x9712)
% 12.04/12.17 [972]P11(a69,f13(x9721),x9722)+~P11(a68,x9721,f26(a69,x9722))
% 12.04/12.17 [998]~P11(a69,x9981,x9982)+P11(a68,f26(a69,x9981),f26(a69,x9982))
% 12.04/12.17 [999]~P12(a69,x9991,x9992)+P12(a68,f26(a69,x9991),f26(a69,x9992))
% 12.04/12.17 [1046]P11(a69,x10461,x10462)+~P11(a68,f26(a69,x10461),f26(a69,x10462))
% 12.04/12.17 [1047]P12(a69,x10471,x10472)+~P12(a68,f26(a69,x10471),f26(a69,x10472))
% 12.04/12.17 [1131]~P13(a69,x11311,x11312)+P13(a69,x11311,f11(a69,x11312,x11311))
% 12.04/12.17 [1140]~P12(a69,x11402,x11401)+P12(a69,f2(a69),f4(a69,x11401,x11402))
% 12.04/12.17 [1141]~P11(a68,x11411,x11412)+P11(a68,f4(a68,x11411,x11412),f2(a68))
% 12.04/12.17 [1142]~P12(a70,x11421,x11422)+P12(a70,f4(a70,x11421,x11422),f2(a70))
% 12.04/12.17 [1213]~P11(a68,f9(a68,x12131),x12132)+P11(a68,f2(a68),f11(a68,x12131,x12132))
% 12.04/12.17 [1214]~P12(a68,f9(a68,x12141),x12142)+P12(a68,f2(a68),f11(a68,x12141,x12142))
% 12.04/12.17 [1215]~P11(a68,x12152,f9(a68,x12151))+P11(a68,f11(a68,x12151,x12152),f2(a68))
% 12.04/12.17 [1216]~P12(a68,x12162,f9(a68,x12161))+P12(a68,f11(a68,x12161,x12162),f2(a68))
% 12.04/12.17 [1236]P13(a69,x12361,x12362)+~P13(a69,x12361,f11(a69,x12362,x12361))
% 12.04/12.17 [1246]P12(a69,x12461,x12462)+~P12(a69,f2(a69),f4(a69,x12462,x12461))
% 12.04/12.17 [1247]P11(a68,x12471,x12472)+~P11(a68,f4(a68,x12471,x12472),f2(a68))
% 12.04/12.17 [1248]P12(a70,x12481,x12482)+~P12(a70,f4(a70,x12481,x12482),f2(a70))
% 12.04/12.17 [1297]P11(a68,x12971,f9(a68,x12972))+~P11(a68,f11(a68,x12972,x12971),f2(a68))
% 12.04/12.17 [1298]P12(a68,x12981,f9(a68,x12982))+~P12(a68,f11(a68,x12982,x12981),f2(a68))
% 12.04/12.17 [1299]P11(a68,f9(a68,x12991),x12992)+~P11(a68,f2(a68),f11(a68,x12991,x12992))
% 12.04/12.17 [1300]P12(a68,f9(a68,x13001),x13002)+~P12(a68,f2(a68),f11(a68,x13001,x13002))
% 12.04/12.17 [654]~P21(x6541)+E(f9(x6541,f9(x6541,x6542)),x6542)
% 12.04/12.17 [677]~P1(x6771)+E(f29(x6771,f9(x6771,x6772)),f29(x6771,x6772))
% 12.04/12.17 [683]~P42(x6831)+E(f27(f27(f14(x6831),x6832),f3(a69)),x6832)
% 12.04/12.17 [684]~P25(x6841)+E(f27(f27(f14(x6841),x6842),f3(a69)),x6842)
% 12.04/12.17 [690]~P42(x6901)+E(f27(f27(f10(x6901),x6902),f3(x6901)),x6902)
% 12.04/12.17 [691]~P22(x6911)+E(f27(f27(f10(x6911),x6912),f3(x6911)),x6912)
% 12.04/12.17 [692]~P25(x6921)+E(f27(f27(f10(x6921),x6922),f3(x6921)),x6922)
% 12.04/12.17 [693]~P42(x6931)+E(f27(f27(f14(x6931),x6932),f2(a69)),f3(x6931))
% 12.04/12.17 [694]~P34(x6941)+E(f27(f27(f14(x6941),x6942),f2(a69)),f3(x6941))
% 12.04/12.17 [698]~P3(x6981)+E(f11(x6981,x6982,f2(x6981)),x6982)
% 12.04/12.17 [699]~P19(x6991)+E(f11(x6991,x6992,f2(x6991)),x6992)
% 12.04/12.17 [700]~P42(x7001)+E(f11(x7001,x7002,f2(x7001)),x7002)
% 12.04/12.17 [701]~P21(x7011)+E(f4(x7011,x7012,f2(x7011)),x7012)
% 12.04/12.17 [702]~P3(x7021)+E(f11(x7021,f2(x7021),x7022),x7022)
% 12.04/12.17 [703]~P19(x7031)+E(f11(x7031,f2(x7031),x7032),x7032)
% 12.04/12.17 [704]~P42(x7041)+E(f11(x7041,f2(x7041),x7042),x7042)
% 12.04/12.17 [705]~P42(x7051)+E(f23(x7051,f3(x7051),x7052),x7052)
% 12.04/12.17 [712]~P42(x7121)+E(f27(f27(f10(x7121),x7122),f2(x7121)),f2(x7121))
% 12.04/12.17 [714]~P33(x7141)+E(f27(f27(f10(x7141),x7142),f2(x7141)),f2(x7141))
% 12.04/12.17 [715]~P52(x7151)+E(f27(f27(f10(x7151),x7152),f2(x7151)),f2(x7151))
% 12.04/12.17 [736]~P37(x7361)+E(f23(x7361,f2(x7361),x7362),f2(f72(x7361)))
% 12.04/12.17 [737]~P26(x7371)+E(f19(x7371,f2(x7371),x7372),f2(f72(x7371)))
% 12.04/12.17 [744]~P21(x7441)+E(f4(x7441,f2(x7441),x7442),f9(x7441,x7442))
% 12.04/12.17 [746]~E(x7461,x7462)+E(f11(a68,x7461,f9(a68,x7462)),f2(a68))
% 12.04/12.17 [782]~P21(x7821)+E(f11(x7821,x7822,f9(x7821,x7822)),f2(x7821))
% 12.04/12.17 [783]~P7(x7831)+E(f11(x7831,f9(x7831,x7832),x7832),f2(x7831))
% 12.04/12.17 [784]~P21(x7841)+E(f11(x7841,f9(x7841,x7842),x7842),f2(x7841))
% 12.04/12.17 [859]E(x8591,x8592)+~E(f11(a68,x8591,f9(a68,x8592)),f2(a68))
% 12.04/12.17 [861]E(x8611,x8612)+~E(f27(x8611,f32(x8612,x8611)),f27(x8612,f32(x8612,x8611)))
% 12.04/12.17 [895]P12(a69,f2(a69),x8951)+~E(x8951,f11(a69,x8952,f3(a69)))
% 12.04/12.17 [932]~P11(a69,x9321,x9322)+E(f11(a69,x9321,f62(x9322,x9321)),x9322)
% 12.04/12.17 [933]~P11(a69,x9331,x9332)+E(f11(a69,x9331,f65(x9332,x9331)),x9332)
% 12.04/12.17 [936]~E(x9361,x9362)+P12(a69,x9361,f11(a69,x9362,f3(a69)))
% 12.04/12.17 [937]~E(x9371,x9372)+P12(a70,x9371,f11(a70,x9372,f3(a70)))
% 12.04/12.17 [941]~E(x9411,f2(a69))+P12(a69,x9411,f11(a69,x9412,f3(a69)))
% 12.04/12.17 [991]~P53(x9911)+P12(x9911,x9912,f11(x9911,x9912,f3(x9911)))
% 12.04/12.17 [1048]P12(a69,x10482,x10481)+E(f11(a69,x10481,f4(a69,x10482,x10481)),x10482)
% 12.04/12.17 [1065]P12(a69,x10651,x10652)+P12(a69,x10652,f11(a69,x10651,f3(a69)))
% 12.04/12.17 [1066]P11(a69,x10661,x10662)+P11(a69,f11(a69,x10662,f3(a69)),x10661)
% 12.04/12.17 [1106]~P13(a70,x11061,x11062)+E(f27(f27(f10(a70),x11061),f7(a70,x11062,x11061)),x11062)
% 12.04/12.17 [1136]~P11(a69,x11361,x11362)+E(f11(a69,x11361,f4(a69,x11362,x11361)),x11362)
% 12.04/12.17 [1137]~P11(a69,x11372,x11371)+E(f4(a69,x11371,f4(a69,x11371,x11372)),x11372)
% 12.04/12.17 [1138]~P11(a69,x11382,x11381)+E(f11(a69,f4(a69,x11381,x11382),x11382),x11381)
% 12.04/12.17 [1145]~P12(a70,x11451,x11452)+P11(a70,x11451,f4(a70,x11452,f3(a70)))
% 12.04/12.17 [1147]~P11(a69,x11471,x11472)+P12(a69,x11471,f11(a69,x11472,f3(a69)))
% 12.04/12.17 [1150]~P11(a70,x11501,x11502)+P12(a70,x11501,f11(a70,x11502,f3(a70)))
% 12.04/12.17 [1151]~P12(a70,x11511,x11512)+P12(a70,x11511,f11(a70,x11512,f3(a70)))
% 12.04/12.17 [1154]~P12(a69,x11541,x11542)+P11(a69,f11(a69,x11541,f3(a69)),x11542)
% 12.04/12.17 [1156]~P12(a70,x11561,x11562)+P11(a70,f11(a70,x11561,f3(a70)),x11562)
% 12.04/12.17 [1232]~P12(a69,x12321,x12322)+E(f11(a69,f11(a69,x12321,f40(x12322,x12321)),f3(a69)),x12322)
% 12.04/12.17 [1235]~P11(a69,x12352,x12351)+E(f4(a68,f26(a69,x12351),f26(a69,x12352)),f26(a69,f4(a69,x12351,x12352)))
% 12.04/12.17 [1254]P11(a69,x12541,x12542)+~P12(a69,x12541,f11(a69,x12542,f3(a69)))
% 12.04/12.17 [1255]P11(a70,x12551,x12552)+~P12(a70,x12551,f11(a70,x12552,f3(a70)))
% 12.04/12.17 [1256]P12(a70,x12561,x12562)+~P11(a70,x12561,f4(a70,x12562,f3(a70)))
% 12.04/12.17 [1260]P12(a69,x12601,x12602)+~P11(a69,f11(a69,x12601,f3(a69)),x12602)
% 12.04/12.17 [1262]P12(a70,x12621,x12622)+~P11(a70,f11(a70,x12621,f3(a70)),x12622)
% 12.04/12.17 [1268]~P11(a69,x12681,x12682)+P12(a68,f26(a69,x12681),f11(a68,f26(a69,x12682),f3(a68)))
% 12.04/12.17 [1269]~P12(a69,x12691,x12692)+P11(a68,f11(a68,f26(a69,x12691),f3(a68)),f26(a69,x12692))
% 12.04/12.17 [1331]~P12(a69,x13311,x13312)+~P12(a69,x13312,f11(a69,x13311,f3(a69)))
% 12.04/12.17 [1332]~P11(a69,x13321,x13322)+~P11(a69,f11(a69,x13322,f3(a69)),x13321)
% 12.04/12.17 [1355]P12(a68,x13551,f26(a69,x13552))+~P11(a69,f11(a69,f12(x13551),f3(a69)),x13552)
% 12.04/12.17 [1457]P11(a69,x14571,x14572)+~P12(a68,f26(a69,x14571),f11(a68,f26(a69,x14572),f3(a68)))
% 12.04/12.17 [1458]P12(a69,x14581,x14582)+~P11(a68,f11(a68,f26(a69,x14581),f3(a68)),f26(a69,x14582))
% 12.04/12.17 [1495]E(x14951,f2(a69))+E(f11(a69,f11(a69,f4(a69,x14951,f3(a69)),x14952),f3(a69)),f11(a69,x14951,x14952))
% 12.04/12.17 [1561]P11(a69,x15611,x15612)+~P11(a69,f11(a69,x15611,f3(a69)),f11(a69,x15612,f3(a69)))
% 12.04/12.17 [1563]P12(a69,x15631,x15632)+~P12(a69,f11(a69,x15631,f3(a69)),f11(a69,x15632,f3(a69)))
% 12.04/12.17 [657]~E(x6572,f2(a69))+E(f27(f27(f10(a69),x6571),x6572),f2(a69))
% 12.04/12.17 [659]~E(x6591,f2(a69))+E(f27(f27(f10(a69),x6591),x6592),f2(a69))
% 12.04/12.17 [660]~E(x6602,f2(a69))+E(f27(f27(f14(a69),x6601),x6602),f3(a69))
% 12.04/12.17 [722]~P42(x7221)+E(f27(f27(f10(x7221),f3(x7221)),x7222),x7222)
% 12.04/12.17 [723]~P22(x7231)+E(f27(f27(f10(x7231),f3(x7231)),x7232),x7232)
% 12.04/12.17 [724]~P25(x7241)+E(f27(f27(f10(x7241),f3(x7241)),x7242),x7242)
% 12.04/12.17 [729]~P42(x7291)+E(f27(f27(f10(x7291),f2(x7291)),x7292),f2(x7291))
% 12.04/12.17 [731]~P33(x7311)+E(f27(f27(f10(x7311),f2(x7311)),x7312),f2(x7311))
% 12.04/12.17 [732]~P52(x7321)+E(f27(f27(f10(x7321),f2(x7321)),x7322),f2(x7321))
% 12.04/12.17 [733]~P25(x7331)+E(f27(f27(f14(x7331),f3(x7331)),x7332),f3(x7331))
% 12.04/12.17 [742]E(x7421,f3(a69))+~E(f27(f27(f10(a69),x7422),x7421),f3(a69))
% 12.04/12.17 [743]E(x7431,f3(a69))+~E(f27(f27(f10(a69),x7431),x7432),f3(a69))
% 12.04/12.17 [751]~P3(x7511)+E(f11(f72(x7511),x7512,f2(f72(x7511))),x7512)
% 12.04/12.17 [752]~P7(x7521)+E(f4(f72(x7521),x7522,f2(f72(x7521))),x7522)
% 12.04/12.17 [753]~P3(x7531)+E(f11(f72(x7531),f2(f72(x7531)),x7532),x7532)
% 12.04/12.17 [776]~P37(x7761)+E(f23(x7761,x7762,f2(f72(x7761))),f2(f72(x7761)))
% 12.04/12.17 [777]~P37(x7771)+E(f8(x7771,f2(f72(x7771)),x7772),f2(f72(x7771)))
% 12.04/12.17 [778]~P37(x7781)+E(f25(x7781,f2(f72(x7781)),x7782),f2(f72(x7781)))
% 12.04/12.17 [779]~P37(x7791)+E(f22(x7791,f2(f72(x7791)),x7792),f2(f72(x7791)))
% 12.04/12.17 [816]~P7(x8161)+E(f4(f72(x8161),f2(f72(x8161)),x8162),f9(f72(x8161),x8162))
% 12.04/12.17 [828]~E(x8282,f2(a69))+E(f27(f27(f14(a69),x8281),x8282),f11(a69,f2(a69),f3(a69)))
% 12.04/12.17 [830]~P37(x8301)+E(f27(f27(f10(f72(x8301)),x8302),f2(f72(x8301))),f2(f72(x8301)))
% 12.04/12.17 [874]~P26(x8741)+E(f16(x8741,x8742,f2(f72(x8741))),f19(x8741,x8742,f2(a69)))
% 12.04/12.17 [926]~E(x9262,f2(a69))+P12(a69,f2(a69),f27(f27(f14(a69),x9261),x9262))
% 12.04/12.17 [958]~P48(x9581)+P11(x9581,f2(x9581),f27(f27(f10(x9581),x9582),x9582))
% 12.04/12.17 [1030]~E(x10301,f11(a69,f2(a69),f3(a69)))+E(f27(f27(f14(a69),x10301),x10302),f11(a69,f2(a69),f3(a69)))
% 12.04/12.17 [1078]E(x10781,f11(a69,f2(a69),f3(a69)))+~E(f27(f27(f10(a69),x10782),x10781),f11(a69,f2(a69),f3(a69)))
% 12.04/12.17 [1079]E(x10791,f11(a69,f2(a69),f3(a69)))+~E(f27(f27(f10(a69),x10791),x10792),f11(a69,f2(a69),f3(a69)))
% 12.04/12.17 [1107]~P11(a70,f2(a70),x11071)+P11(a70,f2(a70),f27(f27(f14(a70),x11071),x11072))
% 12.04/12.17 [1109]~P12(a69,f2(a69),x11091)+P12(a69,f2(a69),f27(f27(f14(a69),x11091),x11092))
% 12.04/12.17 [1183]~P48(x11831)+~P12(x11831,f27(f27(f10(x11831),x11832),x11832),f2(x11831))
% 12.04/12.17 [1217]P12(a69,f2(a69),x12171)+~P12(a69,f2(a69),f27(f27(f10(a69),x12172),x12171))
% 12.04/12.17 [1218]P12(a69,f2(a69),x12181)+~P12(a69,f2(a69),f27(f27(f10(a69),x12181),x12182))
% 12.04/12.17 [1242]~P11(a68,f2(a68),x12421)+E(f12(f11(a68,x12421,f26(a69,x12422))),f11(a69,f12(x12421),x12422))
% 12.04/12.17 [1243]~P11(a68,f2(a68),x12431)+E(f13(f11(a68,x12431,f26(a69,x12432))),f11(a69,f13(x12431),x12432))
% 12.04/12.17 [1314]~P11(a68,f26(a69,x13142),x13141)+E(f12(f4(a68,x13141,f26(a69,x13142))),f4(a69,f12(x13141),x13142))
% 12.04/12.17 [1315]~P11(a68,f26(a69,x13152),x13151)+E(f13(f4(a68,x13151,f26(a69,x13152))),f4(a69,f13(x13151),x13152))
% 12.04/12.17 [1550]~P12(a69,f2(a69),x15501)+P12(a69,f4(a69,x15501,f11(a69,x15502,f3(a69))),x15501)
% 12.04/12.17 [1611]~P11(a69,f11(a69,f2(a69),f3(a69)),x16111)+P11(a69,f11(a69,f2(a69),f3(a69)),f27(f27(f14(a69),x16111),x16112))
% 12.04/12.17 [1664]P11(a69,f11(a69,f2(a69),f3(a69)),x16641)+~P11(a69,f11(a69,f2(a69),f3(a69)),f27(f27(f10(a69),x16642),x16641))
% 12.04/12.17 [1665]P11(a69,f11(a69,f2(a69),f3(a69)),x16651)+~P11(a69,f11(a69,f2(a69),f3(a69)),f27(f27(f10(a69),x16651),x16652))
% 12.04/12.17 [1666]~P62(x16661)+E(f27(f27(f10(x16661),f11(x16661,x16662,f3(x16661))),f4(x16661,x16662,f3(x16661))),f4(x16661,f27(f27(f10(x16661),x16662),x16662),f3(x16661)))
% 12.04/12.17 [761]~P37(x7611)+E(f27(f21(x7611,f2(f72(x7611))),x7612),f2(x7611))
% 12.04/12.17 [762]~P42(x7621)+E(f27(f21(x7621,f3(f72(x7621))),x7622),f3(x7621))
% 12.04/12.17 [863]~P37(x8631)+E(f27(f27(f10(f72(x8631)),f2(f72(x8631))),x8632),f2(f72(x8631)))
% 12.04/12.17 [903]~P40(x9031)+E(f27(f27(f10(x9031),f9(x9031,f3(x9031))),x9032),f9(x9031,x9032))
% 12.04/12.17 [1001]~E(f26(a69,f12(x10011)),x10011)+E(f12(f27(f27(f14(a68),x10011),x10012)),f27(f27(f14(a69),f12(x10011)),x10012))
% 12.04/12.17 [1404]E(x14041,f2(a68))+~E(f11(a68,f27(f27(f10(a68),x14042),x14042),f27(f27(f10(a68),x14041),x14041)),f2(a68))
% 12.04/12.17 [1405]E(x14051,f2(a68))+~E(f11(a68,f27(f27(f10(a68),x14051),x14051),f27(f27(f10(a68),x14052),x14052)),f2(a68))
% 12.04/12.17 [1406]~P42(x14061)+E(f11(x14061,x14062,x14062),f27(f27(f10(x14061),f11(x14061,f3(x14061),f3(x14061))),x14062))
% 12.04/12.17 [1435]E(x14351,f2(a69))+E(f27(f27(f10(a69),x14352),f27(f27(f14(a69),x14352),f4(a69,x14351,f3(a69)))),f27(f27(f14(a69),x14352),x14351))
% 12.04/12.17 [1749]~P11(a68,f2(a68),x17492)+P11(a68,f11(a68,f27(f27(f10(a68),f26(a69,x17491)),x17492),f3(a68)),f27(f27(f14(a68),f11(a68,x17492,f3(a68))),x17491))
% 12.04/12.17 [1692]E(x16921,f2(a69))+E(f11(a69,x16922,f27(f27(f10(a69),f4(a69,x16921,f3(a69))),x16922)),f27(f27(f10(a69),x16921),x16922))
% 12.04/12.17 [838]~P42(x8381)+E(f11(x8381,x8382,x8383),f11(x8381,x8383,x8382))
% 12.04/12.17 [876]P11(a69,x8761,x8762)+~E(x8762,f11(a69,x8761,x8763))
% 12.04/12.17 [939]E(x9391,x9392)+~E(f11(a69,x9393,x9391),f11(a69,x9393,x9392))
% 12.04/12.17 [940]E(x9401,x9402)+~E(f11(a69,x9401,x9403),f11(a69,x9402,x9403))
% 12.04/12.17 [1124]~P11(a69,x11241,x11243)+P11(a69,x11241,f11(a69,x11242,x11243))
% 12.04/12.17 [1126]~P11(a69,x11261,x11262)+P11(a69,x11261,f11(a69,x11262,x11263))
% 12.04/12.17 [1128]~P12(a69,x11281,x11283)+P12(a69,x11281,f11(a69,x11282,x11283))
% 12.04/12.17 [1130]~P12(a69,x11301,x11302)+P12(a69,x11301,f11(a69,x11302,x11303))
% 12.04/12.17 [1132]~P12(a69,x11321,x11323)+P12(a69,f4(a69,x11321,x11322),x11323)
% 12.04/12.17 [1165]~P12(a68,f2(a68),x11653)+P12(a68,f2(a68),f48(x11651,x11652,x11653))
% 12.04/12.17 [1239]P11(a69,x12391,x12392)+~P11(a69,f11(a69,x12393,x12391),x12392)
% 12.04/12.17 [1240]P11(a69,x12401,x12402)+~P11(a69,f11(a69,x12401,x12403),x12402)
% 12.04/12.17 [1241]P12(a69,x12411,x12412)+~P12(a69,f11(a69,x12411,x12413),x12412)
% 12.04/12.17 [1339]~P11(a68,x13392,x13393)+P11(a68,f11(a68,x13391,x13392),f11(a68,x13391,x13393))
% 12.04/12.17 [1340]~P11(a69,x13402,x13403)+P11(a69,f11(a69,x13401,x13402),f11(a69,x13401,x13403))
% 12.04/12.17 [1341]~P11(a69,x13411,x13413)+P11(a69,f11(a69,x13411,x13412),f11(a69,x13413,x13412))
% 12.04/12.17 [1342]~P11(a69,x13423,x13422)+P11(a69,f4(a69,x13421,x13422),f4(a69,x13421,x13423))
% 12.04/12.17 [1343]~P11(a69,x13431,x13433)+P11(a69,f4(a69,x13431,x13432),f4(a69,x13433,x13432))
% 12.04/12.17 [1344]~P11(a70,x13442,x13443)+P11(a70,f11(a70,x13441,x13442),f11(a70,x13441,x13443))
% 12.04/12.17 [1345]~P12(a69,x13452,x13453)+P12(a69,f11(a69,x13451,x13452),f11(a69,x13451,x13453))
% 12.04/12.17 [1346]~P12(a69,x13461,x13463)+P12(a69,f11(a69,x13461,x13462),f11(a69,x13463,x13462))
% 12.04/12.17 [1347]~P12(a70,x13471,x13473)+P12(a70,f11(a70,x13471,x13472),f11(a70,x13473,x13472))
% 12.04/12.17 [1431]~P11(a69,f4(a69,x14311,x14313),x14312)+P11(a69,x14311,f11(a69,x14312,x14313))
% 12.04/12.17 [1432]~P12(a69,f11(a69,x14321,x14323),x14322)+P12(a69,x14321,f4(a69,x14322,x14323))
% 12.04/12.17 [1433]~P11(a69,x14331,f11(a69,x14333,x14332))+P11(a69,f4(a69,x14331,x14332),x14333)
% 12.04/12.17 [1434]~P12(a69,x14341,f4(a69,x14343,x14342))+P12(a69,f11(a69,x14341,x14342),x14343)
% 12.04/12.17 [1547]P11(a69,x15471,x15472)+~P11(a69,f11(a69,x15473,x15471),f11(a69,x15473,x15472))
% 12.04/12.17 [1548]P12(a69,x15481,x15482)+~P12(a69,f11(a69,x15483,x15481),f11(a69,x15483,x15482))
% 12.04/12.17 [887]~P7(x8871)+E(f11(x8871,x8872,f9(x8871,x8873)),f4(x8871,x8872,x8873))
% 12.04/12.17 [888]~P21(x8881)+E(f11(x8881,x8882,f9(x8881,x8883)),f4(x8881,x8882,x8883))
% 12.04/12.17 [889]~P40(x8891)+E(f11(x8891,x8892,f9(x8891,x8893)),f4(x8891,x8892,x8893))
% 12.04/12.17 [890]~P21(x8901)+E(f4(x8901,x8902,f9(x8901,x8903)),f11(x8901,x8902,x8903))
% 12.04/12.17 [944]~P21(x9441)+E(f11(x9441,f4(x9441,x9442,x9443),x9443),x9442)
% 12.04/12.17 [945]~P21(x9451)+E(f4(x9451,f11(x9451,x9452,x9453),x9453),x9452)
% 12.04/12.17 [997]~P7(x9971)+E(f9(x9971,f4(x9971,x9972,x9973)),f4(x9971,x9973,x9972))
% 12.04/12.17 [1027]~P21(x10271)+E(f11(x10271,f9(x10271,x10272),f11(x10271,x10272,x10273)),x10273)
% 12.04/12.17 [1053]~P38(x10531)+E(f9(f72(x10531),f23(x10531,x10532,x10533)),f23(x10531,f9(x10531,x10532),x10533))
% 12.04/12.17 [1054]~P7(x10541)+E(f9(f72(x10541),f19(x10541,x10542,x10543)),f19(x10541,f9(x10541,x10542),x10543))
% 12.04/12.17 [1094]~P21(x10941)+E(f11(x10941,f9(x10941,x10942),f9(x10941,x10943)),f9(x10941,f11(x10941,x10943,x10942)))
% 12.04/12.17 [1095]~P7(x10951)+E(f11(x10951,f9(x10951,x10952),f9(x10951,x10953)),f9(x10951,f11(x10951,x10952,x10953)))
% 12.04/12.17 [1096]~P7(x10961)+E(f4(x10961,f9(x10961,x10962),f9(x10961,x10963)),f9(x10961,f4(x10961,x10962,x10963)))
% 12.04/12.17 [1161]~P1(x11611)+E(f29(x11611,f4(x11611,x11612,x11613)),f29(x11611,f4(x11611,x11613,x11612)))
% 12.04/12.17 [1251]P12(a69,x12511,x12512)+~E(x12512,f11(a69,f11(a69,x12511,x12513),f3(a69)))
% 12.04/12.17 [1426]~P11(a69,x14262,x14263)+E(f4(a69,f11(a69,x14261,x14262),x14263),f4(a69,x14261,f4(a69,x14263,x14262)))
% 12.04/12.17 [1427]~P11(a69,x14273,x14272)+E(f11(a69,x14271,f4(a69,x14272,x14273)),f4(a69,f11(a69,x14271,x14272),x14273))
% 12.04/12.17 [1429]~P11(a69,x14292,x14291)+E(f11(a69,f4(a69,x14291,x14292),x14293),f4(a69,f11(a69,x14291,x14293),x14292))
% 12.04/12.17 [1512]~P11(a69,x15123,x15122)+P11(a69,x15121,f4(a69,f11(a69,x15122,x15121),x15123))
% 12.04/12.17 [1584]~P1(x15841)+P11(a68,f29(x15841,f11(x15841,x15842,x15843)),f11(a68,f29(x15841,x15842),f29(x15841,x15843)))
% 12.04/12.17 [1585]~P1(x15851)+P11(a68,f29(x15851,f4(x15851,x15852,x15853)),f11(a68,f29(x15851,x15852),f29(x15851,x15853)))
% 12.04/12.17 [1586]~P1(x15861)+P11(a68,f4(a68,f29(x15861,x15862),f29(x15861,x15863)),f29(x15861,f11(x15861,x15862,x15863)))
% 12.04/12.17 [1587]~P1(x15871)+P11(a68,f4(a68,f29(x15871,x15872),f29(x15871,x15873)),f29(x15871,f4(x15871,x15872,x15873)))
% 12.04/12.17 [1796]~P41(x17961)+P13(f72(x17961),f27(f27(f14(f72(x17961)),f16(x17961,f9(x17961,x17962),f16(x17961,f3(x17961),f2(f72(x17961))))),f20(x17961,x17962,x17963)),x17963)
% 12.04/12.17 [804]~E(x8042,f2(a69))+E(f27(f27(f10(a69),x8041),x8042),f27(f27(f10(a69),x8043),x8042))
% 12.04/12.17 [806]~E(x8061,f2(a69))+E(f27(f27(f10(a69),x8061),x8062),f27(f27(f10(a69),x8061),x8063))
% 12.04/12.17 [829]~P42(x8291)+E(f27(f27(f10(x8291),x8292),x8293),f27(f27(f10(x8291),x8293),x8292))
% 12.04/12.17 [934]~P42(x9341)+P13(x9341,x9342,f27(f27(f10(x9341),x9343),x9342))
% 12.04/12.17 [935]~P42(x9351)+P13(x9351,x9352,f27(f27(f10(x9351),x9352),x9353))
% 12.04/12.17 [1014]~P45(x10141)+E(f27(f27(f10(x10141),f9(x10141,x10142)),x10143),f27(f27(f10(x10141),x10142),f9(x10141,x10143)))
% 12.04/12.17 [1015]~P45(x10151)+E(f27(f27(f10(x10151),f9(x10151,x10152)),f9(x10151,x10153)),f27(f27(f10(x10151),x10152),x10153))
% 12.04/12.17 [1073]~P21(x10731)+E(f11(x10731,x10732,f11(x10731,f9(x10731,x10732),x10733)),x10733)
% 12.04/12.17 [1082]~P38(x10821)+E(f23(x10821,x10822,f9(f72(x10821),x10823)),f9(f72(x10821),f23(x10821,x10822,x10823)))
% 12.04/12.17 [1117]~E(x11171,f2(a69))+P13(a69,f27(f27(f10(a69),x11171),x11172),f27(f27(f10(a69),x11171),x11173))
% 12.04/12.17 [1167]~P7(x11671)+E(f16(x11671,f9(x11671,x11672),f9(f72(x11671),x11673)),f9(f72(x11671),f16(x11671,x11672,x11673)))
% 12.04/12.17 [1221]P12(a69,f2(a69),x12211)+P11(a69,f27(f27(f10(a69),x12212),x12211),f27(f27(f10(a69),x12213),x12211))
% 12.04/12.17 [1222]P12(a69,f2(a69),x12221)+P11(a69,f27(f27(f10(a69),x12221),x12222),f27(f27(f10(a69),x12221),x12223))
% 12.04/12.17 [1272]~P11(a69,x12722,x12723)+P11(a69,f27(f27(f10(a69),x12721),x12722),f27(f27(f10(a69),x12721),x12723))
% 12.04/12.17 [1274]~P11(a69,x12741,x12743)+P11(a69,f27(f27(f10(a69),x12741),x12742),f27(f27(f10(a69),x12743),x12742))
% 12.04/12.17 [1275]~P13(a69,x12752,x12753)+P13(a69,f27(f27(f10(a69),x12751),x12752),f27(f27(f10(a69),x12751),x12753))
% 12.04/12.17 [1329]~P26(x13291)+E(f16(x13291,f2(x13291),f19(x13291,x13292,x13293)),f19(x13291,x13292,f11(a69,x13293,f3(a69))))
% 12.04/12.17 [1393]~P11(a68,f29(a1,x13932),x13933)+P11(a68,f29(a1,f27(f21(a1,x13931),x13932)),f28(x13931,x13933))
% 12.04/12.17 [1463]P12(a69,x14631,x14632)+~P12(a69,f27(f27(f10(a69),x14633),x14631),f27(f27(f10(a69),x14633),x14632))
% 12.04/12.17 [1464]P12(a69,x14641,x14642)+~P12(a69,f27(f27(f10(a69),x14641),x14643),f27(f27(f10(a69),x14642),x14643))
% 12.04/12.17 [1469]P12(a69,f2(a69),x14691)+~P12(a69,f27(f27(f10(a69),x14692),x14691),f27(f27(f10(a69),x14693),x14691))
% 12.04/12.17 [1470]P12(a69,f2(a69),x14701)+~P12(a69,f27(f27(f10(a69),x14701),x14702),f27(f27(f10(a69),x14701),x14703))
% 12.04/12.17 [1676]~P11(a68,f29(a1,x16763),x16762)+P11(a68,f29(a1,f27(f21(a1,x16761),f63(x16761,x16762))),f29(a1,f27(f21(a1,x16761),x16763)))
% 12.04/12.17 [1681]~P37(x16811)+E(f16(x16811,f27(f21(x16811,x16812),x16813),f25(x16811,x16812,x16813)),f11(f72(x16811),x16812,f23(x16811,x16813,f25(x16811,x16812,x16813))))
% 12.04/12.17 [1709]~P11(a69,x17092,x17093)+E(f4(a69,f11(a69,x17091,x17092),f11(a69,x17093,f3(a69))),f4(a69,x17091,f11(a69,f4(a69,x17093,x17092),f3(a69))))
% 12.04/12.17 [1710]~P11(a69,x17102,x17101)+E(f4(a69,f11(a69,f4(a69,x17101,x17102),f3(a69)),x17103),f4(a69,f11(a69,x17101,f3(a69)),f11(a69,x17102,x17103)))
% 12.04/12.17 [1037]~P45(x10371)+E(f27(f27(f10(x10371),x10372),f9(x10371,x10373)),f9(x10371,f27(f27(f10(x10371),x10372),x10373)))
% 12.04/12.17 [1039]~P33(x10391)+E(f27(f27(f10(x10391),x10392),f9(x10391,x10393)),f9(x10391,f27(f27(f10(x10391),x10392),x10393)))
% 12.04/12.17 [1064]~P38(x10641)+E(f27(f21(x10641,f9(f72(x10641),x10642)),x10643),f9(x10641,f27(f21(x10641,x10642),x10643)))
% 12.04/12.17 [1074]~P35(x10741)+E(f29(x10741,f27(f27(f14(x10741),x10742),x10743)),f27(f27(f14(a68),f29(x10741,x10742)),x10743))
% 12.04/12.17 [1083]~P45(x10831)+E(f27(f27(f10(x10831),f9(x10831,x10832)),x10833),f9(x10831,f27(f27(f10(x10831),x10832),x10833)))
% 12.04/12.17 [1085]~P33(x10851)+E(f27(f27(f10(x10851),f9(x10851,x10852)),x10853),f9(x10851,f27(f27(f10(x10851),x10852),x10853)))
% 12.04/12.17 [1157]~P35(x11571)+E(f27(f27(f10(a68),f29(x11571,x11572)),f29(x11571,x11573)),f29(x11571,f27(f27(f10(x11571),x11572),x11573)))
% 12.04/12.17 [1210]~P37(x12101)+E(f8(x12101,f16(x12101,x12102,f2(f72(x12101))),x12103),f16(x12101,x12102,f2(f72(x12101))))
% 12.04/12.17 [1286]~P42(x12861)+E(f27(f27(f10(x12861),x12862),f27(f27(f14(x12861),x12862),x12863)),f27(f27(f14(x12861),x12862),f11(a69,x12863,f3(a69))))
% 12.04/12.17 [1287]~P34(x12871)+E(f27(f27(f10(x12871),x12872),f27(f27(f14(x12871),x12872),x12873)),f27(f27(f14(x12871),x12872),f11(a69,x12873,f3(a69))))
% 12.04/12.17 [1467]~P13(a70,x14671,x14672)+P13(a70,x14671,f11(a70,x14672,f27(f27(f10(a70),x14671),x14673)))
% 12.04/12.17 [1538]~P42(x15381)+E(f11(x15381,x15382,f27(f27(f10(x15381),x15383),x15382)),f27(f27(f10(x15381),f11(x15381,x15383,f3(x15381))),x15382))
% 12.04/12.17 [1539]~P42(x15391)+E(f11(x15391,f27(f27(f10(x15391),x15392),x15393),x15393),f27(f27(f10(x15391),f11(x15391,x15392,f3(x15391))),x15393))
% 12.04/12.17 [1572]~P36(x15721)+P11(a68,f29(x15721,f27(f27(f14(x15721),x15722),x15723)),f27(f27(f14(a68),f29(x15721,x15722)),x15723))
% 12.04/12.17 [1626]~P33(x16261)+P11(a68,f29(x16261,f27(f27(f10(x16261),x16262),x16263)),f27(f27(f10(a68),f29(x16261,x16263)),f66(x16262,x16261)))
% 12.04/12.17 [1627]~P33(x16271)+P11(a68,f29(x16271,f27(f27(f10(x16271),x16272),x16273)),f27(f27(f10(a68),f29(x16271,x16273)),f36(x16272,x16271)))
% 12.04/12.17 [1628]~P33(x16281)+P11(a68,f29(x16281,f27(f27(f10(x16281),x16282),x16283)),f27(f27(f10(a68),f29(x16281,x16283)),f45(x16282,x16281)))
% 12.04/12.17 [1629]~P33(x16291)+P11(a68,f29(x16291,f27(f27(f10(x16291),x16292),x16293)),f27(f27(f10(a68),f29(x16291,x16292)),f29(x16291,x16293)))
% 12.04/12.17 [1630]~P33(x16301)+P11(a68,f29(x16301,f27(f27(f10(x16301),x16302),x16303)),f27(f27(f10(a68),f29(x16301,x16302)),f67(x16303,x16301)))
% 12.04/12.17 [1631]~P33(x16311)+P11(a68,f29(x16311,f27(f27(f10(x16311),x16312),x16313)),f27(f27(f10(a68),f29(x16311,x16312)),f38(x16313,x16311)))
% 12.04/12.17 [1632]~P33(x16321)+P11(a68,f29(x16321,f27(f27(f10(x16321),x16322),x16323)),f27(f27(f10(a68),f29(x16321,x16322)),f46(x16323,x16321)))
% 12.04/12.17 [1668]P13(a70,x16681,x16682)+~P13(a70,x16681,f11(a70,x16682,f27(f27(f10(a70),x16681),x16683)))
% 12.04/12.17 [1669]~P48(x16691)+P11(x16691,f2(x16691),f11(x16691,f27(f27(f10(x16691),x16692),x16692),f27(f27(f10(x16691),x16693),x16693)))
% 12.04/12.17 [1717]~P62(x17171)+E(f27(f27(f10(x17171),f27(f27(f14(x17171),f9(x17171,f3(x17171))),x17172)),f27(f27(f14(x17171),x17173),x17172)),f27(f27(f14(x17171),f9(x17171,x17173)),x17172))
% 12.04/12.17 [1726]E(x17261,x17262)+~E(f27(f27(f10(a69),f11(a69,x17263,f3(a69))),x17261),f27(f27(f10(a69),f11(a69,x17263,f3(a69))),x17262))
% 12.04/12.17 [1731]~P48(x17311)+~P12(x17311,f11(x17311,f27(f27(f10(x17311),x17312),x17312),f27(f27(f10(x17311),x17313),x17313)),f2(x17311))
% 12.04/12.17 [1754]~P12(a69,x17542,x17543)+P12(a69,f27(f27(f10(a69),f11(a69,x17541,f3(a69))),x17542),f27(f27(f10(a69),f11(a69,x17541,f3(a69))),x17543))
% 12.04/12.17 [1765]~P33(x17651)+P11(a68,f29(x17651,f27(f27(f10(x17651),x17652),x17653)),f27(f27(f10(a68),f27(f27(f10(a68),f29(x17651,x17652)),f29(x17651,x17653))),f60(x17651)))
% 12.04/12.17 [1766]~P33(x17661)+P11(a68,f29(x17661,f27(f27(f10(x17661),x17662),x17663)),f27(f27(f10(a68),f27(f27(f10(a68),f29(x17661,x17662)),f29(x17661,x17663))),f37(x17661)))
% 12.04/12.17 [1767]~P33(x17671)+P11(a68,f29(x17671,f27(f27(f10(x17671),x17672),x17673)),f27(f27(f10(a68),f27(f27(f10(a68),f29(x17671,x17672)),f29(x17671,x17673))),f31(x17671)))
% 12.04/12.17 [1779]P11(a69,x17791,x17792)+~P11(a69,f27(f27(f10(a69),f11(a69,x17793,f3(a69))),x17791),f27(f27(f10(a69),f11(a69,x17793,f3(a69))),x17792))
% 12.04/12.17 [1784]~P40(x17841)+E(f4(x17841,f27(f27(f14(x17841),x17842),f11(a69,f11(a69,f2(a69),f3(a69)),f3(a69))),f27(f27(f14(x17841),x17843),f11(a69,f11(a69,f2(a69),f3(a69)),f3(a69)))),f27(f27(f10(x17841),f4(x17841,x17842,x17843)),f11(x17841,x17842,x17843)))
% 12.04/12.17 [1806]~P40(x18061)+E(f11(f72(x18061),f27(f27(f10(f72(x18061)),f16(x18061,f9(x18061,x18062),f16(x18061,f3(x18061),f2(f72(x18061))))),f25(x18061,x18063,x18062)),f16(x18061,f27(f21(x18061,x18063),x18062),f2(f72(x18061)))),x18063)
% 12.04/12.17 [1462]~P25(x14621)+E(f27(f27(f10(x14621),f27(f27(f14(x14621),x14622),x14623)),x14622),f27(f27(f10(x14621),x14622),f27(f27(f14(x14621),x14622),x14623)))
% 12.04/12.17 [1483]~P25(x14831)+E(f27(f27(f10(x14831),f27(f27(f14(x14831),x14832),x14833)),x14832),f27(f27(f14(x14831),x14832),f11(a69,x14833,f3(a69))))
% 12.04/12.17 [1484]~P42(x14841)+E(f27(f27(f10(x14841),f27(f27(f14(x14841),x14842),x14843)),x14842),f27(f27(f14(x14841),x14842),f11(a69,x14843,f3(a69))))
% 12.04/12.17 [1302]~P42(x13021)+E(f11(x13021,x13022,f11(x13021,x13023,x13024)),f11(x13021,x13023,f11(x13021,x13022,x13024)))
% 12.04/12.17 [1304]~P6(x13041)+E(f11(x13041,f11(x13041,x13042,x13043),x13044),f11(x13041,x13042,f11(x13041,x13043,x13044)))
% 12.04/12.17 [1305]~P42(x13051)+E(f11(x13051,f11(x13051,x13052,x13053),x13054),f11(x13051,x13052,f11(x13051,x13053,x13054)))
% 12.04/12.18 [1306]~P42(x13061)+E(f11(x13061,f11(x13061,x13062,x13063),x13064),f11(x13061,f11(x13061,x13062,x13064),x13063))
% 12.04/12.18 [1452]~P37(x14521)+E(f25(x14521,f16(x14521,x14522,x14523),x14524),f16(x14521,f27(f21(x14521,x14523),x14524),f25(x14521,x14523,x14524)))
% 12.04/12.18 [1492]~P37(x14921)+E(f16(x14921,f27(f27(f10(x14921),x14922),x14923),f23(x14921,x14922,x14924)),f23(x14921,x14922,f16(x14921,x14923,x14924)))
% 12.04/12.18 [1500]~P37(x15001)+E(f11(f72(x15001),f23(x15001,x15002,x15003),f23(x15001,x15004,x15003)),f23(x15001,f11(x15001,x15002,x15004),x15003))
% 12.04/12.18 [1501]~P38(x15011)+E(f4(f72(x15011),f23(x15011,x15012,x15013),f23(x15011,x15014,x15013)),f23(x15011,f4(x15011,x15012,x15014),x15013))
% 12.04/12.18 [1502]~P3(x15021)+E(f11(f72(x15021),f19(x15021,x15022,x15023),f19(x15021,x15024,x15023)),f19(x15021,f11(x15021,x15022,x15024),x15023))
% 12.04/12.18 [1503]~P7(x15031)+E(f4(f72(x15031),f19(x15031,x15032,x15033),f19(x15031,x15034,x15033)),f19(x15031,f4(x15031,x15032,x15034),x15033))
% 12.04/12.18 [1407]~P37(x14071)+E(f27(f21(x14071,x14072),f27(f21(x14071,x14073),x14074)),f27(f21(x14071,f22(x14071,x14072,x14073)),x14074))
% 12.04/12.18 [1417]~P37(x14171)+E(f27(f27(f10(x14171),x14172),f27(f21(x14171,x14173),x14174)),f27(f21(x14171,f23(x14171,x14172,x14173)),x14174))
% 12.04/12.18 [1451]~P37(x14511)+E(f27(f21(x14511,f8(x14511,x14512,x14513)),x14514),f27(f21(x14511,x14512),f11(x14511,x14513,x14514)))
% 12.04/12.18 [1541]~P37(x15411)+E(f11(f72(x15411),f23(x15411,x15412,x15413),f23(x15411,x15412,x15414)),f23(x15411,x15412,f11(f72(x15411),x15413,x15414)))
% 12.04/12.18 [1542]~P38(x15421)+E(f4(f72(x15421),f23(x15421,x15422,x15423),f23(x15421,x15422,x15424)),f23(x15421,x15422,f4(f72(x15421),x15423,x15424)))
% 12.04/12.18 [1713]~P37(x17131)+E(f11(f72(x17131),f16(x17131,x17132,f2(f72(x17131))),f27(f27(f10(f72(x17131)),x17133),f22(x17131,x17134,x17133))),f22(x17131,f16(x17131,x17132,x17134),x17133))
% 12.04/12.18 [1728]~P37(x17281)+E(f11(f72(x17281),f23(x17281,x17282,f8(x17281,x17283,x17282)),f16(x17281,x17284,f8(x17281,x17283,x17282))),f8(x17281,f16(x17281,x17284,x17283),x17282))
% 12.04/12.18 [1270]~P42(x12701)+E(f27(f27(f10(x12701),x12702),f27(f27(f10(x12701),x12703),x12704)),f27(f27(f10(x12701),x12703),f27(f27(f10(x12701),x12702),x12704)))
% 12.04/12.18 [1292]~P37(x12921)+E(f23(x12921,f27(f27(f10(x12921),x12922),x12923),x12924),f23(x12921,x12922,f23(x12921,x12923,x12924)))
% 12.04/12.18 [1293]~P37(x12931)+E(f19(x12931,f27(f27(f10(x12931),x12932),x12933),x12934),f23(x12931,x12932,f19(x12931,x12933,x12934)))
% 12.04/12.18 [1456]~P42(x14561)+E(f27(f27(f10(x14561),x14562),f27(f27(f14(x14561),x14563),x14564)),f27(f21(x14561,f19(x14561,x14562,x14564)),x14563))
% 12.04/12.18 [1478]~P42(x14781)+E(f11(x14781,f27(f27(f10(x14781),x14782),x14783),f27(f27(f10(x14781),x14782),x14784)),f27(f27(f10(x14781),x14782),f11(x14781,x14783,x14784)))
% 12.04/12.18 [1480]~P33(x14801)+E(f11(x14801,f27(f27(f10(x14801),x14802),x14803),f27(f27(f10(x14801),x14802),x14804)),f27(f27(f10(x14801),x14802),f11(x14801,x14803,x14804)))
% 12.04/12.18 [1482]~P33(x14821)+E(f4(x14821,f27(f27(f10(x14821),x14822),x14823),f27(f27(f10(x14821),x14822),x14824)),f27(f27(f10(x14821),x14822),f4(x14821,x14823,x14824)))
% 12.04/12.18 [1581]~P37(x15811)+E(f11(x15811,f27(f21(x15811,x15812),x15813),f27(f21(x15811,x15814),x15813)),f27(f21(x15811,f11(f72(x15811),x15812,x15814)),x15813))
% 12.04/12.18 [1582]~P38(x15821)+E(f4(x15821,f27(f21(x15821,x15822),x15823),f27(f21(x15821,x15824),x15823)),f27(f21(x15821,f4(f72(x15821),x15822,x15824)),x15823))
% 12.04/12.18 [1605]~P25(x16051)+E(f27(f27(f10(x16051),f27(f27(f14(x16051),x16052),x16053)),f27(f27(f14(x16051),x16052),x16054)),f27(f27(f14(x16051),x16052),f11(a69,x16053,x16054)))
% 12.04/12.18 [1606]~P42(x16061)+E(f27(f27(f10(x16061),f27(f27(f14(x16061),x16062),x16063)),f27(f27(f14(x16061),x16062),x16064)),f27(f27(f14(x16061),x16062),f11(a69,x16063,x16064)))
% 12.04/12.18 [1620]~P33(x16201)+E(f11(x16201,f27(f27(f10(x16201),x16202),x16203),f27(f27(f10(x16201),x16204),x16203)),f27(f27(f10(x16201),f11(x16201,x16202,x16204)),x16203))
% 12.04/12.18 [1621]~P39(x16211)+E(f11(x16211,f27(f27(f10(x16211),x16212),x16213),f27(f27(f10(x16211),x16214),x16213)),f27(f27(f10(x16211),f11(x16211,x16212,x16214)),x16213))
% 12.04/12.18 [1623]~P33(x16231)+E(f4(x16231,f27(f27(f10(x16231),x16232),x16233),f27(f27(f10(x16231),x16234),x16233)),f27(f27(f10(x16231),f4(x16231,x16232,x16234)),x16233))
% 12.04/12.18 [1624]~P42(x16241)+E(f11(x16241,f27(f27(f10(x16241),x16242),x16243),f27(f27(f10(x16241),x16244),x16243)),f27(f27(f10(x16241),f11(x16241,x16242,x16244)),x16243))
% 12.04/12.18 [1662]~P37(x16621)+E(f11(x16621,x16622,f27(f27(f10(x16621),x16623),f27(f21(x16621,x16624),x16623))),f27(f21(x16621,f16(x16621,x16622,x16624)),x16623))
% 12.04/12.18 [1420]~P37(x14201)+E(f23(x14201,x14202,f27(f27(f10(f72(x14201)),x14203),x14204)),f27(f27(f10(f72(x14201)),x14203),f23(x14201,x14202,x14204)))
% 12.04/12.18 [1448]~P42(x14481)+E(f27(f27(f14(x14481),f27(f27(f14(x14481),x14482),x14483)),x14484),f27(f27(f14(x14481),x14482),f27(f27(f10(a69),x14483),x14484)))
% 12.04/12.18 [1449]~P25(x14491)+E(f27(f27(f14(x14491),f27(f27(f14(x14491),x14492),x14493)),x14494),f27(f27(f14(x14491),x14492),f27(f27(f10(a69),x14493),x14494)))
% 12.04/12.18 [1460]~P42(x14601)+E(f27(f27(f10(x14601),f27(f27(f10(x14601),x14602),x14603)),x14604),f27(f27(f10(x14601),x14602),f27(f27(f10(x14601),x14603),x14604)))
% 12.04/12.18 [1461]~P15(x14611)+E(f27(f27(f10(x14611),f27(f27(f10(x14611),x14612),x14613)),x14614),f27(f27(f10(x14611),x14612),f27(f27(f10(x14611),x14613),x14614)))
% 12.04/12.18 [1583]~P37(x15831)+E(f23(x15831,x15832,f27(f27(f10(f72(x15831)),x15833),x15834)),f27(f27(f10(f72(x15831)),f23(x15831,x15832,x15833)),x15834))
% 12.04/12.18 [1604]~P42(x16041)+E(f27(f27(f10(x16041),f27(f27(f10(x16041),x16042),x16043)),x16044),f27(f27(f10(x16041),f27(f27(f10(x16041),x16042),x16044)),x16043))
% 12.04/12.18 [1679]~P42(x16791)+E(f27(f27(f10(x16791),f27(f27(f14(x16791),x16792),x16793)),f27(f27(f14(x16791),x16794),x16793)),f27(f27(f14(x16791),f27(f27(f10(x16791),x16792),x16794)),x16793))
% 12.04/12.18 [1680]~P22(x16801)+E(f27(f27(f10(x16801),f27(f27(f14(x16801),x16802),x16803)),f27(f27(f14(x16801),x16804),x16803)),f27(f27(f14(x16801),f27(f27(f10(x16801),x16802),x16804)),x16803))
% 12.04/12.18 [1705]~P37(x17051)+E(f11(f72(x17051),f27(f27(f10(f72(x17051)),x17052),x17053),f27(f27(f10(f72(x17051)),x17054),x17053)),f27(f27(f10(f72(x17051)),f11(f72(x17051),x17052,x17054)),x17053))
% 12.04/12.18 [1643]~P42(x16431)+E(f27(f21(x16431,f27(f27(f14(f72(x16431)),x16432),x16433)),x16434),f27(f27(f14(x16431),f27(f21(x16431,x16432),x16434)),x16433))
% 12.04/12.18 [1693]~P37(x16931)+E(f27(f27(f10(x16931),f27(f21(x16931,x16932),x16933)),f27(f21(x16931,x16934),x16933)),f27(f21(x16931,f27(f27(f10(f72(x16931)),x16932),x16934)),x16933))
% 12.04/12.18 [1718]~P37(x17181)+E(f11(f72(x17181),f23(x17181,x17182,x17183),f16(x17181,f2(x17181),f27(f27(f10(f72(x17181)),x17183),x17184))),f27(f27(f10(f72(x17181)),x17183),f16(x17181,x17182,x17184)))
% 12.04/12.18 [1730]~P37(x17301)+E(f11(f72(x17301),f23(x17301,x17302,x17303),f16(x17301,f2(x17301),f27(f27(f10(f72(x17301)),x17304),x17303))),f27(f27(f10(f72(x17301)),f16(x17301,x17302,x17304)),x17303))
% 12.04/12.18 [1640]~P42(x16401)+E(f11(x16401,f11(x16401,x16402,x16403),f11(x16401,x16404,x16405)),f11(x16401,f11(x16401,x16402,x16404),f11(x16401,x16403,x16405)))
% 12.04/12.18 [1641]~P7(x16411)+E(f11(x16411,f4(x16411,x16412,x16413),f4(x16411,x16414,x16415)),f4(x16411,f11(x16411,x16412,x16414),f11(x16411,x16413,x16415)))
% 12.04/12.18 [1698]~P37(x16981)+E(f27(f27(f10(f72(x16981)),f19(x16981,x16982,x16983)),f19(x16981,x16984,x16985)),f19(x16981,f27(f27(f10(x16981),x16982),x16984),f11(a69,x16983,x16985)))
% 12.04/12.18 [1644]~P3(x16441)+E(f16(x16441,f11(x16441,x16442,x16443),f11(f72(x16441),x16444,x16445)),f11(f72(x16441),f16(x16441,x16442,x16444),f16(x16441,x16443,x16445)))
% 12.04/12.18 [1645]~P7(x16451)+E(f16(x16451,f4(x16451,x16452,x16453),f4(f72(x16451),x16454,x16455)),f4(f72(x16451),f16(x16451,x16452,x16454),f16(x16451,x16453,x16455)))
% 12.04/12.18 [1786]~P1(x17861)+P11(a68,f29(x17861,f4(x17861,f11(x17861,x17862,x17863),f11(x17861,x17864,x17865))),f11(a68,f29(x17861,f4(x17861,x17862,x17864)),f29(x17861,f4(x17861,x17863,x17865))))
% 12.04/12.18 [1712]~P42(x17121)+E(f27(f27(f10(x17121),f27(f27(f10(x17121),x17122),x17123)),f27(f27(f10(x17121),x17124),x17125)),f27(f27(f10(x17121),f27(f27(f10(x17121),x17122),x17124)),f27(f27(f10(x17121),x17123),x17125)))
% 12.04/12.18 [1750]~P45(x17501)+E(f11(x17501,f27(f27(f10(x17501),x17502),f4(x17501,x17503,x17504)),f27(f27(f10(x17501),f4(x17501,x17502,x17505)),x17504)),f4(x17501,f27(f27(f10(x17501),x17502),x17503),f27(f27(f10(x17501),x17505),x17504)))
% 12.04/12.18 [1807]~P33(x18071)+E(f11(x18071,f11(x18071,f27(f27(f10(x18071),f4(x18071,x18072,x18073)),f4(x18071,x18074,x18075)),f27(f27(f10(x18071),f4(x18071,x18072,x18073)),x18075)),f27(f27(f10(x18071),x18073),f4(x18071,x18074,x18075))),f4(x18071,f27(f27(f10(x18071),x18072),x18074),f27(f27(f10(x18071),x18073),x18075)))
% 12.04/12.18 [1741]~P64(x17411)+E(f11(x17411,f27(f27(f10(x17411),x17412),x17413),f11(x17411,f27(f27(f10(x17411),x17414),x17413),x17415)),f11(x17411,f27(f27(f10(x17411),f11(x17411,x17412,x17414)),x17413),x17415))
% 12.04/12.18 [1782]~P11(a69,x17821,x17824)+E(f4(a69,f11(a69,f27(f27(f10(a69),x17821),x17822),x17823),f11(a69,f27(f27(f10(a69),x17824),x17822),x17825)),f4(a69,x17823,f11(a69,f27(f27(f10(a69),f4(a69,x17824,x17821)),x17822),x17825)))
% 12.04/12.18 [1783]~P11(a69,x17834,x17831)+E(f4(a69,f11(a69,f27(f27(f10(a69),x17831),x17832),x17833),f11(a69,f27(f27(f10(a69),x17834),x17832),x17835)),f4(a69,f11(a69,f27(f27(f10(a69),f4(a69,x17831,x17834)),x17832),x17833),x17835))
% 12.04/12.18 [1812]~P26(x18125)+E(f27(f27(f27(x18121,x18122),x18123),f18(x18124,f30(x18123,f2(f72(x18125))),x18126,f24(x18124,x18125,x18126,x18121,x18123))),f24(x18124,x18125,x18126,x18121,f16(x18125,x18122,x18123)))
% 12.04/12.18 [1706]E(x17061,f2(a69))+E(x17061,f11(a69,f2(a69),f3(a69)))+~P12(a69,x17061,f11(a69,f11(a69,f2(a69),f3(a69)),f3(a69)))
% 12.04/12.18 [826]E(x8261,x8262)+P12(a69,x8262,x8261)+P12(a69,x8261,x8262)
% 12.04/12.18 [827]E(x8271,x8272)+P12(a70,x8272,x8271)+P12(a70,x8271,x8272)
% 12.04/12.18 [880]E(x8801,x8802)+P12(a68,x8801,x8802)+~P11(a68,x8801,x8802)
% 12.04/12.18 [883]E(x8831,x8832)+P12(a69,x8831,x8832)+~P11(a69,x8831,x8832)
% 12.04/12.18 [884]E(x8841,x8842)+P12(a70,x8841,x8842)+~P11(a70,x8841,x8842)
% 12.04/12.18 [946]E(x9461,x9462)+~P11(a68,x9462,x9461)+~P11(a68,x9461,x9462)
% 12.04/12.18 [947]E(x9471,x9472)+~P11(a69,x9472,x9471)+~P11(a69,x9471,x9472)
% 12.04/12.18 [948]E(x9481,x9482)+~P11(a70,x9482,x9481)+~P11(a70,x9481,x9482)
% 12.04/12.18 [957]E(x9571,x9572)+~P13(a69,x9572,x9571)+~P13(a69,x9571,x9572)
% 12.04/12.18 [633]~P20(x6331)+~E(x6332,f2(x6331))+E(f9(x6331,x6332),x6332)
% 12.04/12.18 [635]~P1(x6351)+~E(x6352,f2(x6351))+E(f29(x6351,x6352),f2(a68))
% 12.04/12.18 [636]~P21(x6361)+~E(f2(x6361),x6362)+E(f9(x6361,x6362),f2(x6361))
% 12.04/12.18 [637]~P21(x6371)+~E(x6372,f2(x6371))+E(f9(x6371,x6372),f2(x6371))
% 12.04/12.18 [640]~P20(x6402)+~E(f9(x6402,x6401),x6401)+E(x6401,f2(x6402))
% 12.04/12.18 [644]~P1(x6442)+E(x6441,f2(x6442))+~E(f29(x6442,x6441),f2(a68))
% 12.04/12.18 [645]~P21(x6452)+~E(f9(x6452,x6451),f2(x6452))+E(x6451,f2(x6452))
% 12.04/12.18 [646]~P21(x6461)+~E(f9(x6461,x6462),f2(x6461))+E(f2(x6461),x6462)
% 12.04/12.18 [695]~E(x6952,f2(a69))+~E(x6951,f2(a69))+E(f11(a69,x6951,x6952),f2(a69))
% 12.04/12.18 [728]~P20(x7281)+~E(x7282,f2(x7281))+E(f11(x7281,x7282,x7282),f2(x7281))
% 12.04/12.18 [789]~P1(x7892)+E(x7891,f2(x7892))+P12(a68,f2(a68),f29(x7892,x7891))
% 12.04/12.18 [803]~P1(x8031)+~E(x8032,f2(x8031))+P11(a68,f29(x8031,x8032),f2(a68))
% 12.04/12.18 [815]~P20(x8152)+~E(f11(x8152,x8151,x8151),f2(x8152))+E(x8151,f2(x8152))
% 12.04/12.18 [823]~P42(x8232)+~P13(x8232,f2(x8232),x8231)+E(x8231,f2(x8232))
% 12.04/12.18 [886]~P1(x8862)+E(x8861,f2(x8862))+~P11(a68,f29(x8862,x8861),f2(a68))
% 12.04/12.18 [891]~P1(x8912)+~E(x8911,f2(x8912))+~P12(a68,f2(a68),f29(x8912,x8911))
% 12.04/12.18 [967]E(x9671,x9672)+~E(f4(a69,x9672,x9671),f2(a69))+~E(f4(a69,x9671,x9672),f2(a69))
% 12.04/12.18 [1004]~P20(x10041)+~P11(x10041,x10042,f2(x10041))+P11(x10041,x10042,f9(x10041,x10042))
% 12.04/12.18 [1005]~P49(x10051)+~P12(x10051,x10052,f2(x10051))+P12(x10051,x10052,f9(x10051,x10052))
% 12.04/12.18 [1006]~P20(x10061)+~P11(x10061,f2(x10061),x10062)+P11(x10061,f9(x10061,x10062),x10062)
% 12.04/12.18 [1007]~P20(x10071)+~P12(x10071,f2(x10071),x10072)+P12(x10071,f9(x10071,x10072),x10072)
% 12.04/12.18 [1017]~P23(x10171)+~P11(x10171,x10172,f2(x10171))+P11(x10171,f2(x10171),f9(x10171,x10172))
% 12.04/12.18 [1018]~P23(x10181)+~P12(x10181,x10182,f2(x10181))+P12(x10181,f2(x10181),f9(x10181,x10182))
% 12.04/12.18 [1019]~P23(x10191)+~P11(x10191,f2(x10191),x10192)+P11(x10191,f9(x10191,x10192),f2(x10191))
% 12.04/12.18 [1020]~P23(x10201)+~P12(x10201,f2(x10201),x10202)+P12(x10201,f9(x10201,x10202),f2(x10201))
% 12.04/12.18 [1023]~P20(x10231)+~P11(x10231,x10232,f9(x10231,x10232))+P11(x10231,x10232,f2(x10231))
% 12.04/12.18 [1024]~P49(x10241)+~P12(x10241,x10242,f9(x10241,x10242))+P12(x10241,x10242,f2(x10241))
% 12.04/12.18 [1025]~P20(x10251)+~P11(x10251,f9(x10251,x10252),x10252)+P11(x10251,f2(x10251),x10252)
% 12.04/12.18 [1026]~P20(x10261)+~P12(x10261,f9(x10261,x10262),x10262)+P12(x10261,f2(x10261),x10262)
% 12.04/12.18 [1042]~P23(x10421)+~P11(x10421,f2(x10421),f9(x10421,x10422))+P11(x10421,x10422,f2(x10421))
% 12.04/12.18 [1043]~P23(x10431)+~P12(x10431,f2(x10431),f9(x10431,x10432))+P12(x10431,x10432,f2(x10431))
% 12.04/12.18 [1044]~P23(x10441)+~P11(x10441,f9(x10441,x10442),f2(x10441))+P11(x10441,f2(x10441),x10442)
% 12.04/12.18 [1045]~P23(x10451)+~P12(x10451,f9(x10451,x10452),f2(x10451))+P12(x10451,f2(x10451),x10452)
% 12.04/12.18 [1080]~P13(a69,x10801,x10802)+P11(a69,x10801,x10802)+~P12(a69,f2(a69),x10802)
% 12.04/12.18 [1081]~P13(a70,x10811,x10812)+P11(a70,x10811,x10812)+~P12(a70,f2(a70),x10812)
% 12.04/12.18 [1087]~P12(a70,x10872,x10871)+~P11(a70,x10871,f2(a70))+E(f7(a70,x10871,x10872),f2(a70))
% 12.04/12.18 [1089]~P12(a70,x10891,x10892)+~P11(a70,f2(a70),x10891)+E(f7(a70,x10891,x10892),f2(a70))
% 12.04/12.18 [1090]~P13(a69,x10901,x10902)+~P12(a69,f2(a69),x10902)+P12(a69,f2(a69),x10901)
% 12.04/12.18 [1174]~P13(a69,x11742,x11741)+~P12(a69,x11741,x11742)+~P12(a69,f2(a69),x11741)
% 12.04/12.18 [1175]~P13(a70,x11752,x11751)+~P12(a70,x11751,x11752)+~P12(a70,f2(a70),x11751)
% 12.04/12.18 [1177]~P11(a69,f13(x11771),x11772)+P11(a68,x11771,f26(a69,x11772))+~P11(a68,f2(a68),x11771)
% 12.04/12.18 [1178]~P11(a69,x11781,f12(x11782))+P11(a68,f26(a69,x11781),x11782)+~P11(a68,f2(a68),x11782)
% 12.04/12.18 [1179]~P11(a70,f2(a70),x11792)+~P11(a70,f2(a70),x11791)+P11(a70,f2(a70),f17(x11791,x11792))
% 12.04/12.18 [1192]P12(a69,f12(x11921),x11922)+~P12(a68,x11921,f26(a69,x11922))+~P11(a68,f2(a68),x11921)
% 12.04/12.18 [1195]~P20(x11951)+~P11(x11951,f2(x11951),x11952)+P11(x11951,f2(x11951),f11(x11951,x11952,x11952))
% 12.04/12.18 [1196]~P20(x11961)+~P12(x11961,f2(x11961),x11962)+P12(x11961,f2(x11961),f11(x11961,x11962,x11962))
% 12.04/12.18 [1197]~P20(x11971)+~P11(x11971,x11972,f2(x11971))+P11(x11971,f11(x11971,x11972,x11972),f2(x11971))
% 12.04/12.18 [1198]~P20(x11981)+~P12(x11981,x11982,f2(x11981))+P12(x11981,f11(x11981,x11982,x11982),f2(x11981))
% 12.04/12.18 [1199]~P49(x11991)+~P12(x11991,x11992,f2(x11991))+P12(x11991,f11(x11991,x11992,x11992),f2(x11991))
% 12.04/12.18 [1308]~P20(x13081)+~P11(x13081,f11(x13081,x13082,x13082),f2(x13081))+P11(x13081,x13082,f2(x13081))
% 12.04/12.18 [1309]~P20(x13091)+~P12(x13091,f11(x13091,x13092,x13092),f2(x13091))+P12(x13091,x13092,f2(x13091))
% 12.04/12.18 [1310]~P49(x13101)+~P12(x13101,f11(x13101,x13102,x13102),f2(x13101))+P12(x13101,x13102,f2(x13101))
% 12.04/12.18 [1311]~P20(x13111)+~P11(x13111,f2(x13111),f11(x13111,x13112,x13112))+P11(x13111,f2(x13111),x13112)
% 12.04/12.18 [1312]~P20(x13121)+~P12(x13121,f2(x13121),f11(x13121,x13122,x13122))+P12(x13121,f2(x13121),x13122)
% 12.04/12.18 [1316]~P11(a70,x13162,x13161)+~P12(a70,f2(a70),x13162)+P12(a70,f2(a70),f7(a70,x13161,x13162))
% 12.04/12.18 [1317]P12(a69,f4(a69,x13171,x13172),x13171)+~P12(a69,f2(a69),x13171)+~P12(a69,f2(a69),x13172)
% 12.04/12.18 [1318]P12(a70,f7(a70,x13181,x13182),x13181)+~P12(a70,f2(a70),x13181)+~P12(a70,f3(a70),x13182)
% 12.04/12.18 [1324]~P11(a70,x13241,f2(a70))+~P12(a70,x13242,f2(a70))+P11(a70,f2(a70),f7(a70,x13241,x13242))
% 12.04/12.18 [1325]~P11(a70,f2(a70),x13252)+~P11(a70,f2(a70),x13251)+P11(a70,f2(a70),f11(a70,x13251,x13252))
% 12.04/12.18 [1326]~P11(a70,f2(a70),x13261)+~P12(a70,f2(a70),x13262)+P11(a70,f2(a70),f7(a70,x13261,x13262))
% 12.04/12.18 [1327]~P11(a70,x13271,f2(a70))+~P12(a70,f2(a70),x13272)+P11(a70,f7(a70,x13271,x13272),f2(a70))
% 12.04/12.18 [1328]~P12(a70,x13282,f2(a70))+~P11(a70,f2(a70),x13281)+P11(a70,f7(a70,x13281,x13282),f2(a70))
% 12.04/12.18 [1392]P12(a69,f2(a69),x13921)+P12(a69,f2(a69),x13922)+~P12(a69,f2(a69),f11(a69,x13922,x13921))
% 12.04/12.18 [1418]P11(a70,x14181,x14182)+~P12(a70,f2(a70),x14181)+~P12(a70,f2(a70),f7(a70,x14182,x14181))
% 12.04/12.18 [1419]P11(a70,x14191,x14192)+~P11(a70,f2(a70),x14192)+~P12(a70,f2(a70),f7(a70,x14192,x14191))
% 12.04/12.18 [1421]P11(a70,x14211,f2(a70))+~P12(a70,x14212,f2(a70))+~P11(a70,f2(a70),f7(a70,x14211,x14212))
% 12.04/12.18 [1422]P11(a70,f2(a70),x14221)+~P12(a70,f2(a70),x14222)+~P11(a70,f2(a70),f7(a70,x14221,x14222))
% 12.04/12.18 [1423]P12(a70,f2(a70),x14231)+~P11(a70,f2(a70),x14232)+~P12(a70,f2(a70),f7(a70,x14232,x14231))
% 12.04/12.18 [648]~P26(x6481)+E(f6(x6481,x6482),f2(a69))+~E(x6482,f2(f72(x6481)))
% 12.04/12.18 [649]~P26(x6492)+~E(f6(x6492,x6491),f2(a69))+E(x6491,f2(f72(x6492)))
% 12.04/12.18 [931]P12(a69,f34(x9312,x9311),x9312)+~P68(f27(x9311,x9312))+P68(f27(x9311,f2(a69)))
% 12.04/12.18 [1002]E(x10021,f2(a69))+E(x10022,f2(a69))+~E(f11(a69,x10022,x10021),f11(a69,f2(a69),f3(a69)))
% 12.04/12.18 [1003]E(x10031,f2(a69))+E(x10032,f2(a69))+~E(f11(a69,f2(a69),f3(a69)),f11(a69,x10032,x10031))
% 12.04/12.18 [1049]~E(x10492,f2(a69))+~E(x10491,f11(a69,f2(a69),f3(a69)))+E(f11(a69,x10491,x10492),f11(a69,f2(a69),f3(a69)))
% 12.04/12.18 [1050]~E(x10501,f2(a69))+~E(x10502,f11(a69,f2(a69),f3(a69)))+E(f11(a69,x10501,x10502),f11(a69,f2(a69),f3(a69)))
% 12.04/12.18 [1051]~E(x10512,f2(a69))+~E(x10511,f11(a69,f2(a69),f3(a69)))+E(f11(a69,f2(a69),f3(a69)),f11(a69,x10511,x10512))
% 12.04/12.18 [1052]~E(x10521,f2(a69))+~E(x10522,f11(a69,f2(a69),f3(a69)))+E(f11(a69,f2(a69),f3(a69)),f11(a69,x10521,x10522))
% 12.04/12.18 [1119]E(x11191,f2(a69))+E(x11191,f11(a69,f2(a69),f3(a69)))+~E(f11(a69,x11192,x11191),f11(a69,f2(a69),f3(a69)))
% 12.04/12.18 [1120]E(x11201,f2(a69))+E(x11201,f11(a69,f2(a69),f3(a69)))+~E(f11(a69,x11201,x11202),f11(a69,f2(a69),f3(a69)))
% 12.04/12.18 [1121]E(x11211,f2(a69))+E(x11211,f11(a69,f2(a69),f3(a69)))+~E(f11(a69,f2(a69),f3(a69)),f11(a69,x11212,x11211))
% 12.04/12.18 [1122]E(x11221,f2(a69))+E(x11221,f11(a69,f2(a69),f3(a69)))+~E(f11(a69,f2(a69),f3(a69)),f11(a69,x11221,x11222))
% 12.04/12.18 [1233]E(x12331,f11(a69,f2(a69),f3(a69)))+E(x12332,f11(a69,f2(a69),f3(a69)))+~E(f11(a69,x12331,x12332),f11(a69,f2(a69),f3(a69)))
% 12.04/12.18 [1234]E(x12341,f11(a69,f2(a69),f3(a69)))+E(x12342,f11(a69,f2(a69),f3(a69)))+~E(f11(a69,f2(a69),f3(a69)),f11(a69,x12341,x12342))
% 12.04/12.18 [1245]~P12(a69,x12451,x12452)+P12(a69,f11(a69,x12451,f3(a69)),x12452)+E(f11(a69,x12451,f3(a69)),x12452)
% 12.04/12.18 [1266]E(x12661,x12662)+P12(a69,x12661,x12662)+~P12(a69,x12661,f11(a69,x12662,f3(a69)))
% 12.04/12.18 [1267]E(x12671,x12672)+P12(a70,x12671,x12672)+~P12(a70,x12671,f11(a70,x12672,f3(a70)))
% 12.04/12.18 [1330]P12(a69,f41(x13302,x13301),x13302)+E(x13301,f2(a69))+~P12(a69,x13301,f11(a69,x13302,f3(a69)))
% 12.04/12.18 [1337]E(x13371,x13372)+~P11(a69,x13372,x13371)+~P12(a69,x13371,f11(a69,x13372,f3(a69)))
% 12.04/12.18 [1338]E(x13381,f2(a69))+~P12(a69,x13381,f11(a69,x13382,f3(a69)))+E(f11(a69,f41(x13382,x13381),f3(a69)),x13381)
% 12.04/12.18 [1403]P11(a69,x14031,x14032)+~P11(a69,x14031,f11(a69,x14032,f3(a69)))+E(x14031,f11(a69,x14032,f3(a69)))
% 12.04/12.18 [1537]E(f12(x15371),x15372)+~P11(a68,f26(a69,x15372),x15371)+~P12(a68,x15371,f11(a68,f26(a69,x15372),f3(a68)))
% 12.04/12.18 [1588]~P12(a68,f26(a69,x15882),x15881)+~P11(a68,x15881,f11(a68,f26(a69,x15882),f3(a68)))+E(f13(x15881),f11(a69,x15882,f3(a69)))
% 12.04/12.18 [675]~E(x6752,f3(a69))+~E(x6751,f3(a69))+E(f27(f27(f10(a69),x6751),x6752),f3(a69))
% 12.04/12.18 [721]~P63(x7211)+~E(x7212,f3(x7211))+E(f27(f27(f10(x7211),x7212),x7212),f3(x7211))
% 12.04/12.18 [745]E(x7451,f3(a69))+E(x7452,f2(a69))+~E(f27(f27(f10(a69),x7452),x7451),x7452)
% 12.04/12.18 [747]E(x7471,f2(a69))+E(x7472,f2(a69))+~E(f27(f27(f10(a69),x7472),x7471),f2(a69))
% 12.04/12.18 [801]~P63(x8011)+~E(x8012,f9(x8011,f3(x8011)))+E(f27(f27(f10(x8011),x8012),x8012),f3(x8011))
% 12.04/12.18 [942]E(x9421,f3(a70))+~P12(a70,f2(a70),x9422)+~E(f27(f27(f10(a70),x9422),x9421),f3(a70))
% 12.04/12.18 [943]E(x9431,f3(a70))+~P12(a70,f2(a70),x9431)+~E(f27(f27(f10(a70),x9431),x9432),f3(a70))
% 12.04/12.18 [1022]~P34(x10221)+~P66(x10221)+E(f27(f27(f14(x10221),f2(x10221)),f11(a69,x10222,f3(a69))),f2(x10221))
% 12.04/12.18 [1091]E(x10911,f2(a69))+E(x10912,f11(a69,f2(a69),f3(a69)))+~E(f27(f27(f14(a69),x10912),x10911),f11(a69,f2(a69),f3(a69)))
% 12.04/12.18 [1113]~E(x11132,f3(a69))+~P12(a69,f2(a69),x11131)+P13(a69,f27(f27(f10(a69),x11131),x11132),x11131)
% 12.04/12.18 [1114]~E(x11141,f3(a69))+~P12(a69,f2(a69),x11142)+P13(a69,f27(f27(f10(a69),x11141),x11142),x11142)
% 12.04/12.18 [1224]E(x12241,f2(a69))+P12(a69,f2(a69),x12242)+~P12(a69,f2(a69),f27(f27(f14(a69),x12242),x12241))
% 12.04/12.18 [1226]~E(x12262,f11(a69,f2(a69),f3(a69)))+~E(x12261,f11(a69,f2(a69),f3(a69)))+E(f27(f27(f10(a69),x12261),x12262),f11(a69,f2(a69),f3(a69)))
% 12.04/12.18 [1276]E(x12761,f3(a69))+~P12(a69,f2(a69),x12762)+~P13(a69,f27(f27(f10(a69),x12762),x12761),x12762)
% 12.04/12.18 [1277]E(x12771,f3(a69))+~P12(a69,f2(a69),x12772)+~P13(a69,f27(f27(f10(a69),x12771),x12772),x12772)
% 12.04/12.18 [1288]~P11(a70,f2(a70),x12882)+~P11(a70,f2(a70),x12881)+P11(a70,f2(a70),f27(f27(f10(a70),x12881),x12882))
% 12.04/12.18 [1289]~P12(a68,f2(a68),x12892)+~P12(a68,f2(a68),x12891)+P12(a68,f2(a68),f27(f27(f10(a68),x12891),x12892))
% 12.04/12.18 [1290]~P12(a69,f2(a69),x12902)+~P12(a69,f2(a69),x12901)+P12(a69,f2(a69),f27(f27(f10(a69),x12901),x12902))
% 12.04/12.18 [1498]~P68(f27(x14981,x14982))+P68(f27(x14981,f2(a69)))+P68(f27(x14981,f11(a69,f34(x14982,x14981),f3(a69))))
% 12.04/12.18 [1701]~P12(a69,f11(a69,f2(a69),f3(a69)),x17012)+~P12(a69,f11(a69,f2(a69),f3(a69)),x17011)+P12(a69,x17011,f27(f27(f10(a69),x17012),x17011))
% 12.04/12.18 [1702]~P12(a69,f11(a69,f2(a69),f3(a69)),x17022)+~P12(a69,f11(a69,f2(a69),f3(a69)),x17021)+P12(a69,x17021,f27(f27(f10(a69),x17021),x17022))
% 12.04/12.18 [1719]~P11(a69,f11(a69,f2(a69),f3(a69)),x17192)+~P11(a69,f11(a69,f2(a69),f3(a69)),x17191)+P11(a69,f11(a69,f2(a69),f3(a69)),f27(f27(f10(a69),x17191),x17192))
% 12.04/12.18 [1720]~P12(a69,f11(a69,f2(a69),f3(a69)),x17201)+~P12(a69,f11(a69,f2(a69),f3(a69)),x17202)+P12(a69,f11(a69,f2(a69),f3(a69)),f27(f27(f10(a69),x17201),x17202))
% 12.04/12.18 [1158]~E(x11582,f2(a68))+~E(x11581,f2(a68))+E(f11(a68,f27(f27(f10(a68),x11581),x11581),f27(f27(f10(a68),x11582),x11582)),f2(a68))
% 12.04/12.18 [1642]~P11(a68,f2(a68),x16422)+~P11(a68,f2(a68),x16421)+P11(a69,f27(f27(f10(a69),f12(x16421)),f12(x16422)),f12(f27(f27(f10(a68),x16421),x16422)))
% 12.04/12.18 [1678]~P11(a68,f2(a68),x16781)+~P12(a68,f2(a68),x16782)+P11(a68,f27(f27(f10(a68),f26(a69,f58(x16781,x16782))),x16782),x16781)
% 12.04/12.18 [1707]~P12(a69,f2(a69),x17072)+~P12(a70,f2(a70),x17071)+E(f7(a70,f27(f27(f14(a70),x17071),x17072),x17071),f27(f27(f14(a70),x17071),f4(a69,x17072,f11(a69,f2(a69),f3(a69)))))
% 12.04/12.18 [1778]~P11(a68,f2(a68),x17781)+~P12(a68,f2(a68),x17782)+P12(a68,x17781,f27(f27(f10(a68),f26(a69,f11(a69,f58(x17781,x17782),f3(a69)))),x17782))
% 12.04/12.18 [1787]E(x17871,f2(a69))+E(x17872,f2(a1))+P12(a68,f29(a1,f11(a1,f3(a1),f27(f27(f10(a1),x17872),f27(f27(f14(a1),f44(x17871,x17872)),x17871)))),f3(a68))
% 12.04/12.18 [686]~E(x6862,x6863)+~P2(x6861)+P11(x6861,x6862,x6863)
% 12.04/12.18 [688]~E(x6882,x6883)+~P32(x6881)+P11(x6881,x6882,x6883)
% 12.04/12.18 [799]~P12(x7993,x7991,x7992)+~E(x7991,x7992)+~P30(x7993)
% 12.04/12.18 [800]~P12(x8003,x8001,x8002)+~E(x8001,x8002)+~P32(x8003)
% 12.04/12.18 [840]P11(x8401,x8403,x8402)+~P30(x8401)+P11(x8401,x8402,x8403)
% 12.04/12.18 [845]P12(x8451,x8453,x8452)+~P30(x8451)+P11(x8451,x8452,x8453)
% 12.04/12.18 [897]~P2(x8971)+~P12(x8971,x8972,x8973)+P11(x8971,x8972,x8973)
% 12.04/12.18 [899]~P32(x8991)+~P12(x8991,x8992,x8993)+P11(x8991,x8992,x8993)
% 12.04/12.18 [973]~P12(x9731,x9733,x9732)+~P2(x9731)+~P11(x9731,x9732,x9733)
% 12.04/12.18 [977]~P12(x9771,x9773,x9772)+~P2(x9771)+~P12(x9771,x9772,x9773)
% 12.04/12.18 [980]~P12(x9801,x9803,x9802)+~P30(x9801)+~P11(x9801,x9802,x9803)
% 12.04/12.18 [981]~P12(x9811,x9813,x9812)+~P30(x9811)+~P12(x9811,x9812,x9813)
% 12.04/12.18 [982]~P12(x9821,x9823,x9822)+~P32(x9821)+~P12(x9821,x9822,x9823)
% 12.04/12.18 [1069]~P11(a68,x10691,x10693)+P11(a68,x10691,x10692)+~P11(a68,x10693,x10692)
% 12.04/12.18 [1070]~P11(a69,x10701,x10703)+P11(a69,x10701,x10702)+~P11(a69,x10703,x10702)
% 12.04/12.18 [1071]~P11(a70,x10711,x10713)+P11(a70,x10711,x10712)+~P11(a70,x10713,x10712)
% 12.04/12.18 [1072]~P13(a69,x10721,x10723)+P13(a69,x10721,x10722)+~P13(a69,x10723,x10722)
% 12.04/12.18 [651]~P21(x6512)+~E(x6513,f9(x6512,x6511))+E(x6511,f9(x6512,x6513))
% 12.04/12.18 [653]~P21(x6531)+~E(f9(x6531,x6533),x6532)+E(f9(x6531,x6532),x6533)
% 12.04/12.18 [656]~P21(x6563)+E(x6561,x6562)+~E(f9(x6563,x6561),f9(x6563,x6562))
% 12.04/12.18 [707]~E(x7072,x7073)+~P7(x7071)+E(f4(x7071,x7072,x7073),f2(x7071))
% 12.04/12.18 [708]~E(x7082,x7083)+~P21(x7081)+E(f4(x7081,x7082,x7083),f2(x7081))
% 12.04/12.18 [717]~P44(x7171)+~E(x7173,f2(x7171))+E(f11(x7171,x7172,x7173),x7172)
% 12.04/12.18 [718]~E(x7182,x7183)+~P49(x7181)+P11(f72(x7181),x7182,x7183)
% 12.04/12.18 [771]~P21(x7711)+~E(x7713,f9(x7711,x7712))+E(f11(x7711,x7712,x7713),f2(x7711))
% 12.04/12.18 [772]~P21(x7721)+~E(x7722,f9(x7721,x7723))+E(f11(x7721,x7722,x7723),f2(x7721))
% 12.04/12.18 [809]~P44(x8092)+~E(f11(x8092,x8093,x8091),x8093)+E(x8091,f2(x8092))
% 12.04/12.18 [812]~P7(x8123)+E(x8121,x8122)+~E(f4(x8123,x8121,x8122),f2(x8123))
% 12.04/12.18 [813]~P21(x8133)+E(x8131,x8132)+~E(f4(x8133,x8131,x8132),f2(x8133))
% 12.04/12.18 [835]~P21(x8352)+~E(f11(x8352,x8353,x8351),f2(x8352))+E(x8351,f9(x8352,x8353))
% 12.04/12.18 [836]~P21(x8362)+~E(f11(x8362,x8361,x8363),f2(x8362))+E(x8361,f9(x8362,x8363))
% 12.04/12.18 [837]~P21(x8371)+~E(f11(x8371,x8372,x8373),f2(x8371))+E(f9(x8371,x8372),x8373)
% 12.04/12.18 [923]~P49(x9231)+~P14(x9231,x9233)+P14(x9231,f16(x9231,x9232,x9233))
% 12.04/12.18 [962]~P40(x9621)+~P13(x9621,x9622,x9623)+P13(x9621,x9622,f9(x9621,x9623))
% 12.04/12.18 [963]~P40(x9631)+~P13(x9631,x9632,x9633)+P13(x9631,f9(x9631,x9632),x9633)
% 12.04/12.18 [1012]~P40(x10121)+P13(x10121,x10122,x10123)+~P13(x10121,x10122,f9(x10121,x10123))
% 12.04/12.18 [1013]~P40(x10131)+P13(x10131,x10132,x10133)+~P13(x10131,f9(x10131,x10132),x10133)
% 12.04/12.18 [1032]~P23(x10321)+~P11(x10321,x10323,x10322)+P11(x10321,f9(x10321,x10322),f9(x10321,x10323))
% 12.04/12.18 [1033]~P23(x10331)+~P12(x10331,x10333,x10332)+P12(x10331,f9(x10331,x10332),f9(x10331,x10333))
% 12.04/12.18 [1056]~P23(x10561)+~P11(x10561,x10563,f9(x10561,x10562))+P11(x10561,x10562,f9(x10561,x10563))
% 12.04/12.18 [1058]~P23(x10581)+~P12(x10581,x10583,f9(x10581,x10582))+P12(x10581,x10582,f9(x10581,x10583))
% 12.04/12.18 [1060]~P23(x10601)+~P11(x10601,f9(x10601,x10603),x10602)+P11(x10601,f9(x10601,x10602),x10603)
% 12.04/12.18 [1062]~P23(x10621)+~P12(x10621,f9(x10621,x10623),x10622)+P12(x10621,f9(x10621,x10622),x10623)
% 12.04/12.18 [1075]~P11(a69,x10753,x10751)+~E(f4(a69,x10751,x10753),x10752)+E(x10751,f11(a69,x10752,x10753))
% 12.04/12.18 [1076]~P11(a69,x10762,x10761)+~E(x10761,f11(a69,x10763,x10762))+E(f4(a69,x10761,x10762),x10763)
% 12.04/12.18 [1092]~P23(x10921)+P11(x10921,x10922,x10923)+~P11(x10921,f9(x10921,x10923),f9(x10921,x10922))
% 12.04/12.18 [1093]~P23(x10931)+P12(x10931,x10932,x10933)+~P12(x10931,f9(x10931,x10933),f9(x10931,x10932))
% 12.04/12.18 [1180]~P23(x11801)+~P11(x11801,x11802,x11803)+P11(x11801,f4(x11801,x11802,x11803),f2(x11801))
% 12.04/12.18 [1181]~P23(x11811)+~P12(x11811,x11812,x11813)+P12(x11811,f4(x11811,x11812,x11813),f2(x11811))
% 12.04/12.18 [1291]~P13(a69,x12911,x12913)+~P13(a69,x12911,x12912)+P13(a69,x12911,f4(a69,x12912,x12913))
% 12.04/12.18 [1294]~P23(x12941)+P11(x12941,x12942,x12943)+~P11(x12941,f4(x12941,x12942,x12943),f2(x12941))
% 12.04/12.18 [1295]~P23(x12951)+P12(x12951,x12952,x12953)+~P12(x12951,f4(x12951,x12952,x12953),f2(x12951))
% 12.04/12.18 [1408]P13(a70,x14081,x14082)+~P13(a70,x14081,x14083)+~P13(a70,x14081,f4(a70,x14082,x14083))
% 12.04/12.18 [1489]~P12(a69,x14893,x14891)+~P12(a69,x14893,x14892)+P12(a69,f4(a69,x14891,x14892),f4(a69,x14891,x14893))
% 12.04/12.18 [1490]~P11(a69,x14902,x14901)+~P12(a69,x14901,x14903)+P12(a69,f4(a69,x14901,x14902),f4(a69,x14903,x14902))
% 12.04/12.18 [1493]~P11(a70,x14933,x14931)+P11(a70,f7(a70,x14931,x14932),f7(a70,x14933,x14932))+~P12(a70,x14932,f2(a70))
% 12.04/12.18 [1494]~P11(a70,x14941,x14943)+P11(a70,f7(a70,x14941,x14942),f7(a70,x14943,x14942))+~P12(a70,f2(a70),x14942)
% 12.04/12.18 [1574]~P11(a69,x15743,x15742)+~P11(a69,f11(a69,x15741,x15743),x15742)+P11(a69,x15741,f4(a69,x15742,x15743))
% 12.04/12.18 [1575]~P11(a69,x15752,x15753)+~P11(a69,x15751,f4(a69,x15753,x15752))+P11(a69,f11(a69,x15751,x15752),x15753)
% 12.04/12.18 [706]~P41(x7061)+~E(x7062,f2(f72(x7061)))+E(f27(f21(x7061,x7062),x7063),f2(x7061))
% 12.04/12.18 [738]~P41(x7381)+~E(x7382,f2(x7381))+E(f23(x7381,x7382,x7383),f2(f72(x7381)))
% 12.04/12.18 [739]~P26(x7391)+~E(x7392,f2(x7391))+E(f19(x7391,x7392,x7393),f2(f72(x7391)))
% 12.04/12.18 [774]~P37(x7741)+~E(x7742,f2(f72(x7741)))+E(f8(x7741,x7742,x7743),f2(f72(x7741)))
% 12.04/12.18 [775]~P41(x7751)+~E(x7753,f2(f72(x7751)))+E(f23(x7751,x7752,x7753),f2(f72(x7751)))
% 12.04/12.18 [824]~P41(x8241)+E(f20(x8241,x8242,x8243),f2(a69))+E(f27(f21(x8241,x8243),x8242),f2(x8241))
% 12.04/12.18 [833]~P26(x8332)+E(x8331,f2(x8332))+~E(f19(x8332,x8331,x8333),f2(f72(x8332)))
% 12.04/12.18 [834]~P26(x8342)+E(x8341,f2(x8342))+~E(f16(x8342,x8341,x8343),f2(f72(x8342)))
% 12.04/12.18 [853]~P37(x8532)+~E(f8(x8532,x8531,x8533),f2(f72(x8532)))+E(x8531,f2(f72(x8532)))
% 12.04/12.18 [854]~P26(x8542)+~E(f16(x8542,x8543,x8541),f2(f72(x8542)))+E(x8541,f2(f72(x8542)))
% 12.04/12.18 [1112]~P49(x11121)+~P12(f72(x11121),x11123,x11122)+P14(x11121,f4(f72(x11121),x11122,x11123))
% 12.04/12.18 [1170]~P9(x11701)+~P13(x11701,x11702,x11703)+E(f27(f27(f10(x11701),x11702),f7(x11701,x11703,x11702)),x11703)
% 12.04/12.18 [1211]~P49(x12111)+P11(f72(x12111),x12112,x12113)+~P14(x12111,f4(f72(x12111),x12113,x12112))
% 12.04/12.18 [1212]~P49(x12121)+P12(f72(x12121),x12122,x12123)+~P14(x12121,f4(f72(x12121),x12123,x12122))
% 12.04/12.18 [1227]~P10(x12271)+~P13(x12271,x12273,x12272)+E(f7(x12271,x12272,f9(x12271,x12273)),f9(x12271,f7(x12271,x12272,x12273)))
% 12.04/12.18 [1228]~P10(x12281)+~P13(x12281,x12283,x12282)+E(f7(x12281,f9(x12281,x12282),x12283),f9(x12281,f7(x12281,x12282,x12283)))
% 12.04/12.18 [1307]~P12(a69,x13071,x13073)+~P12(a69,x13073,x13072)+P12(a69,f11(a69,x13071,f3(a69)),x13072)
% 12.04/12.18 [1320]~P12(a69,x13203,x13202)+P12(a69,x13201,f11(a69,x13202,f3(a69)))+~E(x13201,f11(a69,x13203,f3(a69)))
% 12.04/12.18 [1333]~P9(x13332)+E(x13331,f2(x13332))+E(f7(x13332,f11(x13332,x13333,x13331),x13331),f11(x13332,f7(x13332,x13333,x13331),f3(x13332)))
% 12.04/12.18 [1334]~P9(x13342)+E(x13341,f2(x13342))+E(f7(x13342,f11(x13342,x13341,x13343),x13341),f11(x13342,f7(x13342,x13343,x13341),f3(x13342)))
% 12.04/12.18 [1535]P12(a69,x15352,x15351)+E(f11(a69,x15351,f35(x15351,x15352,x15353)),x15352)+P68(f27(x15353,f4(a69,x15352,x15351)))
% 12.04/12.18 [1536]P12(a69,x15362,x15361)+E(f11(a69,x15361,f39(x15361,x15362,x15363)),x15362)+P68(f27(x15363,f4(a69,x15362,x15361)))
% 12.04/12.18 [1544]E(f11(a69,x15441,f35(x15441,x15442,x15443)),x15442)+P68(f27(x15443,f4(a69,x15442,x15441)))+~P68(f27(x15443,f2(a69)))
% 12.04/12.18 [1545]E(f11(a69,x15451,f39(x15451,x15452,x15453)),x15452)+P68(f27(x15453,f4(a69,x15452,x15451)))+~P68(f27(x15453,f2(a69)))
% 12.04/12.18 [1559]~P11(a69,x15592,x15593)+~P11(a69,x15592,x15591)+E(f4(a69,f4(a69,x15591,x15592),f4(a69,x15593,x15592)),f4(a69,x15591,x15593))
% 12.04/12.18 [1579]~P12(a69,x15792,x15793)+~P68(f27(x15791,f4(a69,x15792,x15793)))+P68(f27(x15791,f2(a69)))
% 12.04/12.18 [1699]P12(a69,x16991,x16992)+~P68(f27(x16993,f35(x16992,x16991,x16993)))+P68(f27(x16993,f4(a69,x16991,x16992)))
% 12.04/12.18 [1700]P12(a69,x17001,x17002)+~P68(f27(x17003,f39(x17002,x17001,x17003)))+P68(f27(x17003,f4(a69,x17001,x17002)))
% 12.04/12.18 [1703]~P68(f27(x17031,f35(x17033,x17032,x17031)))+P68(f27(x17031,f4(a69,x17032,x17033)))+~P68(f27(x17031,f2(a69)))
% 12.04/12.18 [1704]~P68(f27(x17041,f39(x17043,x17042,x17041)))+P68(f27(x17041,f4(a69,x17042,x17043)))+~P68(f27(x17041,f2(a69)))
% 12.04/12.18 [709]~P34(x7091)+~E(x7093,f2(a69))+E(f27(f27(f14(x7091),x7092),x7093),f3(x7091))
% 12.04/12.18 [719]~P61(x7191)+~E(x7193,f2(x7191))+E(f27(f27(f10(x7191),x7192),x7193),f2(x7191))
% 12.04/12.18 [720]~P61(x7201)+~E(x7202,f2(x7201))+E(f27(f27(f10(x7201),x7202),x7203),f2(x7201))
% 12.04/12.18 [811]~P63(x8112)+E(x8111,f2(x8112))+~E(f27(f27(f14(x8112),x8111),x8113),f2(x8112))
% 12.04/12.18 [864]~P41(x8641)+~E(x8642,f9(x8641,x8643))+E(f27(f27(f10(x8641),x8642),x8642),f27(f27(f10(x8641),x8643),x8643))
% 12.04/12.18 [916]E(x9161,x9162)+E(x9163,f2(a68))+~E(f27(f27(f10(a68),x9163),x9161),f27(f27(f10(a68),x9163),x9162))
% 12.04/12.18 [918]E(x9181,x9182)+E(x9183,f2(a69))+~E(f27(f27(f10(a69),x9183),x9181),f27(f27(f10(a69),x9183),x9182))
% 12.04/12.18 [919]E(x9191,x9192)+E(x9193,f2(a68))+~E(f27(f27(f10(a68),x9191),x9193),f27(f27(f10(a68),x9192),x9193))
% 12.04/12.18 [920]E(x9201,x9202)+E(x9203,f2(a69))+~E(f27(f27(f10(a69),x9201),x9203),f27(f27(f10(a69),x9202),x9203))
% 12.04/12.18 [959]~P42(x9591)+~E(x9592,f3(x9591))+P13(x9591,x9592,f27(f27(f14(x9591),x9592),x9593))
% 12.04/12.18 [1110]E(x11101,x11102)+~P12(a69,f2(a69),x11103)+~E(f27(f27(f10(a69),x11103),x11101),f27(f27(f10(a69),x11103),x11102))
% 12.04/12.18 [1168]~P42(x11681)+~P12(a69,f2(a69),x11683)+P13(x11681,x11682,f27(f27(f14(x11681),x11682),x11683))
% 12.04/12.18 [1187]~P53(x11871)+~P11(x11871,f2(x11871),x11872)+P11(x11871,f2(x11871),f27(f27(f14(x11871),x11872),x11873))
% 12.04/12.18 [1188]~P53(x11881)+~P11(x11881,f3(x11881),x11882)+P11(x11881,f3(x11881),f27(f27(f14(x11881),x11882),x11883))
% 12.04/12.18 [1189]~P53(x11891)+~P12(x11891,f2(x11891),x11892)+P12(x11891,f2(x11891),f27(f27(f14(x11891),x11892),x11893))
% 12.04/12.18 [1282]~P13(a69,x12822,x12823)+E(x12821,f2(a69))+P13(a69,f27(f27(f14(a69),x12822),x12821),f27(f27(f14(a69),x12823),x12821))
% 12.04/12.18 [1283]~P13(a70,x12832,x12833)+E(x12831,f2(a69))+P13(a70,f27(f27(f14(a70),x12832),x12831),f27(f27(f14(a70),x12833),x12831))
% 12.04/12.18 [1284]~P13(a70,x12842,x12843)+E(x12841,f2(a70))+P13(a70,f27(f27(f10(a70),x12841),x12842),f27(f27(f10(a70),x12841),x12843))
% 12.04/12.18 [1364]~P9(x13641)+~P13(x13641,x13643,x13642)+E(f27(f27(f10(x13641),f7(x13641,x13642,x13643)),x13643),x13642)
% 12.04/12.18 [1436]~P11(a68,x14362,x14363)+~P12(a68,f2(a68),x14361)+P11(a68,f27(f27(f10(a68),x14361),x14362),f27(f27(f10(a68),x14361),x14363))
% 12.04/12.18 [1437]~P11(a68,x14371,x14373)+~P12(a68,f2(a68),x14372)+P11(a68,f27(f27(f10(a68),x14371),x14372),f27(f27(f10(a68),x14373),x14372))
% 12.04/12.18 [1439]~P12(a68,x14391,x14393)+~P12(a68,f2(a68),x14392)+P12(a68,f27(f27(f10(a68),x14391),x14392),f27(f27(f10(a68),x14393),x14392))
% 12.04/12.18 [1440]~P12(a68,x14402,x14403)+~P12(a68,f2(a68),x14401)+P12(a68,f27(f27(f10(a68),x14401),x14402),f27(f27(f10(a68),x14401),x14403))
% 12.04/12.18 [1444]~P12(a69,x14441,x14443)+~P12(a69,f2(a69),x14442)+P12(a69,f27(f27(f10(a69),x14441),x14442),f27(f27(f10(a69),x14443),x14442))
% 12.04/12.18 [1445]~P12(a69,x14452,x14453)+~P12(a69,f2(a69),x14451)+P12(a69,f27(f27(f10(a69),x14451),x14452),f27(f27(f10(a69),x14451),x14453))
% 12.04/12.18 [1446]~P12(a70,x14462,x14463)+~P12(a70,f2(a70),x14461)+P12(a70,f27(f27(f10(a70),x14461),x14462),f27(f27(f10(a70),x14461),x14463))
% 12.04/12.18 [1472]P13(a69,x14722,x14723)+E(x14721,f2(a69))+~P13(a69,f27(f27(f14(a69),x14722),x14721),f27(f27(f14(a69),x14723),x14721))
% 12.04/12.18 [1474]P13(a70,x14742,x14743)+E(x14741,f2(a69))+~P13(a70,f27(f27(f14(a70),x14742),x14741),f27(f27(f14(a70),x14743),x14741))
% 12.04/12.18 [1475]P13(a69,x14752,x14753)+E(x14751,f2(a69))+~P13(a69,f27(f27(f10(a69),x14751),x14752),f27(f27(f10(a69),x14751),x14753))
% 12.04/12.18 [1477]P13(a70,x14772,x14773)+E(x14771,f2(a70))+~P13(a70,f27(f27(f10(a70),x14771),x14772),f27(f27(f10(a70),x14771),x14773))
% 12.04/12.18 [1573]~P53(x15731)+~P12(x15731,f3(x15731),x15732)+P12(x15731,f3(x15731),f27(f27(f14(x15731),x15732),f11(a69,x15733,f3(a69))))
% 12.04/12.18 [1589]P11(a68,x15891,x15892)+~P12(a68,f2(a68),x15893)+~P11(a68,f27(f27(f10(a68),x15893),x15891),f27(f27(f10(a68),x15893),x15892))
% 12.04/12.18 [1590]P11(a68,x15901,x15902)+~P12(a68,f2(a68),x15903)+~P11(a68,f27(f27(f10(a68),x15901),x15903),f27(f27(f10(a68),x15902),x15903))
% 12.04/12.18 [1592]P11(a69,x15921,x15922)+~P12(a69,f2(a69),x15923)+~P11(a69,f27(f27(f10(a69),x15923),x15921),f27(f27(f10(a69),x15923),x15922))
% 12.04/12.18 [1593]P11(a69,x15931,x15932)+~P12(a69,f3(a69),x15933)+~P13(a69,f27(f27(f14(a69),x15933),x15931),f27(f27(f14(a69),x15933),x15932))
% 12.04/12.18 [1594]P11(a69,x15941,x15942)+~P12(a69,f2(a69),x15943)+~P11(a69,f27(f27(f10(a69),x15941),x15943),f27(f27(f10(a69),x15942),x15943))
% 12.04/12.18 [1595]P12(a68,x15951,x15952)+~P12(a68,f2(a68),x15953)+~P12(a68,f27(f27(f10(a68),x15951),x15953),f27(f27(f10(a68),x15952),x15953))
% 12.04/12.18 [1597]P12(a69,x15971,x15972)+~P12(a69,f2(a69),x15973)+~P12(a69,f27(f27(f14(a69),x15973),x15971),f27(f27(f14(a69),x15973),x15972))
% 12.04/12.18 [1599]P13(a69,x15991,x15992)+~P12(a69,f2(a69),x15993)+~P13(a69,f27(f27(f10(a69),x15993),x15991),f27(f27(f10(a69),x15993),x15992))
% 12.04/12.18 [1722]~P41(x17221)+~E(x17222,f9(x17221,x17223))+E(f27(f27(f14(x17221),x17222),f11(a69,f11(a69,f2(a69),f3(a69)),f3(a69))),f27(f27(f14(x17221),x17223),f11(a69,f11(a69,f2(a69),f3(a69)),f3(a69))))
% 12.04/12.18 [1763]~P1(x17632)+P12(a68,f2(a68),f50(x17631,x17632))+~P11(a68,f29(x17632,f27(x17631,f51(x17631,x17632,x17633))),f26(a69,f11(a69,x17633,f3(a69))))
% 12.04/12.18 [1764]~P1(x17642)+P12(a68,f2(a68),f54(x17641,x17642))+~P12(a68,f29(x17642,f27(x17641,f55(x17641,x17642,x17643))),f26(a69,f11(a69,x17643,f3(a69))))
% 12.04/12.18 [1811]~P41(x18112)+E(x18111,f2(f72(x18112)))+~P13(f72(x18112),f27(f27(f14(f72(x18112)),f16(x18112,f9(x18112,x18113),f16(x18112,f3(x18112),f2(f72(x18112))))),f11(a69,f20(x18112,x18113,x18111),f3(a69))),x18111)
% 12.04/12.18 [1485]~P47(x14852)+E(x14851,f2(x14852))+~E(f11(x14852,f27(f27(f10(x14852),x14853),x14853),f27(f27(f10(x14852),x14851),x14851)),f2(x14852))
% 12.04/12.18 [1486]~P47(x14862)+E(x14861,f2(x14862))+~E(f11(x14862,f27(f27(f10(x14862),x14861),x14861),f27(f27(f10(x14862),x14863),x14863)),f2(x14862))
% 12.04/12.18 [1497]~P34(x14972)+E(x14971,f2(a69))+E(f27(f27(f10(x14972),x14973),f27(f27(f14(x14972),x14973),f4(a69,x14971,f3(a69)))),f27(f27(f14(x14972),x14973),x14971))
% 12.04/12.18 [1556]~P53(x15561)+~P12(x15561,f3(x15561),x15562)+P12(x15561,f3(x15561),f27(f27(f10(x15561),x15562),f27(f27(f14(x15561),x15562),x15563)))
% 12.04/12.18 [1661]~P53(x16611)+~P12(x16611,f3(x16611),x16612)+P12(x16611,f27(f27(f14(x16611),x16612),x16613),f27(f27(f10(x16611),x16612),f27(f27(f14(x16611),x16612),x16613)))
% 12.04/12.18 [1670]~P47(x16702)+E(x16701,f2(x16702))+P12(x16702,f2(x16702),f11(x16702,f27(f27(f10(x16702),x16703),x16703),f27(f27(f10(x16702),x16701),x16701)))
% 12.04/12.18 [1671]~P47(x16712)+E(x16711,f2(x16712))+P12(x16712,f2(x16712),f11(x16712,f27(f27(f10(x16712),x16711),x16711),f27(f27(f10(x16712),x16713),x16713)))
% 12.04/12.18 [1672]~P41(x16721)+~E(f27(f21(x16721,x16723),f9(x16721,x16722)),f2(x16721))+P13(f72(x16721),f16(x16721,x16722,f16(x16721,f3(x16721),f2(f72(x16721)))),x16723)
% 12.04/12.18 [1674]~P41(x16741)+~E(f27(f21(x16741,x16743),x16742),f2(x16741))+P13(f72(x16741),f16(x16741,f9(x16741,x16742),f16(x16741,f3(x16741),f2(f72(x16741)))),x16743)
% 12.04/12.18 [1725]~P41(x17251)+E(f27(f21(x17251,x17252),f9(x17251,x17253)),f2(x17251))+~P13(f72(x17251),f16(x17251,x17253,f16(x17251,f3(x17251),f2(f72(x17251)))),x17252)
% 12.04/12.18 [1729]~P41(x17291)+E(f27(f21(x17291,x17292),x17293),f2(x17291))+~P13(f72(x17291),f16(x17291,f9(x17291,x17293),f16(x17291,f3(x17291),f2(f72(x17291)))),x17292)
% 12.04/12.18 [1732]~P47(x17322)+E(x17321,f2(x17322))+~P11(x17322,f11(x17322,f27(f27(f10(x17322),x17323),x17323),f27(f27(f10(x17322),x17321),x17321)),f2(x17322))
% 12.04/12.18 [1733]~P47(x17332)+E(x17331,f2(x17332))+~P11(x17332,f11(x17332,f27(f27(f10(x17332),x17331),x17331),f27(f27(f10(x17332),x17333),x17333)),f2(x17332))
% 12.04/12.18 [1752]~P11(a68,f49(x17522,x17521),f29(a1,x17523))+E(f2(f72(a1)),a73)+P11(a68,x17521,f29(a1,f27(f21(a1,f16(a1,x17522,a73)),x17523)))
% 12.04/12.18 [1727]~P25(x17271)+~P12(a69,f2(a69),x17273)+E(f27(f27(f10(x17271),f27(f27(f14(x17271),x17272),f4(a69,x17273,f3(a69)))),x17272),f27(f27(f14(x17271),x17272),x17273))
% 12.04/12.18 [984]~P4(x9843)+E(x9841,x9842)+~E(f11(x9843,x9844,x9841),f11(x9843,x9844,x9842))
% 12.04/12.18 [985]~P5(x9853)+E(x9851,x9852)+~E(f11(x9853,x9854,x9851),f11(x9853,x9854,x9852))
% 12.04/12.18 [987]~P4(x9873)+E(x9871,x9872)+~E(f11(x9873,x9871,x9874),f11(x9873,x9872,x9874))
% 12.04/12.18 [988]~P26(x9883)+E(x9881,x9882)+~E(f19(x9883,x9881,x9884),f19(x9883,x9882,x9884))
% 12.04/12.18 [1063]~P31(x10632)+~P12(f75(x10631,x10632),x10633,x10634)+P11(f75(x10631,x10632),x10633,x10634)
% 12.04/12.18 [1182]~P31(x11821)+~P12(f75(x11822,x11821),x11824,x11823)+~P11(f75(x11822,x11821),x11823,x11824)
% 12.04/12.18 [1200]~P42(x12001)+~P13(f72(x12001),x12002,x12004)+P13(f72(x12001),x12002,f23(x12001,x12003,x12004))
% 12.04/12.18 [1244]~P12(a69,x12443,x12444)+P12(a69,x12441,x12442)+~E(f11(a69,x12443,x12442),f11(a69,x12441,x12444))
% 12.04/12.18 [1313]~P42(x13131)+~P13(f72(x13131),f23(x13131,x13134,x13132),x13133)+P13(f72(x13131),x13132,x13133)
% 12.04/12.18 [1365]~P17(x13651)+~P11(x13651,x13653,x13654)+P11(x13651,f11(x13651,x13652,x13653),f11(x13651,x13652,x13654))
% 12.04/12.18 [1366]~P18(x13661)+~P11(x13661,x13663,x13664)+P11(x13661,f11(x13661,x13662,x13663),f11(x13661,x13662,x13664))
% 12.04/12.18 [1367]~P17(x13671)+~P11(x13671,x13672,x13674)+P11(x13671,f11(x13671,x13672,x13673),f11(x13671,x13674,x13673))
% 12.04/12.18 [1368]~P18(x13681)+~P11(x13681,x13682,x13684)+P11(x13681,f11(x13681,x13682,x13683),f11(x13681,x13684,x13683))
% 12.04/12.18 [1369]~P17(x13691)+~P12(x13691,x13693,x13694)+P12(x13691,f11(x13691,x13692,x13693),f11(x13691,x13692,x13694))
% 12.04/12.18 [1370]~P28(x13701)+~P12(x13701,x13703,x13704)+P12(x13701,f11(x13701,x13702,x13703),f11(x13701,x13702,x13704))
% 12.04/12.18 [1371]~P17(x13711)+~P12(x13711,x13712,x13714)+P12(x13711,f11(x13711,x13712,x13713),f11(x13711,x13714,x13713))
% 12.04/12.18 [1372]~P28(x13721)+~P12(x13721,x13722,x13724)+P12(x13721,f11(x13721,x13722,x13723),f11(x13721,x13724,x13723))
% 12.04/12.18 [1487]~P11(a69,x14872,x14874)+~P11(a69,x14871,x14873)+P11(a69,f11(a69,x14871,x14872),f11(a69,x14873,x14874))
% 12.04/12.18 [1488]~P12(a69,x14882,x14884)+~P12(a69,x14881,x14883)+P12(a69,f11(a69,x14881,x14882),f11(a69,x14883,x14884))
% 12.04/12.18 [1491]~P11(a70,x14912,x14914)+~P12(a70,x14911,x14913)+P12(a70,f11(a70,x14911,x14912),f11(a70,x14913,x14914))
% 12.04/12.18 [1565]~P17(x15651)+P11(x15651,x15652,x15653)+~P11(x15651,f11(x15651,x15654,x15652),f11(x15651,x15654,x15653))
% 12.04/12.18 [1567]~P17(x15671)+P11(x15671,x15672,x15673)+~P11(x15671,f11(x15671,x15672,x15674),f11(x15671,x15673,x15674))
% 12.04/12.18 [1569]~P17(x15691)+P12(x15691,x15692,x15693)+~P12(x15691,f11(x15691,x15694,x15692),f11(x15691,x15694,x15693))
% 12.04/12.18 [1571]~P17(x15711)+P12(x15711,x15712,x15713)+~P12(x15711,f11(x15711,x15712,x15714),f11(x15711,x15713,x15714))
% 12.04/12.18 [1016]~P37(x10162)+~E(f23(x10162,x10163,x10161),f16(x10162,x10164,x10161))+E(x10161,f2(f72(x10162)))
% 12.04/12.18 [1551]~P37(x15512)+~E(f11(f72(x15512),f23(x15512,x15513,x15511),f16(x15512,x15514,x15511)),f2(f72(x15512)))+E(x15511,f2(f72(x15512)))
% 12.04/12.18 [1577]~E(x15773,f11(a69,x15774,x15772))+P68(f27(x15771,x15772))+~P68(f27(x15771,f4(a69,x15773,x15774)))
% 12.04/12.18 [1808]~P31(x18082)+P11(f75(x18081,x18082),x18083,x18084)+~P11(x18082,f27(x18083,f64(x18084,x18083,x18081,x18082)),f27(x18084,f64(x18084,x18083,x18081,x18082)))
% 12.04/12.18 [894]~P43(x8941)+P13(x8941,x8942,x8943)+~E(x8943,f27(f27(f10(x8941),x8942),x8944))
% 12.04/12.18 [1162]~P42(x11621)+~P13(x11621,x11622,x11624)+P13(x11621,x11622,f27(f27(f10(x11621),x11623),x11624))
% 12.04/12.18 [1163]~P42(x11631)+~P13(x11631,x11632,x11633)+P13(x11631,x11632,f27(f27(f10(x11631),x11633),x11634))
% 12.04/12.18 [1205]~P41(x12051)+~E(x12053,f2(x12051))+P13(x12051,f27(f27(f10(x12051),x12052),x12053),f27(f27(f10(x12051),x12054),x12053))
% 12.04/12.18 [1206]~P41(x12061)+~E(x12062,f2(x12061))+P13(x12061,f27(f27(f10(x12061),x12062),x12063),f27(f27(f10(x12061),x12062),x12064))
% 12.04/12.18 [1252]~P42(x12521)+P13(x12521,x12522,x12523)+~P13(x12521,f27(f27(f10(x12521),x12524),x12522),x12523)
% 12.04/12.18 [1253]~P42(x12531)+P13(x12531,x12532,x12533)+~P13(x12531,f27(f27(f10(x12531),x12532),x12534),x12533)
% 12.04/12.18 [1349]~P42(x13491)+~P11(a69,x13493,x13494)+P13(x13491,f27(f27(f14(x13491),x13492),x13493),f27(f27(f14(x13491),x13492),x13494))
% 12.04/12.18 [1356]~P41(x13561)+~P13(x13561,x13563,x13564)+P13(x13561,f27(f27(f10(x13561),x13562),x13563),f27(f27(f10(x13561),x13562),x13564))
% 12.04/12.18 [1357]~P41(x13571)+~P13(x13571,x13572,x13574)+P13(x13571,f27(f27(f10(x13571),x13572),x13573),f27(f27(f10(x13571),x13574),x13573))
% 12.04/12.18 [1358]~P42(x13581)+~P13(x13581,x13582,x13584)+P13(x13581,f27(f27(f14(x13581),x13582),x13583),f27(f27(f14(x13581),x13584),x13583))
% 12.04/12.18 [1430]~P11(a69,x14302,x14304)+~P11(a69,x14301,x14303)+P11(a69,f27(f27(f10(a69),x14301),x14302),f27(f27(f10(a69),x14303),x14304))
% 12.04/12.18 [1771]~P1(x17711)+P11(a68,f29(x17711,f27(x17712,x17713)),f50(x17712,x17711))+~P11(a68,f29(x17711,f27(x17712,f51(x17712,x17711,x17714))),f26(a69,f11(a69,x17714,f3(a69))))
% 12.04/12.18 [1772]~P1(x17721)+P11(a68,f29(x17721,f27(x17722,x17723)),f54(x17722,x17721))+~P12(a68,f29(x17721,f27(x17722,f55(x17722,x17721,x17724))),f26(a69,f11(a69,x17724,f3(a69))))
% 12.04/12.18 [1454]~P9(x14541)+~P13(x14541,x14544,x14543)+E(f7(x14541,f27(f27(f10(x14541),x14542),x14543),x14544),f27(f27(f10(x14541),x14542),f7(x14541,x14543,x14544)))
% 12.04/12.18 [1603]~P9(x16031)+~P13(x16031,x16034,x16032)+E(f7(x16031,f27(f27(f10(x16031),x16032),x16033),x16034),f27(f27(f10(x16031),f7(x16031,x16032,x16034)),x16033))
% 12.04/12.18 [1677]~P9(x16771)+~P13(x16771,x16774,x16772)+E(f7(x16771,f27(f27(f14(x16771),x16772),x16773),f27(f27(f14(x16771),x16774),x16773)),f27(f27(f14(x16771),f7(x16771,x16772,x16774)),x16773))
% 12.04/12.18 [1746]~P25(x17461)+~P11(a69,x17464,x17463)+E(f27(f27(f10(x17461),f27(f27(f14(x17461),x17462),f4(a69,x17463,x17464))),x17462),f27(f27(f14(x17461),x17462),f4(a69,f11(a69,x17463,f3(a69)),x17464)))
% 12.04/12.18 [1775]~P26(x17752)+E(f24(x17751,x17752,x17753,x17754,f2(f72(x17752))),x17753)+~E(f27(f27(f27(x17754,f2(x17752)),f2(f72(x17752))),x17753),x17753)
% 12.04/12.18 [1636]~P9(x16362)+E(x16361,f2(x16362))+E(f7(x16362,f11(x16362,x16363,f27(f27(f10(x16362),x16364),x16361)),x16361),f11(x16362,x16364,f7(x16362,x16363,x16361)))
% 12.04/12.18 [1637]~P9(x16372)+E(x16371,f2(x16372))+E(f7(x16372,f11(x16372,x16373,f27(f27(f10(x16372),x16371),x16374)),x16371),f11(x16372,x16374,f7(x16372,x16373,x16371)))
% 12.04/12.18 [989]~P26(x9893)+E(x9891,x9892)+~E(f16(x9893,x9894,x9891),f16(x9893,x9895,x9892))
% 12.04/12.18 [990]~P26(x9903)+E(x9901,x9902)+~E(f16(x9903,x9901,x9904),f16(x9903,x9902,x9905))
% 12.04/12.18 [1135]~P31(x11351)+P11(x11351,f27(x11352,x11353),f27(x11354,x11353))+~P11(f75(x11355,x11351),x11352,x11354)
% 12.04/12.18 [1424]~P37(x14242)+~E(f11(f72(x14242),x14243,f23(x14242,x14244,x14245)),f16(x14242,x14241,x14245))+E(x14241,f27(f21(x14242,x14243),x14244))
% 12.04/12.18 [1455]~P37(x14552)+E(x14551,f25(x14552,x14553,x14554))+~E(f11(f72(x14552),x14553,f23(x14552,x14554,x14551)),f16(x14552,x14555,x14551))
% 12.04/12.18 [1613]~E(x16132,x16134)+~P44(x16131)+E(f11(x16131,f27(f27(f10(x16131),x16132),x16133),f27(f27(f10(x16131),x16134),x16135)),f11(x16131,f27(f27(f10(x16131),x16132),x16135),f27(f27(f10(x16131),x16134),x16133)))
% 12.04/12.18 [1744]~P11(a69,x17443,x17442)+E(x17441,f11(a69,f27(f27(f10(a69),f4(a69,x17442,x17443)),x17444),x17445))+~E(f11(a69,f27(f27(f10(a69),x17443),x17444),x17441),f11(a69,f27(f27(f10(a69),x17442),x17444),x17445))
% 12.04/12.18 [1745]~P11(a69,x17452,x17451)+E(f11(a69,f27(f27(f10(a69),f4(a69,x17451,x17452)),x17453),x17454),x17455)+~E(f11(a69,f27(f27(f10(a69),x17451),x17453),x17454),f11(a69,f27(f27(f10(a69),x17452),x17453),x17455))
% 12.04/12.18 [1757]~P11(a69,x17574,x17571)+~E(x17575,f11(a69,f27(f27(f10(a69),f4(a69,x17571,x17574)),x17572),x17573))+E(f11(a69,f27(f27(f10(a69),x17571),x17572),x17573),f11(a69,f27(f27(f10(a69),x17574),x17572),x17575))
% 12.04/12.18 [1758]~P11(a69,x17584,x17581)+~E(f11(a69,f27(f27(f10(a69),f4(a69,x17581,x17584)),x17582),x17583),x17585)+E(f11(a69,f27(f27(f10(a69),x17581),x17582),x17583),f11(a69,f27(f27(f10(a69),x17584),x17582),x17585))
% 12.04/12.18 [1788]~P11(a69,x17883,x17882)+P11(a69,x17881,f11(a69,f27(f27(f10(a69),f4(a69,x17882,x17883)),x17884),x17885))+~P11(a69,f11(a69,f27(f27(f10(a69),x17883),x17884),x17881),f11(a69,f27(f27(f10(a69),x17882),x17884),x17885))
% 12.04/12.18 [1789]~P11(a69,x17893,x17892)+P12(a69,x17891,f11(a69,f27(f27(f10(a69),f4(a69,x17892,x17893)),x17894),x17895))+~P12(a69,f11(a69,f27(f27(f10(a69),x17893),x17894),x17891),f11(a69,f27(f27(f10(a69),x17892),x17894),x17895))
% 12.04/12.18 [1790]~P11(a69,x17902,x17901)+P11(a69,f11(a69,f27(f27(f10(a69),f4(a69,x17901,x17902)),x17903),x17904),x17905)+~P11(a69,f11(a69,f27(f27(f10(a69),x17901),x17903),x17904),f11(a69,f27(f27(f10(a69),x17902),x17903),x17905))
% 12.04/12.18 [1791]~P11(a69,x17912,x17911)+P12(a69,f11(a69,f27(f27(f10(a69),f4(a69,x17911,x17912)),x17913),x17914),x17915)+~P12(a69,f11(a69,f27(f27(f10(a69),x17911),x17913),x17914),f11(a69,f27(f27(f10(a69),x17912),x17913),x17915))
% 12.04/12.18 [1798]~P11(a69,x17981,x17984)+~P11(a69,x17983,f11(a69,f27(f27(f10(a69),f4(a69,x17984,x17981)),x17982),x17985))+P11(a69,f11(a69,f27(f27(f10(a69),x17981),x17982),x17983),f11(a69,f27(f27(f10(a69),x17984),x17982),x17985))
% 12.04/12.18 [1799]~P11(a69,x17991,x17994)+~P12(a69,x17993,f11(a69,f27(f27(f10(a69),f4(a69,x17994,x17991)),x17992),x17995))+P12(a69,f11(a69,f27(f27(f10(a69),x17991),x17992),x17993),f11(a69,f27(f27(f10(a69),x17994),x17992),x17995))
% 12.04/12.18 [1800]~P11(a69,x18004,x18001)+~P11(a69,f11(a69,f27(f27(f10(a69),f4(a69,x18001,x18004)),x18002),x18003),x18005)+P11(a69,f11(a69,f27(f27(f10(a69),x18001),x18002),x18003),f11(a69,f27(f27(f10(a69),x18004),x18002),x18005))
% 12.04/12.18 [1801]~P11(a69,x18014,x18011)+~P12(a69,f11(a69,f27(f27(f10(a69),f4(a69,x18011,x18014)),x18012),x18013),x18015)+P12(a69,f11(a69,f27(f27(f10(a69),x18011),x18012),x18013),f11(a69,f27(f27(f10(a69),x18014),x18012),x18015))
% 12.04/12.18 [1740]~P13(a70,x17401,x17404)+~P13(a70,x17401,f11(a70,x17402,x17405))+P13(a70,x17401,f11(a70,f11(a70,x17402,f27(f27(f10(a70),x17403),x17404)),x17405))
% 12.04/12.18 [1768]~P13(a70,x17681,x17684)+P13(a70,x17681,f11(a70,x17682,x17683))+~P13(a70,x17681,f11(a70,f11(a70,x17682,f27(f27(f10(a70),x17685),x17684)),x17683))
% 12.04/12.18 [1742]~P45(x17422)+~E(f11(x17422,f27(f27(f10(x17422),x17424),x17425),x17421),f11(x17422,f27(f27(f10(x17422),x17423),x17425),x17426))+E(x17421,f11(x17422,f27(f27(f10(x17422),f4(x17422,x17423,x17424)),x17425),x17426))
% 12.04/12.18 [1743]~P45(x17431)+~E(f11(x17431,f27(f27(f10(x17431),x17432),x17434),x17435),f11(x17431,f27(f27(f10(x17431),x17433),x17434),x17436))+E(f11(x17431,f27(f27(f10(x17431),f4(x17431,x17432,x17433)),x17434),x17435),x17436)
% 12.04/12.18 [1755]~P45(x17551)+~E(x17556,f11(x17551,f27(f27(f10(x17551),f4(x17551,x17552,x17555)),x17553),x17554))+E(f11(x17551,f27(f27(f10(x17551),x17552),x17553),x17554),f11(x17551,f27(f27(f10(x17551),x17555),x17553),x17556))
% 12.04/12.18 [1756]~P45(x17561)+~E(f11(x17561,f27(f27(f10(x17561),f4(x17561,x17562,x17565)),x17563),x17564),x17566)+E(f11(x17561,f27(f27(f10(x17561),x17562),x17563),x17564),f11(x17561,f27(f27(f10(x17561),x17565),x17563),x17566))
% 12.04/12.18 [1792]~P46(x17921)+~P11(x17921,f11(x17921,f27(f27(f10(x17921),x17924),x17925),x17922),f11(x17921,f27(f27(f10(x17921),x17923),x17925),x17926))+P11(x17921,x17922,f11(x17921,f27(f27(f10(x17921),f4(x17921,x17923,x17924)),x17925),x17926))
% 12.04/12.18 [1793]~P46(x17931)+~P12(x17931,f11(x17931,f27(f27(f10(x17931),x17934),x17935),x17932),f11(x17931,f27(f27(f10(x17931),x17933),x17935),x17936))+P12(x17931,x17932,f11(x17931,f27(f27(f10(x17931),f4(x17931,x17933,x17934)),x17935),x17936))
% 12.04/12.18 [1794]~P46(x17941)+~P11(x17941,f11(x17941,f27(f27(f10(x17941),x17942),x17944),x17945),f11(x17941,f27(f27(f10(x17941),x17943),x17944),x17946))+P11(x17941,f11(x17941,f27(f27(f10(x17941),f4(x17941,x17942,x17943)),x17944),x17945),x17946)
% 12.04/12.18 [1795]~P46(x17951)+~P12(x17951,f11(x17951,f27(f27(f10(x17951),x17952),x17954),x17955),f11(x17951,f27(f27(f10(x17951),x17953),x17954),x17956))+P12(x17951,f11(x17951,f27(f27(f10(x17951),f4(x17951,x17952,x17953)),x17954),x17955),x17956)
% 12.04/12.18 [1802]~P46(x18021)+~P11(x18021,x18024,f11(x18021,f27(f27(f10(x18021),f4(x18021,x18025,x18022)),x18023),x18026))+P11(x18021,f11(x18021,f27(f27(f10(x18021),x18022),x18023),x18024),f11(x18021,f27(f27(f10(x18021),x18025),x18023),x18026))
% 12.04/12.18 [1803]~P46(x18031)+~P12(x18031,x18034,f11(x18031,f27(f27(f10(x18031),f4(x18031,x18035,x18032)),x18033),x18036))+P12(x18031,f11(x18031,f27(f27(f10(x18031),x18032),x18033),x18034),f11(x18031,f27(f27(f10(x18031),x18035),x18033),x18036))
% 12.04/12.18 [1804]~P46(x18041)+~P11(x18041,f11(x18041,f27(f27(f10(x18041),f4(x18041,x18042,x18045)),x18043),x18044),x18046)+P11(x18041,f11(x18041,f27(f27(f10(x18041),x18042),x18043),x18044),f11(x18041,f27(f27(f10(x18041),x18045),x18043),x18046))
% 12.04/12.18 [1805]~P46(x18051)+~P12(x18051,f11(x18051,f27(f27(f10(x18051),f4(x18051,x18052,x18055)),x18053),x18054),x18056)+P12(x18051,f11(x18051,f27(f27(f10(x18051),x18052),x18053),x18054),f11(x18051,f27(f27(f10(x18051),x18055),x18053),x18056))
% 12.04/12.18 [1809]~P26(x18092)+E(f24(x18091,x18092,x18093,x18094,f16(x18092,x18095,x18096)),f27(f27(f27(x18094,x18095),x18096),f24(x18091,x18092,x18093,x18094,x18096)))+~E(f27(f27(f27(x18094,f2(x18092)),f2(f72(x18092))),x18093),x18093)
% 12.04/12.18 [1028]P12(a70,x10281,x10282)+P12(a70,x10282,x10281)+E(x10281,f2(a70))+~E(f7(a70,x10282,x10281),f2(a70))
% 12.04/12.18 [1034]P12(a70,x10342,x10341)+E(x10341,f2(a70))+P11(a70,x10342,f2(a70))+~E(f7(a70,x10342,x10341),f2(a70))
% 12.04/12.18 [1035]P12(a70,x10351,x10352)+E(x10351,f2(a70))+P11(a70,f2(a70),x10352)+~E(f7(a70,x10352,x10351),f2(a70))
% 12.04/12.18 [749]P14(x7492,x7491)+~P49(x7492)+P14(x7492,f9(f72(x7492),x7491))+E(x7491,f2(f72(x7492)))
% 12.04/12.18 [750]~P34(x7502)+~P66(x7502)+E(x7501,f2(a69))+E(f27(f27(f14(x7502),f2(x7502)),x7501),f2(x7502))
% 12.04/12.18 [856]~P63(x8562)+E(x8561,f3(x8562))+E(x8561,f9(x8562,f3(x8562)))+~E(f27(f27(f10(x8562),x8561),x8561),f3(x8562))
% 12.04/12.18 [902]~E(x9022,f3(a70))+~E(x9021,f3(a70))+~P12(a70,f2(a70),x9021)+E(f27(f27(f10(a70),x9021),x9022),f3(a70))
% 12.04/12.18 [851]P12(x8513,x8511,x8512)+~P49(x8513)+E(x8511,x8512)+P12(x8513,x8512,x8511)
% 12.04/12.18 [852]P12(x8523,x8521,x8522)+~P30(x8523)+E(x8521,x8522)+P12(x8523,x8522,x8521)
% 12.04/12.18 [855]P12(x8551,x8552,x8553)+~E(x8552,x8553)+~P30(x8551)+P11(x8551,x8552,x8553)
% 12.04/12.18 [905]~P32(x9053)+~P11(x9053,x9052,x9051)+E(x9051,x9052)+P12(x9053,x9052,x9051)
% 12.04/12.18 [907]~P30(x9073)+~P11(x9073,x9071,x9072)+E(x9071,x9072)+P12(x9073,x9071,x9072)
% 12.04/12.18 [913]~P32(x9133)+~P11(x9133,x9131,x9132)+E(x9131,x9132)+P12(x9133,x9131,x9132)
% 12.04/12.18 [996]~P11(x9963,x9962,x9961)+~P11(x9963,x9961,x9962)+E(x9961,x9962)+~P32(x9963)
% 12.04/12.18 [1040]P12(x10401,x10403,x10402)+~P2(x10401)+~P11(x10401,x10403,x10402)+P11(x10401,x10402,x10403)
% 12.04/12.18 [676]~P29(x6763)+~P41(x6763)+E(x6761,x6762)+~E(f21(x6763,x6761),f21(x6763,x6762))
% 12.04/12.18 [1201]~P49(x12011)+P14(x12011,x12012)+P12(x12011,f2(x12011),x12013)+~P14(x12011,f16(x12011,x12013,x12012))
% 12.04/12.18 [1319]E(x13191,x13192)+~P11(a69,x13193,x13192)+~P11(a69,x13193,x13191)+~E(f4(a69,x13191,x13193),f4(a69,x13192,x13193))
% 12.04/12.18 [1397]~P27(x13971)+~P12(x13971,f2(x13971),x13973)+~P12(x13971,f2(x13971),x13972)+P12(x13971,f2(x13971),f11(x13971,x13972,x13973))
% 12.04/12.18 [1398]~P27(x13981)+~P11(x13981,x13983,f2(x13981))+~P11(x13981,x13982,f2(x13981))+P11(x13981,f11(x13981,x13982,x13983),f2(x13981))
% 12.04/12.18 [1399]~P27(x13991)+~P11(x13991,x13993,f2(x13991))+~P12(x13991,x13992,f2(x13991))+P12(x13991,f11(x13991,x13992,x13993),f2(x13991))
% 12.04/12.18 [1400]~P27(x14001)+~P11(x14001,x14002,f2(x14001))+~P12(x14001,x14003,f2(x14001))+P12(x14001,f11(x14001,x14002,x14003),f2(x14001))
% 12.04/12.18 [1401]~P27(x14011)+~P12(x14011,x14013,f2(x14011))+~P12(x14011,x14012,f2(x14011))+P12(x14011,f11(x14011,x14012,x14013),f2(x14011))
% 12.04/12.18 [1553]~P13(a69,x15531,x15533)+P13(a69,x15531,x15532)+~P11(a69,x15532,x15533)+~P13(a69,x15531,f4(a69,x15533,x15532))
% 12.04/12.18 [1554]~P13(a69,x15541,x15543)+P13(a69,x15541,x15542)+~P11(a69,x15543,x15542)+~P13(a69,x15541,f4(a69,x15542,x15543))
% 12.04/12.18 [1607]~P11(a70,x16072,x16073)+P11(a70,f7(a70,x16071,x16072),f7(a70,x16071,x16073))+~P12(a70,x16071,f2(a70))+~P12(a70,f2(a70),x16072)
% 12.04/12.18 [1608]~P11(a70,x16083,x16082)+P11(a70,f7(a70,x16081,x16082),f7(a70,x16081,x16083))+~P11(a70,f2(a70),x16081)+~P12(a70,f2(a70),x16083)
% 12.04/12.18 [1690]~P11(a69,x16903,x16901)+P11(a69,x16901,x16902)+~P11(a69,x16903,x16902)+~P11(a69,f4(a69,x16901,x16903),f4(a69,x16902,x16903))
% 12.04/12.18 [1691]~P11(a69,x16913,x16911)+P12(a69,x16911,x16912)+~P11(a69,x16913,x16912)+~P12(a69,f4(a69,x16911,x16913),f4(a69,x16912,x16913))
% 12.04/12.18 [807]~P26(x8071)+~E(x8072,f2(x8071))+~E(x8073,f2(f72(x8071)))+E(f16(x8071,x8072,x8073),f2(f72(x8071)))
% 12.04/12.18 [860]~P41(x8602)+E(x8601,f2(x8602))+~E(f23(x8602,x8601,x8603),f2(f72(x8602)))+E(x8603,f2(f72(x8602)))
% 12.04/12.18 [968]~P41(x9682)+~E(f20(x9682,x9683,x9681),f2(a69))+~E(f27(f21(x9682,x9681),x9683),f2(x9682))+E(x9681,f2(f72(x9682)))
% 12.04/12.18 [1010]~P49(x10101)+~P14(x10101,x10103)+~P14(x10101,x10102)+P14(x10101,f11(f72(x10101),x10102,x10103))
% 12.04/12.18 [1077]P14(x10772,x10771)+~P49(x10772)+~P14(x10772,f16(x10772,x10773,x10771))+E(x10771,f2(f72(x10772)))
% 12.04/12.18 [1116]~P49(x11163)+E(x11161,x11162)+~P11(f72(x11163),x11161,x11162)+P14(x11163,f4(f72(x11163),x11162,x11161))
% 12.04/12.18 [1139]~P49(x11391)+~P12(x11391,f2(x11391),x11392)+P14(x11391,f16(x11391,x11392,x11393))+~E(x11393,f2(f72(x11391)))
% 12.04/12.18 [1176]~P11(a69,x11763,f34(x11762,x11761))+~P68(f27(x11761,x11762))+~P68(f27(x11761,x11763))+P68(f27(x11761,f2(a69)))
% 12.04/12.18 [818]~P51(x8182)+E(x8181,f2(x8182))+E(x8183,f2(x8182))+~E(f27(f27(f10(x8182),x8183),x8181),f2(x8182))
% 12.04/12.18 [819]~P61(x8192)+E(x8191,f2(x8192))+E(x8193,f2(x8192))+~E(f27(f27(f10(x8192),x8193),x8191),f2(x8192))
% 12.04/12.18 [1011]~P41(x10113)+E(x10111,x10112)+E(x10111,f9(x10113,x10112))+~E(f27(f27(f10(x10113),x10111),x10111),f27(f27(f10(x10113),x10112),x10112))
% 12.04/12.18 [1359]~P53(x13591)+~P12(x13591,f3(x13591),x13592)+~P12(a69,f2(a69),x13593)+P12(x13591,f3(x13591),f27(f27(f14(x13591),x13592),x13593))
% 12.04/12.18 [1374]~P46(x13741)+~P11(x13741,x13743,f2(x13741))+~P11(x13741,x13742,f2(x13741))+P11(x13741,f2(x13741),f27(f27(f10(x13741),x13742),x13743))
% 12.04/12.18 [1375]~P47(x13751)+~P11(x13751,x13753,f2(x13751))+~P11(x13751,x13752,f2(x13751))+P11(x13751,f2(x13751),f27(f27(f10(x13751),x13752),x13753))
% 12.04/12.18 [1376]~P47(x13761)+~P12(x13761,x13763,f2(x13761))+~P12(x13761,x13762,f2(x13761))+P12(x13761,f2(x13761),f27(f27(f10(x13761),x13762),x13763))
% 12.04/12.18 [1377]~P46(x13771)+~P11(x13771,f2(x13771),x13773)+~P11(x13771,f2(x13771),x13772)+P11(x13771,f2(x13771),f27(f27(f10(x13771),x13772),x13773))
% 12.04/12.18 [1378]~P47(x13781)+~P11(x13781,f2(x13781),x13783)+~P11(x13781,f2(x13781),x13782)+P11(x13781,f2(x13781),f27(f27(f10(x13781),x13782),x13783))
% 12.04/12.18 [1379]~P58(x13791)+~P11(x13791,f2(x13791),x13793)+~P11(x13791,f2(x13791),x13792)+P11(x13791,f2(x13791),f27(f27(f10(x13791),x13792),x13793))
% 12.04/12.18 [1380]~P57(x13801)+~P12(x13801,f2(x13801),x13803)+~P12(x13801,f2(x13801),x13802)+P12(x13801,f2(x13801),f27(f27(f10(x13801),x13802),x13803))
% 12.04/12.18 [1381]~P53(x13811)+~P12(x13811,f3(x13811),x13813)+~P12(x13811,f3(x13811),x13812)+P12(x13811,f3(x13811),f27(f27(f10(x13811),x13812),x13813))
% 12.04/12.18 [1383]~P47(x13831)+~P11(x13831,x13833,f2(x13831))+~P11(x13831,f2(x13831),x13832)+P11(x13831,f27(f27(f10(x13831),x13832),x13833),f2(x13831))
% 12.04/12.18 [1384]~P47(x13841)+~P11(x13841,x13842,f2(x13841))+~P11(x13841,f2(x13841),x13843)+P11(x13841,f27(f27(f10(x13841),x13842),x13843),f2(x13841))
% 12.04/12.18 [1386]~P58(x13861)+~P11(x13861,x13863,f2(x13861))+~P11(x13861,f2(x13861),x13862)+P11(x13861,f27(f27(f10(x13861),x13862),x13863),f2(x13861))
% 12.04/12.18 [1388]~P58(x13881)+~P11(x13881,x13882,f2(x13881))+~P11(x13881,f2(x13881),x13883)+P11(x13881,f27(f27(f10(x13881),x13882),x13883),f2(x13881))
% 12.04/12.18 [1390]~P57(x13901)+~P12(x13901,x13903,f2(x13901))+~P12(x13901,f2(x13901),x13902)+P12(x13901,f27(f27(f10(x13901),x13902),x13903),f2(x13901))
% 12.04/12.18 [1391]~P57(x13911)+~P12(x13911,x13912,f2(x13911))+~P12(x13911,f2(x13911),x13913)+P12(x13911,f27(f27(f10(x13911),x13912),x13913),f2(x13911))
% 12.04/12.18 [1409]~P47(x14091)+P11(x14091,x14092,f2(x14091))+P11(x14091,x14093,f2(x14091))+~P11(x14091,f27(f27(f10(x14091),x14093),x14092),f2(x14091))
% 12.04/12.18 [1410]~P47(x14101)+P11(x14101,x14102,f2(x14101))+P11(x14101,f2(x14101),x14103)+~P11(x14101,f2(x14101),f27(f27(f10(x14101),x14103),x14102))
% 12.04/12.18 [1411]~P47(x14111)+P11(x14111,x14112,f2(x14111))+P11(x14111,f2(x14111),x14113)+~P11(x14111,f2(x14111),f27(f27(f10(x14111),x14112),x14113))
% 12.04/12.18 [1412]~P47(x14121)+P11(x14121,f2(x14121),x14122)+P11(x14121,x14122,f2(x14121))+~P11(x14121,f2(x14121),f27(f27(f10(x14121),x14123),x14122))
% 12.04/12.18 [1413]~P47(x14131)+P11(x14131,f2(x14131),x14132)+P11(x14131,x14132,f2(x14131))+~P11(x14131,f2(x14131),f27(f27(f10(x14131),x14132),x14133))
% 12.04/12.18 [1414]~P47(x14141)+P11(x14141,f2(x14141),x14142)+P11(x14141,x14142,f2(x14141))+~P11(x14141,f27(f27(f10(x14141),x14143),x14142),f2(x14141))
% 12.04/12.18 [1415]~P47(x14151)+P11(x14151,f2(x14151),x14152)+P11(x14151,x14152,f2(x14151))+~P11(x14151,f27(f27(f10(x14151),x14152),x14153),f2(x14151))
% 12.04/12.18 [1416]~P47(x14161)+P11(x14161,f2(x14161),x14162)+P11(x14161,f2(x14161),x14163)+~P11(x14161,f27(f27(f10(x14161),x14162),x14163),f2(x14161))
% 12.04/12.18 [1465]~P57(x14651)+P12(x14651,f2(x14651),x14652)+~P12(x14651,f2(x14651),x14653)+~P12(x14651,f2(x14651),f27(f27(f10(x14651),x14653),x14652))
% 12.04/12.18 [1466]~P57(x14661)+P12(x14661,f2(x14661),x14662)+~P12(x14661,f2(x14661),x14663)+~P12(x14661,f2(x14661),f27(f27(f10(x14661),x14662),x14663))
% 12.04/12.18 [1663]~P53(x16631)+~P11(x16631,x16632,f3(x16631))+~P11(x16631,f2(x16631),x16632)+P11(x16631,f27(f27(f14(x16631),x16632),f11(a69,x16633,f3(a69))),x16632)
% 12.04/12.18 [1667]~P53(x16671)+~P12(x16671,x16672,f3(x16671))+~P12(x16671,f2(x16671),x16672)+P12(x16671,f27(f27(f14(x16671),x16672),f11(a69,x16673,f3(a69))),f3(x16671))
% 12.04/12.18 [1760]~P41(x17603)+E(x17601,x17602)+E(x17601,f9(x17603,x17602))+~E(f27(f27(f14(x17603),x17601),f11(a69,f11(a69,f2(a69),f3(a69)),f3(a69))),f27(f27(f14(x17603),x17602),f11(a69,f11(a69,f2(a69),f3(a69)),f3(a69))))
% 12.04/12.18 [1067]~P49(x10671)+~P14(x10671,x10673)+~P14(x10671,x10672)+P14(x10671,f27(f27(f10(f72(x10671)),x10672),x10673))
% 12.04/12.18 [1219]~P47(x12191)+~E(x12193,f2(x12191))+~E(x12192,f2(x12191))+E(f11(x12191,f27(f27(f10(x12191),x12192),x12192),f27(f27(f10(x12191),x12193),x12193)),f2(x12191))
% 12.04/12.18 [1543]~P12(a70,x15432,x15433)+~P12(a70,f2(a70),x15433)+P11(a70,f3(a70),x15431)+~E(f11(a70,x15432,f27(f27(f10(a70),x15433),x15431)),x15433)
% 12.04/12.18 [1546]~P11(a70,f2(a70),x15462)+~P12(a70,f2(a70),x15463)+P11(a70,x15461,f3(a70))+~E(f11(a70,x15462,f27(f27(f10(a70),x15463),x15461)),x15463)
% 12.04/12.18 [1673]~P47(x16731)+~E(x16733,f2(x16731))+~E(x16732,f2(x16731))+P11(x16731,f11(x16731,f27(f27(f10(x16731),x16732),x16732),f27(f27(f10(x16731),x16733),x16733)),f2(x16731))
% 12.04/12.18 [1697]~P53(x16971)+~P12(x16971,x16972,f3(x16971))+~P12(x16971,f2(x16971),x16972)+P12(x16971,f27(f27(f10(x16971),x16972),f27(f27(f14(x16971),x16972),x16973)),f27(f27(f14(x16971),x16972),x16973))
% 12.04/12.18 [1714]~P12(a70,x17142,x17143)+~P12(a70,f2(a70),x17143)+P11(a70,f2(a70),x17141)+~P11(a70,f2(a70),f11(a70,f27(f27(f10(a70),x17143),x17141),x17142))
% 12.04/12.18 [1715]P11(a70,x17151,f2(a70))+~P11(a70,f2(a70),x17152)+~P12(a70,f2(a70),x17153)+~P12(a70,f11(a70,f27(f27(f10(a70),x17153),x17151),x17152),f2(a70))
% 12.04/12.18 [1735]~P47(x17352)+~E(x17351,f2(x17352))+~E(x17353,f2(x17352))+~P12(x17352,f2(x17352),f11(x17352,f27(f27(f10(x17352),x17353),x17353),f27(f27(f10(x17352),x17351),x17351)))
% 12.04/12.18 [1097]~P32(x10971)+~P11(x10971,x10974,x10973)+P11(x10971,x10972,x10973)+~P11(x10971,x10972,x10974)
% 12.04/12.18 [1098]~P2(x10981)+~P11(x10981,x10982,x10984)+P11(x10981,x10982,x10983)+~P11(x10981,x10984,x10983)
% 12.04/12.18 [1099]~P32(x10991)+~P12(x10991,x10994,x10993)+P12(x10991,x10992,x10993)+~P11(x10991,x10992,x10994)
% 12.04/12.18 [1100]~P32(x11001)+~P12(x11001,x11002,x11004)+P12(x11001,x11002,x11003)+~P11(x11001,x11004,x11003)
% 12.04/12.18 [1101]~P32(x11011)+~P12(x11011,x11014,x11013)+P12(x11011,x11012,x11013)+~P12(x11011,x11012,x11014)
% 12.04/12.18 [1102]~P2(x11021)+~P12(x11021,x11022,x11024)+P12(x11021,x11022,x11023)+~P11(x11021,x11024,x11023)
% 12.04/12.18 [1103]~P2(x11031)+~P12(x11031,x11034,x11033)+P12(x11031,x11032,x11033)+~P11(x11031,x11032,x11034)
% 12.04/12.18 [1104]~P2(x11041)+~P12(x11041,x11042,x11044)+P12(x11041,x11042,x11043)+~P12(x11041,x11044,x11043)
% 12.04/12.18 [1105]~P42(x11051)+~P13(x11051,x11052,x11054)+P13(x11051,x11052,x11053)+~P13(x11051,x11054,x11053)
% 12.04/12.18 [1207]~P8(x12072)+~P13(f72(x12072),x12073,x12074)+P13(f72(x12072),x12073,f23(x12072,x12071,x12074))+E(x12071,f2(x12072))
% 12.04/12.18 [1209]~P8(x12092)+~P13(f72(x12092),x12093,x12094)+P13(f72(x12092),f23(x12092,x12091,x12093),x12094)+E(x12091,f2(x12092))
% 12.04/12.18 [1229]~P31(x12292)+P12(f75(x12291,x12292),x12294,x12293)+~P11(f75(x12291,x12292),x12294,x12293)+P11(f75(x12291,x12292),x12293,x12294)
% 12.04/12.18 [1322]~P8(x13222)+~P13(f72(x13222),x13223,f23(x13222,x13221,x13224))+P13(f72(x13222),x13223,x13224)+E(x13221,f2(x13222))
% 12.04/12.18 [1323]~P8(x13232)+~P13(f72(x13232),f23(x13232,x13231,x13233),x13234)+P13(f72(x13232),x13233,x13234)+E(x13231,f2(x13232))
% 12.04/12.18 [1335]~P42(x13351)+~P13(x13351,x13352,x13354)+~P13(x13351,x13352,x13353)+P13(x13351,x13352,f11(x13351,x13353,x13354))
% 12.04/12.18 [1336]~P40(x13361)+~P13(x13361,x13362,x13364)+~P13(x13361,x13362,x13363)+P13(x13361,x13362,f4(x13361,x13363,x13364))
% 12.04/12.18 [1350]~P27(x13501)+~P11(x13501,x13502,x13503)+~P11(x13501,f2(x13501),x13504)+P11(x13501,x13502,f11(x13501,x13503,x13504))
% 12.04/12.18 [1351]~P27(x13511)+~P11(x13511,x13512,x13514)+~P11(x13511,f2(x13511),x13513)+P11(x13511,x13512,f11(x13511,x13513,x13514))
% 12.04/12.18 [1352]~P27(x13521)+~P11(x13521,x13522,x13524)+~P12(x13521,f2(x13521),x13523)+P12(x13521,x13522,f11(x13521,x13523,x13524))
% 12.04/12.18 [1353]~P27(x13531)+~P12(x13531,x13532,x13534)+~P11(x13531,f2(x13531),x13533)+P12(x13531,x13532,f11(x13531,x13533,x13534))
% 12.04/12.18 [1354]~P53(x13541)+~P12(x13541,x13542,x13544)+~P12(x13541,f2(x13541),x13543)+P12(x13541,x13542,f11(x13541,x13543,x13544))
% 12.04/12.18 [1036]~P8(x10361)+P13(f72(x10361),f23(x10361,x10362,x10363),x10364)+~E(x10362,f2(x10361))+~E(x10364,f2(f72(x10361)))
% 12.04/12.18 [1220]~P8(x12201)+~P13(f72(x12201),x12203,x12204)+P13(f72(x12201),f23(x12201,x12202,x12203),x12204)+~E(x12204,f2(f72(x12201)))
% 12.04/12.18 [1225]~P8(x12252)+~P13(f72(x12252),f23(x12252,x12253,x12254),x12251)+~E(x12253,f2(x12252))+E(x12251,f2(f72(x12252)))
% 12.04/12.18 [1532]~P1(x15322)+E(x15321,f2(x15322))+~P11(a68,x15323,f2(a68))+~P11(a68,f29(x15322,x15321),f27(f27(f10(a68),x15323),f29(x15322,x15324)))
% 12.04/12.18 [1675]~P9(x16751)+~P13(x16751,x16753,x16754)+~P13(x16751,x16753,x16752)+E(f11(x16751,f7(x16751,x16752,x16753),f7(x16751,x16754,x16753)),f7(x16751,f11(x16751,x16752,x16754),x16753))
% 12.04/12.18 [1193]~P53(x11933)+E(x11931,x11932)+~P12(x11933,f3(x11933),x11934)+~E(f27(f27(f14(x11933),x11934),x11931),f27(f27(f14(x11933),x11934),x11932))
% 12.04/12.18 [1504]~P53(x15041)+~P11(a69,x15043,x15044)+~P12(x15041,f3(x15041),x15042)+P11(x15041,f27(f27(f14(x15041),x15042),x15043),f27(f27(f14(x15041),x15042),x15044))
% 12.04/12.18 [1505]~P53(x15051)+~P11(a69,x15053,x15054)+~P11(x15051,f3(x15051),x15052)+P11(x15051,f27(f27(f14(x15051),x15052),x15053),f27(f27(f14(x15051),x15052),x15054))
% 12.04/12.18 [1507]~P53(x15071)+~P12(a69,x15073,x15074)+~P12(x15071,f3(x15071),x15072)+P12(x15071,f27(f27(f14(x15071),x15072),x15073),f27(f27(f14(x15071),x15072),x15074))
% 12.04/12.18 [1513]~P46(x15131)+~P11(x15131,x15134,x15133)+~P11(x15131,x15132,f2(x15131))+P11(x15131,f27(f27(f10(x15131),x15132),x15133),f27(f27(f10(x15131),x15132),x15134))
% 12.04/12.18 [1514]~P47(x15141)+~P11(x15141,x15144,x15143)+~P12(x15141,x15142,f2(x15141))+P11(x15141,f27(f27(f10(x15141),x15142),x15143),f27(f27(f10(x15141),x15142),x15144))
% 12.04/12.18 [1515]~P46(x15151)+~P11(x15151,x15154,x15152)+~P11(x15151,x15153,f2(x15151))+P11(x15151,f27(f27(f10(x15151),x15152),x15153),f27(f27(f10(x15151),x15154),x15153))
% 12.04/12.18 [1519]~P47(x15191)+~P12(x15191,x15194,x15192)+~P12(x15191,x15193,f2(x15191))+P12(x15191,f27(f27(f10(x15191),x15192),x15193),f27(f27(f10(x15191),x15194),x15193))
% 12.04/12.18 [1520]~P47(x15201)+~P12(x15201,x15204,x15203)+~P12(x15201,x15202,f2(x15201))+P12(x15201,f27(f27(f10(x15201),x15202),x15203),f27(f27(f10(x15201),x15202),x15204))
% 12.04/12.18 [1521]~P47(x15211)+~P11(x15211,x15213,x15214)+~P12(x15211,f2(x15211),x15212)+P11(x15211,f27(f27(f10(x15211),x15212),x15213),f27(f27(f10(x15211),x15212),x15214))
% 12.04/12.18 [1522]~P60(x15221)+~P11(x15221,x15223,x15224)+~P11(x15221,f2(x15221),x15222)+P11(x15221,f27(f27(f10(x15221),x15222),x15223),f27(f27(f10(x15221),x15222),x15224))
% 12.04/12.18 [1523]~P59(x15231)+~P11(x15231,x15233,x15234)+~P11(x15231,f2(x15231),x15232)+P11(x15231,f27(f27(f10(x15231),x15232),x15233),f27(f27(f10(x15231),x15232),x15234))
% 12.04/12.18 [1524]~P60(x15241)+~P11(x15241,x15242,x15244)+~P11(x15241,f2(x15241),x15243)+P11(x15241,f27(f27(f10(x15241),x15242),x15243),f27(f27(f10(x15241),x15244),x15243))
% 12.04/12.18 [1525]~P53(x15251)+~P11(x15251,x15252,x15254)+~P11(x15251,f2(x15251),x15252)+P11(x15251,f27(f27(f14(x15251),x15252),x15253),f27(f27(f14(x15251),x15254),x15253))
% 12.04/12.18 [1527]~P57(x15271)+~P12(x15271,x15273,x15274)+~P12(x15271,f2(x15271),x15272)+P12(x15271,f27(f27(f10(x15271),x15272),x15273),f27(f27(f10(x15271),x15272),x15274))
% 12.04/12.18 [1528]~P50(x15281)+~P12(x15281,x15283,x15284)+~P12(x15281,f2(x15281),x15282)+P12(x15281,f27(f27(f10(x15281),x15282),x15283),f27(f27(f10(x15281),x15282),x15284))
% 12.04/12.18 [1529]~P47(x15291)+~P12(x15291,x15292,x15294)+~P12(x15291,f2(x15291),x15293)+P12(x15291,f27(f27(f10(x15291),x15292),x15293),f27(f27(f10(x15291),x15294),x15293))
% 12.04/12.18 [1530]~P57(x15301)+~P12(x15301,x15302,x15304)+~P12(x15301,f2(x15301),x15303)+P12(x15301,f27(f27(f10(x15301),x15302),x15303),f27(f27(f10(x15301),x15304),x15303))
% 12.04/12.18 [1531]~P47(x15311)+~P12(x15311,x15313,x15314)+~P12(x15311,f2(x15311),x15312)+P12(x15311,f27(f27(f10(x15311),x15312),x15313),f27(f27(f10(x15311),x15312),x15314))
% 12.04/12.18 [1557]~P41(x15572)+P13(x15572,x15573,x15574)+E(x15571,f2(x15572))+~P13(x15572,f27(f27(f10(x15572),x15573),x15571),f27(f27(f10(x15572),x15574),x15571))
% 12.04/12.18 [1558]~P41(x15582)+P13(x15582,x15583,x15584)+E(x15581,f2(x15582))+~P13(x15582,f27(f27(f10(x15582),x15581),x15583),f27(f27(f10(x15582),x15581),x15584))
% 12.04/12.18 [1609]P12(x16091,x16093,x16092)+~P47(x16091)+P12(x16091,x16092,x16093)+~P12(x16091,f27(f27(f10(x16091),x16094),x16092),f27(f27(f10(x16091),x16094),x16093))
% 12.04/12.18 [1610]P12(x16101,x16103,x16102)+~P47(x16101)+P12(x16101,x16102,x16103)+~P12(x16101,f27(f27(f10(x16101),x16102),x16104),f27(f27(f10(x16101),x16103),x16104))
% 12.04/12.18 [1614]~P47(x16141)+P12(x16141,x16142,x16143)+P12(x16141,x16144,f2(x16141))+~P12(x16141,f27(f27(f10(x16141),x16142),x16144),f27(f27(f10(x16141),x16143),x16144))
% 12.04/12.18 [1615]~P47(x16151)+P12(x16151,x16152,x16153)+P12(x16151,x16154,f2(x16151))+~P12(x16151,f27(f27(f10(x16151),x16154),x16152),f27(f27(f10(x16151),x16154),x16153))
% 12.04/12.18 [1616]~P47(x16161)+P12(x16161,x16162,x16163)+P12(x16161,f2(x16161),x16164)+~P12(x16161,f27(f27(f10(x16161),x16164),x16163),f27(f27(f10(x16161),x16164),x16162))
% 12.04/12.18 [1617]~P47(x16171)+P12(x16171,x16172,x16173)+P12(x16171,f2(x16171),x16174)+~P12(x16171,f27(f27(f10(x16171),x16173),x16174),f27(f27(f10(x16171),x16172),x16174))
% 12.04/12.18 [1633]~P47(x16331)+P12(x16331,f2(x16331),x16332)+P12(x16331,x16332,f2(x16331))+~P12(x16331,f27(f27(f10(x16331),x16333),x16332),f27(f27(f10(x16331),x16334),x16332))
% 12.04/12.18 [1634]~P47(x16341)+P12(x16341,f2(x16341),x16342)+P12(x16341,x16342,f2(x16341))+~P12(x16341,f27(f27(f10(x16341),x16342),x16343),f27(f27(f10(x16341),x16342),x16344))
% 12.04/12.18 [1647]~P53(x16473)+P11(a69,x16471,x16472)+~P12(x16473,f3(x16473),x16474)+~P11(x16473,f27(f27(f14(x16473),x16474),x16471),f27(f27(f14(x16473),x16474),x16472))
% 12.04/12.18 [1649]~P53(x16493)+P12(a69,x16491,x16492)+~P12(x16493,f3(x16493),x16494)+~P12(x16493,f27(f27(f14(x16493),x16494),x16491),f27(f27(f14(x16493),x16494),x16492))
% 12.04/12.18 [1650]~P47(x16501)+P11(x16501,x16502,x16503)+~P12(x16501,x16504,f2(x16501))+~P11(x16501,f27(f27(f10(x16501),x16504),x16503),f27(f27(f10(x16501),x16504),x16502))
% 12.04/12.18 [1651]~P47(x16511)+P12(x16511,x16512,x16513)+~P12(x16511,x16514,f2(x16511))+~P12(x16511,f27(f27(f10(x16511),x16514),x16513),f27(f27(f10(x16511),x16514),x16512))
% 12.04/12.18 [1652]~P47(x16521)+P11(x16521,x16522,x16523)+~P12(x16521,f2(x16521),x16524)+~P11(x16521,f27(f27(f10(x16521),x16524),x16522),f27(f27(f10(x16521),x16524),x16523))
% 12.04/12.18 [1653]~P57(x16531)+P11(x16531,x16532,x16533)+~P12(x16531,f2(x16531),x16534)+~P11(x16531,f27(f27(f10(x16531),x16534),x16532),f27(f27(f10(x16531),x16534),x16533))
% 12.04/12.18 [1654]~P57(x16541)+P11(x16541,x16542,x16543)+~P12(x16541,f2(x16541),x16544)+~P11(x16541,f27(f27(f10(x16541),x16542),x16544),f27(f27(f10(x16541),x16543),x16544))
% 12.04/12.18 [1655]~P47(x16551)+P12(x16551,x16552,x16553)+~P12(x16551,f2(x16551),x16554)+~P12(x16551,f27(f27(f10(x16551),x16554),x16552),f27(f27(f10(x16551),x16554),x16553))
% 12.04/12.18 [1656]~P57(x16561)+P12(x16561,x16562,x16563)+~P11(x16561,f2(x16561),x16564)+~P12(x16561,f27(f27(f10(x16561),x16564),x16562),f27(f27(f10(x16561),x16564),x16563))
% 12.04/12.18 [1657]~P55(x16571)+P12(x16571,x16572,x16573)+~P11(x16571,f2(x16571),x16574)+~P12(x16571,f27(f27(f10(x16571),x16574),x16572),f27(f27(f10(x16571),x16574),x16573))
% 12.04/12.18 [1658]~P53(x16581)+P12(x16581,x16582,x16583)+~P11(x16581,f2(x16581),x16583)+~P12(x16581,f27(f27(f14(x16581),x16582),x16584),f27(f27(f14(x16581),x16583),x16584))
% 12.04/12.18 [1659]~P57(x16591)+P12(x16591,x16592,x16593)+~P11(x16591,f2(x16591),x16594)+~P12(x16591,f27(f27(f10(x16591),x16592),x16594),f27(f27(f10(x16591),x16593),x16594))
% 12.04/12.18 [1660]~P55(x16601)+P12(x16601,x16602,x16603)+~P11(x16601,f2(x16601),x16604)+~P12(x16601,f27(f27(f10(x16601),x16602),x16604),f27(f27(f10(x16601),x16603),x16604))
% 12.04/12.18 [1759]~P53(x17591)+P11(x17591,x17592,x17593)+~P11(x17591,f2(x17591),x17593)+~P11(x17591,f27(f27(f14(x17591),x17592),f11(a69,x17594,f3(a69))),f27(f27(f14(x17591),x17593),f11(a69,x17594,f3(a69))))
% 12.04/12.18 [1773]~P1(x17731)+~P12(a68,f2(a68),x17734)+~P11(a68,f29(x17731,f27(x17732,f53(x17732,x17731,x17734))),x17734)+P11(a68,f29(x17731,f27(x17732,x17733)),f26(a69,f11(a69,f52(x17732,x17731),f3(a69))))
% 12.04/12.18 [1774]~P1(x17741)+~P12(a68,f2(a68),x17744)+~P11(a68,f29(x17741,f27(x17742,f57(x17742,x17741,x17744))),x17744)+P12(a68,f29(x17741,f27(x17742,x17743)),f26(a69,f11(a69,f56(x17742,x17741),f3(a69))))
% 12.04/12.18 [1682]~P66(x16823)+~P43(x16823)+P68(f27(x16821,f42(x16822,x16821,x16823)))+~P68(f27(x16821,f27(f27(f10(x16823),x16822),x16824)))
% 12.04/12.18 [1716]~P66(x17161)+~P43(x17161)+P13(x17161,x17162,f11(x17161,f42(x17162,x17163,x17161),f2(x17161)))+~P68(f27(x17163,f27(f27(f10(x17161),x17162),x17164)))
% 12.04/12.18 [1785]~P12(a68,f2(a68),x17854)+~P12(a68,f29(a1,f4(a1,x17852,x17853)),f48(x17851,x17853,x17854))+~P12(a68,f2(a68),f29(a1,f4(a1,x17852,x17853)))+P12(a68,f29(a1,f4(a1,f27(f21(a1,x17851),x17852),f27(f21(a1,x17851),x17853))),x17854)
% 12.04/12.18 [1009]~P7(x10095)+E(x10091,x10092)+~E(x10093,x10094)+~E(f4(x10095,x10093,x10094),f4(x10095,x10091,x10092))
% 12.04/12.18 [1279]~P23(x12791)+~P11(x12791,x12794,x12795)+P11(x12791,x12792,x12793)+~E(f4(x12791,x12794,x12795),f4(x12791,x12792,x12793))
% 12.04/12.18 [1281]~P23(x12811)+~P12(x12811,x12814,x12815)+P12(x12811,x12812,x12813)+~E(f4(x12811,x12814,x12815),f4(x12811,x12812,x12813))
% 12.04/12.18 [1508]~P18(x15081)+~P11(x15081,x15083,x15085)+~P11(x15081,x15082,x15084)+P11(x15081,f11(x15081,x15082,x15083),f11(x15081,x15084,x15085))
% 12.04/12.18 [1509]~P28(x15091)+~P11(x15091,x15093,x15095)+~P12(x15091,x15092,x15094)+P12(x15091,f11(x15091,x15092,x15093),f11(x15091,x15094,x15095))
% 12.04/12.18 [1510]~P28(x15101)+~P11(x15101,x15102,x15104)+~P12(x15101,x15103,x15105)+P12(x15101,f11(x15101,x15102,x15103),f11(x15101,x15104,x15105))
% 12.04/12.18 [1511]~P28(x15111)+~P12(x15111,x15113,x15115)+~P12(x15111,x15112,x15114)+P12(x15111,f11(x15111,x15112,x15113),f11(x15111,x15114,x15115))
% 12.04/12.18 [1694]~P1(x16941)+~P12(a68,f29(x16941,x16943),x16945)+~P12(a68,f29(x16941,x16942),x16944)+P12(a68,f29(x16941,f11(x16941,x16942,x16943)),f11(a68,x16944,x16945))
% 12.04/12.18 [1496]~P42(x14961)+~P13(x14961,x14962,x14964)+~P11(a69,x14963,x14965)+P13(x14961,f27(f27(f14(x14961),x14962),x14963),f27(f27(f14(x14961),x14964),x14965))
% 12.04/12.18 [1499]~P42(x14991)+~P13(x14991,x14993,x14995)+~P13(x14991,x14992,x14994)+P13(x14991,f27(f27(f10(x14991),x14992),x14993),f27(f27(f10(x14991),x14994),x14995))
% 12.04/12.18 [1580]~P42(x15801)+~P11(a69,x15803,x15805)+~P13(x15801,f27(f27(f14(x15801),x15802),x15805),x15804)+P13(x15801,f27(f27(f14(x15801),x15802),x15803),x15804)
% 12.04/12.18 [1683]~P33(x16831)+~P12(a68,f29(x16831,x16833),x16835)+~P12(a68,f29(x16831,x16832),x16834)+P12(a68,f29(x16831,f27(f27(f10(x16831),x16832),x16833)),f27(f27(f10(a68),x16834),x16835))
% 12.04/12.18 [1721]~P9(x17211)+~P13(x17211,x17215,x17213)+~P13(x17211,x17214,x17212)+E(f7(x17211,f27(f27(f10(x17211),x17212),x17213),f27(f27(f10(x17211),x17214),x17215)),f27(f27(f10(x17211),f7(x17211,x17212,x17214)),f7(x17211,x17213,x17215)))
% 12.04/12.18 [1724]~P44(x17245)+E(x17241,x17242)+E(x17243,x17244)+~E(f11(x17245,f27(f27(f10(x17245),x17243),x17241),f27(f27(f10(x17245),x17244),x17242)),f11(x17245,f27(f27(f10(x17245),x17243),x17242),f27(f27(f10(x17245),x17244),x17241)))
% 12.04/12.18 [1751]~E(f29(a1,x17511),f3(a68))+P12(a68,f29(a1,f4(a1,x17511,a5)),f3(a68))+P12(a68,f29(a1,f11(a1,x17511,a5)),f3(a68))+P12(a68,f29(a1,f11(a1,x17511,f3(a1))),f3(a68))+P12(a68,f29(a1,f4(a1,x17511,f3(a1))),f3(a68))
% 12.04/12.18 [1348]E(x13481,x13482)+~P13(a70,x13482,x13481)+~P13(a70,x13481,x13482)+~P11(a70,f2(a70),x13482)+~P11(a70,f2(a70),x13481)
% 12.04/12.18 [1230]~P27(x12302)+~P11(x12302,f2(x12302),x12303)+~P11(x12302,f2(x12302),x12301)+~E(f11(x12302,x12303,x12301),f2(x12302))+E(x12301,f2(x12302))
% 12.04/12.18 [1231]~P27(x12312)+~P11(x12312,f2(x12312),x12313)+~P11(x12312,f2(x12312),x12311)+~E(f11(x12312,x12311,x12313),f2(x12312))+E(x12311,f2(x12312))
% 12.04/12.18 [1533]~P49(x15331)+~P11(x15331,x15332,f3(x15331))+~P11(x15331,f2(x15331),x15332)+~P11(x15331,f2(x15331),x15333)+P11(x15331,f27(f27(f10(x15331),x15332),x15333),x15333)
% 12.04/12.18 [1534]~P49(x15341)+~P11(x15341,x15343,f3(x15341))+~P11(x15341,f2(x15341),x15343)+~P11(x15341,f2(x15341),x15342)+P11(x15341,f27(f27(f10(x15341),x15342),x15343),x15342)
% 12.04/12.18 [1625]~P9(x16251)+~P13(x16251,x16253,x16254)+~P13(x16251,x16253,x16252)+~P13(x16251,x16252,x16254)+P13(x16251,f7(x16251,x16252,x16253),f7(x16251,x16254,x16253))
% 12.04/12.18 [1696]~P9(x16961)+~P13(x16961,x16964,x16962)+P13(x16961,x16962,x16963)+~P13(x16961,x16964,x16963)+~P13(x16961,f7(x16961,x16962,x16964),f7(x16961,x16963,x16964))
% 12.04/12.18 [1115]~P9(x11152)+~P13(x11152,x11151,x11153)+E(x11151,f2(x11152))+E(f7(x11152,x11153,x11151),x11154)+~E(x11153,f27(f27(f10(x11152),x11154),x11151))
% 12.04/12.18 [1118]~P9(x11182)+~P13(x11182,x11181,x11183)+~E(f7(x11182,x11183,x11181),x11184)+E(x11181,f2(x11182))+E(x11183,f27(f27(f10(x11182),x11184),x11181))
% 12.04/12.18 [1635]~P53(x16351)+~P12(x16351,x16352,x16354)+~P11(x16351,f2(x16351),x16352)+~P12(a69,f2(a69),x16353)+P12(x16351,f27(f27(f14(x16351),x16352),x16353),f27(f27(f14(x16351),x16354),x16353))
% 12.04/12.18 [1638]~P53(x16381)+~P11(a69,x16384,x16383)+~P11(x16381,x16382,f3(x16381))+~P11(x16381,f2(x16381),x16382)+P11(x16381,f27(f27(f14(x16381),x16382),x16383),f27(f27(f14(x16381),x16382),x16384))
% 12.04/12.18 [1639]~P53(x16391)+~P12(a69,x16394,x16393)+~P12(x16391,x16392,f3(x16391))+~P12(x16391,f2(x16391),x16392)+P12(x16391,f27(f27(f14(x16391),x16392),x16393),f27(f27(f14(x16391),x16392),x16394))
% 12.04/12.18 [1708]~P53(x17083)+E(x17081,x17082)+~P11(x17083,f2(x17083),x17082)+~P11(x17083,f2(x17083),x17081)+~E(f27(f27(f14(x17083),x17081),f11(a69,x17084,f3(a69))),f27(f27(f14(x17083),x17082),f11(a69,x17084,f3(a69))))
% 12.04/12.18 [1736]~P66(x17362)+~P43(x17362)+~P13(x17362,x17363,f11(x17362,x17364,f2(x17362)))+~P68(f27(x17361,x17364))+P68(f27(x17361,f27(f27(f10(x17362),x17363),f43(x17363,x17361,x17362))))
% 12.04/12.18 [1739]~P1(x17394)+~P31(x17391)+~P11(x17391,x17392,x17395)+P11(x17391,x17392,f59(x17393,x17392,x17391,x17394))+P12(a68,f29(x17394,f27(x17393,x17395)),f11(a68,f3(a68),f29(x17394,f27(x17393,x17392))))
% 12.04/12.18 [1761]P11(a70,x17611,x17612)+~P12(a70,x17613,x17614)+~P12(a70,x17613,x17615)+~P11(a70,x17614,f2(a70))+~P11(a70,f11(a70,f27(f27(f10(a70),x17613),x17612),x17615),f11(a70,f27(f27(f10(a70),x17613),x17611),x17614))
% 12.04/12.18 [1762]P11(a70,x17621,x17622)+~P12(a70,x17623,x17624)+~P12(a70,x17625,x17624)+~P11(a70,f2(a70),x17625)+~P11(a70,f11(a70,f27(f27(f10(a70),x17624),x17621),x17625),f11(a70,f27(f27(f10(a70),x17624),x17622),x17623))
% 12.04/12.18 [1813]~P1(x18131)+~P11(x18135,x18134,x18133)+~P31(x18135)+P12(a68,f29(x18131,f27(x18132,x18133)),f11(a68,f3(a68),f29(x18131,f27(x18132,x18134))))+~P12(a68,f29(x18131,f4(x18131,f27(x18132,x18134),f27(x18132,f59(x18132,x18134,x18135,x18131)))),f3(a68))
% 12.04/12.18 [1600]~P44(x16004)+E(x16001,x16002)+~E(x16005,x16006)+E(x16003,f2(x16004))+~E(f11(x16004,x16005,f27(f27(f10(x16004),x16003),x16001)),f11(x16004,x16006,f27(f27(f10(x16004),x16003),x16002)))
% 12.04/12.18 [1748]~P38(x17481)+~P43(x17481)+~P13(x17481,x17482,x17485)+~P13(x17481,x17482,f11(x17481,x17483,x17486))+P13(x17481,x17482,f11(x17481,f4(x17481,x17483,f27(f27(f10(x17481),x17484),x17485)),x17486))
% 12.04/12.18 [1777]~P38(x17771)+~P43(x17771)+~P13(x17771,x17772,x17775)+P13(x17771,x17772,f11(x17771,x17773,x17774))+~P13(x17771,x17772,f11(x17771,f4(x17771,x17773,f27(f27(f10(x17771),x17776),x17775)),x17774))
% 12.04/12.18 [1202]~P27(x12021)+~P11(x12021,f2(x12021),x12023)+~P11(x12021,f2(x12021),x12022)+~E(x12023,f2(x12021))+~E(x12022,f2(x12021))+E(f11(x12021,x12022,x12023),f2(x12021))
% 12.04/12.18 [857]~P51(x8572)+~P52(x8572)+~P65(x8572)+~P34(x8572)+E(x8571,f2(x8572))+~E(f27(f27(f14(x8572),x8571),x8573),f2(x8572))
% 12.04/12.18 [858]~P51(x8582)+~P52(x8582)+~P65(x8582)+~P34(x8582)+~E(x8581,f2(a69))+~E(f27(f27(f14(x8582),x8583),x8581),f2(x8582))
% 12.04/12.18 [1540]~P53(x15403)+E(x15401,x15402)+~P11(x15403,f2(x15403),x15402)+~P11(x15403,f2(x15403),x15401)+~P12(a69,f2(a69),x15404)+~E(f27(f27(f14(x15403),x15401),x15404),f27(f27(f14(x15403),x15402),x15404))
% 12.04/12.18 [1684]~P60(x16841)+~P11(x16841,x16843,x16845)+~P11(x16841,x16842,x16844)+~P11(x16841,f2(x16841),x16843)+~P11(x16841,f2(x16841),x16844)+P11(x16841,f27(f27(f10(x16841),x16842),x16843),f27(f27(f10(x16841),x16844),x16845))
% 12.04/12.18 [1685]~P60(x16851)+~P11(x16851,x16853,x16855)+~P11(x16851,x16852,x16854)+~P11(x16851,f2(x16851),x16853)+~P11(x16851,f2(x16851),x16852)+P11(x16851,f27(f27(f10(x16851),x16852),x16853),f27(f27(f10(x16851),x16854),x16855))
% 12.04/12.18 [1686]~P57(x16861)+~P11(x16861,x16863,x16865)+~P12(x16861,x16862,x16864)+~P11(x16861,f2(x16861),x16862)+~P12(x16861,f2(x16861),x16863)+P12(x16861,f27(f27(f10(x16861),x16862),x16863),f27(f27(f10(x16861),x16864),x16865))
% 12.04/12.18 [1687]~P57(x16871)+~P11(x16871,x16872,x16874)+~P12(x16871,x16873,x16875)+~P11(x16871,f2(x16871),x16873)+~P12(x16871,f2(x16871),x16872)+P12(x16871,f27(f27(f10(x16871),x16872),x16873),f27(f27(f10(x16871),x16874),x16875))
% 12.04/12.18 [1688]~P57(x16881)+~P12(x16881,x16883,x16885)+~P12(x16881,x16882,x16884)+~P11(x16881,f2(x16881),x16883)+~P11(x16881,f2(x16881),x16882)+P12(x16881,f27(f27(f10(x16881),x16882),x16883),f27(f27(f10(x16881),x16884),x16885))
% 12.04/12.18 [1689]~P57(x16891)+~P12(x16891,x16893,x16895)+~P12(x16891,x16892,x16894)+~P11(x16891,f2(x16891),x16893)+~P12(x16891,f2(x16891),x16894)+P12(x16891,f27(f27(f10(x16891),x16892),x16893),f27(f27(f10(x16891),x16894),x16895))
% 12.04/12.18 [802]~P51(x8022)+~P52(x8022)+~P65(x8022)+~P34(x8022)+~E(x8023,f2(x8022))+E(x8021,f2(a69))+E(f27(f27(f14(x8022),x8023),x8021),f2(x8022))
% 12.04/12.18 [1549]~P9(x15492)+~P13(x15492,x15491,x15494)+~P13(x15492,x15493,x15495)+E(f7(x15492,x15494,x15491),f7(x15492,x15495,x15493))+E(x15491,f2(x15492))+E(x15493,f2(x15492))+~E(f27(f27(f10(x15492),x15494),x15493),f27(f27(f10(x15492),x15491),x15495))
% 12.04/12.18 [1552]~P9(x15522)+~P13(x15522,x15521,x15525)+~P13(x15522,x15523,x15524)+~E(f7(x15522,x15524,x15523),f7(x15522,x15525,x15521))+E(x15521,f2(x15522))+E(x15523,f2(x15522))+E(f27(f27(f10(x15522),x15524),x15521),f27(f27(f10(x15522),x15523),x15525))
% 12.04/12.18 [1737]~P56(x17371)+~P11(x17371,x17375,x17376)+~P11(x17371,x17373,x17376)+~P11(x17371,f2(x17371),x17374)+~P11(x17371,f2(x17371),x17372)+~E(f11(x17371,x17372,x17374),f3(x17371))+P11(x17371,f11(x17371,f27(f27(f10(x17371),x17372),x17373),f27(f27(f10(x17371),x17374),x17375)),x17376)
% 12.04/12.18 [1738]~P54(x17381)+~P12(x17381,x17385,x17386)+~P12(x17381,x17383,x17386)+~P11(x17381,f2(x17381),x17384)+~P11(x17381,f2(x17381),x17382)+~E(f11(x17381,x17382,x17384),f3(x17381))+P12(x17381,f11(x17381,f27(f27(f10(x17381),x17382),x17383),f27(f27(f10(x17381),x17384),x17385)),x17386)
% 12.04/12.18 [1769]~P11(a70,x17695,x17693)+~P12(a70,x17696,x17695)+P11(a70,x17691,x17692)+~P11(a70,f2(a70),x17694)+~P12(a70,f2(a70),x17695)+~P11(a70,f2(a70),f11(a70,f27(f27(f10(a70),x17695),x17692),x17696))+~E(f11(a70,f27(f27(f10(a70),x17693),x17691),x17694),f11(a70,f27(f27(f10(a70),x17695),x17692),x17696))
% 12.04/12.18 [1770]~P11(a70,x17705,x17703)+~P12(a70,x17704,x17703)+P11(a70,x17701,x17702)+~P11(a70,f2(a70),x17706)+~P12(a70,f2(a70),x17705)+~P12(a70,f11(a70,f27(f27(f10(a70),x17705),x17701),x17706),f2(a70))+~E(f11(a70,f27(f27(f10(a70),x17703),x17702),x17704),f11(a70,f27(f27(f10(a70),x17705),x17701),x17706))
% 12.04/12.18 %EqnAxiom
% 12.04/12.18 [1]E(x11,x11)
% 12.04/12.18 [2]E(x22,x21)+~E(x21,x22)
% 12.04/12.18 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 12.04/12.18 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 12.04/12.18 [5]~E(x51,x52)+E(f12(x51),f12(x52))
% 12.04/12.18 [6]~E(x61,x62)+E(f3(x61),f3(x62))
% 12.04/12.18 [7]~E(x71,x72)+E(f72(x71),f72(x72))
% 12.04/12.18 [8]~E(x81,x82)+E(f8(x81,x83,x84),f8(x82,x83,x84))
% 12.04/12.18 [9]~E(x91,x92)+E(f8(x93,x91,x94),f8(x93,x92,x94))
% 12.04/12.18 [10]~E(x101,x102)+E(f8(x103,x104,x101),f8(x103,x104,x102))
% 12.04/12.18 [11]~E(x111,x112)+E(f27(x111,x113),f27(x112,x113))
% 12.04/12.18 [12]~E(x121,x122)+E(f27(x123,x121),f27(x123,x122))
% 12.04/12.18 [13]~E(x131,x132)+E(f29(x131,x133),f29(x132,x133))
% 12.04/12.18 [14]~E(x141,x142)+E(f29(x143,x141),f29(x143,x142))
% 12.04/12.18 [15]~E(x151,x152)+E(f13(x151),f13(x152))
% 12.04/12.18 [16]~E(x161,x162)+E(f4(x161,x163,x164),f4(x162,x163,x164))
% 12.04/12.18 [17]~E(x171,x172)+E(f4(x173,x171,x174),f4(x173,x172,x174))
% 12.04/12.18 [18]~E(x181,x182)+E(f4(x183,x184,x181),f4(x183,x184,x182))
% 12.04/12.18 [19]~E(x191,x192)+E(f16(x191,x193,x194),f16(x192,x193,x194))
% 12.04/12.18 [20]~E(x201,x202)+E(f16(x203,x201,x204),f16(x203,x202,x204))
% 12.04/12.18 [21]~E(x211,x212)+E(f16(x213,x214,x211),f16(x213,x214,x212))
% 12.04/12.18 [22]~E(x221,x222)+E(f7(x221,x223,x224),f7(x222,x223,x224))
% 12.04/12.18 [23]~E(x231,x232)+E(f7(x233,x231,x234),f7(x233,x232,x234))
% 12.04/12.18 [24]~E(x241,x242)+E(f7(x243,x244,x241),f7(x243,x244,x242))
% 12.04/12.18 [25]~E(x251,x252)+E(f10(x251),f10(x252))
% 12.04/12.18 [26]~E(x261,x262)+E(f11(x261,x263,x264),f11(x262,x263,x264))
% 12.04/12.18 [27]~E(x271,x272)+E(f11(x273,x271,x274),f11(x273,x272,x274))
% 12.04/12.18 [28]~E(x281,x282)+E(f11(x283,x284,x281),f11(x283,x284,x282))
% 12.04/12.18 [29]~E(x291,x292)+E(f9(x291,x293),f9(x292,x293))
% 12.04/12.18 [30]~E(x301,x302)+E(f9(x303,x301),f9(x303,x302))
% 12.04/12.18 [31]~E(x311,x312)+E(f59(x311,x313,x314,x315),f59(x312,x313,x314,x315))
% 12.04/12.18 [32]~E(x321,x322)+E(f59(x323,x321,x324,x325),f59(x323,x322,x324,x325))
% 12.04/12.18 [33]~E(x331,x332)+E(f59(x333,x334,x331,x335),f59(x333,x334,x332,x335))
% 12.04/12.18 [34]~E(x341,x342)+E(f59(x343,x344,x345,x341),f59(x343,x344,x345,x342))
% 12.04/12.18 [35]~E(x351,x352)+E(f39(x351,x353,x354),f39(x352,x353,x354))
% 12.04/12.18 [36]~E(x361,x362)+E(f39(x363,x361,x364),f39(x363,x362,x364))
% 12.04/12.18 [37]~E(x371,x372)+E(f39(x373,x374,x371),f39(x373,x374,x372))
% 12.04/12.18 [38]~E(x381,x382)+E(f26(x381,x383),f26(x382,x383))
% 12.04/12.18 [39]~E(x391,x392)+E(f26(x393,x391),f26(x393,x392))
% 12.04/12.18 [40]~E(x401,x402)+E(f31(x401),f31(x402))
% 12.04/12.18 [41]~E(x411,x412)+E(f75(x411,x413),f75(x412,x413))
% 12.04/12.18 [42]~E(x421,x422)+E(f75(x423,x421),f75(x423,x422))
% 12.04/12.18 [43]~E(x431,x432)+E(f14(x431),f14(x432))
% 12.04/12.18 [44]~E(x441,x442)+E(f21(x441,x443),f21(x442,x443))
% 12.04/12.18 [45]~E(x451,x452)+E(f21(x453,x451),f21(x453,x452))
% 12.04/12.18 [46]~E(x461,x462)+E(f19(x461,x463,x464),f19(x462,x463,x464))
% 12.04/12.18 [47]~E(x471,x472)+E(f19(x473,x471,x474),f19(x473,x472,x474))
% 12.04/12.18 [48]~E(x481,x482)+E(f19(x483,x484,x481),f19(x483,x484,x482))
% 12.04/12.18 [49]~E(x491,x492)+E(f23(x491,x493,x494),f23(x492,x493,x494))
% 12.04/12.18 [50]~E(x501,x502)+E(f23(x503,x501,x504),f23(x503,x502,x504))
% 12.04/12.18 [51]~E(x511,x512)+E(f23(x513,x514,x511),f23(x513,x514,x512))
% 12.04/12.18 [52]~E(x521,x522)+E(f60(x521),f60(x522))
% 12.04/12.18 [53]~E(x531,x532)+E(f48(x531,x533,x534),f48(x532,x533,x534))
% 12.04/12.18 [54]~E(x541,x542)+E(f48(x543,x541,x544),f48(x543,x542,x544))
% 12.04/12.18 [55]~E(x551,x552)+E(f48(x553,x554,x551),f48(x553,x554,x552))
% 12.04/12.18 [56]~E(x561,x562)+E(f42(x561,x563,x564),f42(x562,x563,x564))
% 12.04/12.18 [57]~E(x571,x572)+E(f42(x573,x571,x574),f42(x573,x572,x574))
% 12.04/12.18 [58]~E(x581,x582)+E(f42(x583,x584,x581),f42(x583,x584,x582))
% 12.04/12.18 [59]~E(x591,x592)+E(f30(x591,x593),f30(x592,x593))
% 12.04/12.18 [60]~E(x601,x602)+E(f30(x603,x601),f30(x603,x602))
% 12.04/12.18 [61]~E(x611,x612)+E(f54(x611,x613),f54(x612,x613))
% 12.04/12.18 [62]~E(x621,x622)+E(f54(x623,x621),f54(x623,x622))
% 12.04/12.18 [63]~E(x631,x632)+E(f28(x631,x633),f28(x632,x633))
% 12.04/12.18 [64]~E(x641,x642)+E(f28(x643,x641),f28(x643,x642))
% 12.04/12.18 [65]~E(x651,x652)+E(f51(x651,x653,x654),f51(x652,x653,x654))
% 12.04/12.18 [66]~E(x661,x662)+E(f51(x663,x661,x664),f51(x663,x662,x664))
% 12.04/12.18 [67]~E(x671,x672)+E(f51(x673,x674,x671),f51(x673,x674,x672))
% 12.04/12.18 [68]~E(x681,x682)+E(f35(x681,x683,x684),f35(x682,x683,x684))
% 12.04/12.18 [69]~E(x691,x692)+E(f35(x693,x691,x694),f35(x693,x692,x694))
% 12.04/12.18 [70]~E(x701,x702)+E(f35(x703,x704,x701),f35(x703,x704,x702))
% 12.04/12.18 [71]~E(x711,x712)+E(f49(x711,x713),f49(x712,x713))
% 12.04/12.18 [72]~E(x721,x722)+E(f49(x723,x721),f49(x723,x722))
% 12.04/12.18 [73]~E(x731,x732)+E(f22(x731,x733,x734),f22(x732,x733,x734))
% 12.04/12.18 [74]~E(x741,x742)+E(f22(x743,x741,x744),f22(x743,x742,x744))
% 12.04/12.18 [75]~E(x751,x752)+E(f22(x753,x754,x751),f22(x753,x754,x752))
% 12.04/12.18 [76]~E(x761,x762)+E(f32(x761,x763),f32(x762,x763))
% 12.04/12.18 [77]~E(x771,x772)+E(f32(x773,x771),f32(x773,x772))
% 12.04/12.18 [78]~E(x781,x782)+E(f38(x781,x783),f38(x782,x783))
% 12.04/12.18 [79]~E(x791,x792)+E(f38(x793,x791),f38(x793,x792))
% 12.04/12.18 [80]~E(x801,x802)+E(f65(x801,x803),f65(x802,x803))
% 12.04/12.18 [81]~E(x811,x812)+E(f65(x813,x811),f65(x813,x812))
% 12.04/12.18 [82]~E(x821,x822)+E(f50(x821,x823),f50(x822,x823))
% 12.04/12.18 [83]~E(x831,x832)+E(f50(x833,x831),f50(x833,x832))
% 12.04/12.18 [84]~E(x841,x842)+E(f52(x841,x843),f52(x842,x843))
% 12.04/12.18 [85]~E(x851,x852)+E(f52(x853,x851),f52(x853,x852))
% 12.04/12.18 [86]~E(x861,x862)+E(f61(x861),f61(x862))
% 12.04/12.18 [87]~E(x871,x872)+E(f66(x871,x873),f66(x872,x873))
% 12.04/12.18 [88]~E(x881,x882)+E(f66(x883,x881),f66(x883,x882))
% 12.04/12.18 [89]~E(x891,x892)+E(f62(x891,x893),f62(x892,x893))
% 12.04/12.18 [90]~E(x901,x902)+E(f62(x903,x901),f62(x903,x902))
% 12.04/12.18 [91]~E(x911,x912)+E(f67(x911,x913),f67(x912,x913))
% 12.04/12.18 [92]~E(x921,x922)+E(f67(x923,x921),f67(x923,x922))
% 12.04/12.18 [93]~E(x931,x932)+E(f45(x931,x933),f45(x932,x933))
% 12.04/12.18 [94]~E(x941,x942)+E(f45(x943,x941),f45(x943,x942))
% 12.04/12.18 [95]~E(x951,x952)+E(f34(x951,x953),f34(x952,x953))
% 12.04/12.18 [96]~E(x961,x962)+E(f34(x963,x961),f34(x963,x962))
% 12.04/12.18 [97]~E(x971,x972)+E(f25(x971,x973,x974),f25(x972,x973,x974))
% 12.04/12.18 [98]~E(x981,x982)+E(f25(x983,x981,x984),f25(x983,x982,x984))
% 12.04/12.18 [99]~E(x991,x992)+E(f25(x993,x994,x991),f25(x993,x994,x992))
% 12.04/12.18 [100]~E(x1001,x1002)+E(f56(x1001,x1003),f56(x1002,x1003))
% 12.04/12.18 [101]~E(x1011,x1012)+E(f56(x1013,x1011),f56(x1013,x1012))
% 12.04/12.18 [102]~E(x1021,x1022)+E(f40(x1021,x1023),f40(x1022,x1023))
% 12.04/12.18 [103]~E(x1031,x1032)+E(f40(x1033,x1031),f40(x1033,x1032))
% 12.04/12.18 [104]~E(x1041,x1042)+E(f43(x1041,x1043,x1044),f43(x1042,x1043,x1044))
% 12.04/12.18 [105]~E(x1051,x1052)+E(f43(x1053,x1051,x1054),f43(x1053,x1052,x1054))
% 12.04/12.18 [106]~E(x1061,x1062)+E(f43(x1063,x1064,x1061),f43(x1063,x1064,x1062))
% 12.04/12.18 [107]~E(x1071,x1072)+E(f46(x1071,x1073),f46(x1072,x1073))
% 12.04/12.18 [108]~E(x1081,x1082)+E(f46(x1083,x1081),f46(x1083,x1082))
% 12.04/12.18 [109]~E(x1091,x1092)+E(f63(x1091,x1093),f63(x1092,x1093))
% 12.04/12.18 [110]~E(x1101,x1102)+E(f63(x1103,x1101),f63(x1103,x1102))
% 12.04/12.18 [111]~E(x1111,x1112)+E(f20(x1111,x1113,x1114),f20(x1112,x1113,x1114))
% 12.04/12.18 [112]~E(x1121,x1122)+E(f20(x1123,x1121,x1124),f20(x1123,x1122,x1124))
% 12.04/12.18 [113]~E(x1131,x1132)+E(f20(x1133,x1134,x1131),f20(x1133,x1134,x1132))
% 12.04/12.18 [114]~E(x1141,x1142)+E(f15(x1141,x1143,x1144),f15(x1142,x1143,x1144))
% 12.04/12.18 [115]~E(x1151,x1152)+E(f15(x1153,x1151,x1154),f15(x1153,x1152,x1154))
% 12.04/12.18 [116]~E(x1161,x1162)+E(f15(x1163,x1164,x1161),f15(x1163,x1164,x1162))
% 12.04/12.18 [117]~E(x1171,x1172)+E(f17(x1171,x1173),f17(x1172,x1173))
% 12.04/12.18 [118]~E(x1181,x1182)+E(f17(x1183,x1181),f17(x1183,x1182))
% 12.04/12.18 [119]~E(x1191,x1192)+E(f41(x1191,x1193),f41(x1192,x1193))
% 12.04/12.18 [120]~E(x1201,x1202)+E(f41(x1203,x1201),f41(x1203,x1202))
% 12.04/12.18 [121]~E(x1211,x1212)+E(f58(x1211,x1213),f58(x1212,x1213))
% 12.04/12.18 [122]~E(x1221,x1222)+E(f58(x1223,x1221),f58(x1223,x1222))
% 12.04/12.18 [123]~E(x1231,x1232)+E(f57(x1231,x1233,x1234),f57(x1232,x1233,x1234))
% 12.04/12.18 [124]~E(x1241,x1242)+E(f57(x1243,x1241,x1244),f57(x1243,x1242,x1244))
% 12.04/12.18 [125]~E(x1251,x1252)+E(f57(x1253,x1254,x1251),f57(x1253,x1254,x1252))
% 12.04/12.18 [126]~E(x1261,x1262)+E(f64(x1261,x1263,x1264,x1265),f64(x1262,x1263,x1264,x1265))
% 12.04/12.18 [127]~E(x1271,x1272)+E(f64(x1273,x1271,x1274,x1275),f64(x1273,x1272,x1274,x1275))
% 12.04/12.18 [128]~E(x1281,x1282)+E(f64(x1283,x1284,x1281,x1285),f64(x1283,x1284,x1282,x1285))
% 12.04/12.18 [129]~E(x1291,x1292)+E(f64(x1293,x1294,x1295,x1291),f64(x1293,x1294,x1295,x1292))
% 12.04/12.18 [130]~E(x1301,x1302)+E(f24(x1301,x1303,x1304,x1305,x1306),f24(x1302,x1303,x1304,x1305,x1306))
% 12.04/12.18 [131]~E(x1311,x1312)+E(f24(x1313,x1311,x1314,x1315,x1316),f24(x1313,x1312,x1314,x1315,x1316))
% 12.04/12.18 [132]~E(x1321,x1322)+E(f24(x1323,x1324,x1321,x1325,x1326),f24(x1323,x1324,x1322,x1325,x1326))
% 12.04/12.18 [133]~E(x1331,x1332)+E(f24(x1333,x1334,x1335,x1331,x1336),f24(x1333,x1334,x1335,x1332,x1336))
% 12.04/12.18 [134]~E(x1341,x1342)+E(f24(x1343,x1344,x1345,x1346,x1341),f24(x1343,x1344,x1345,x1346,x1342))
% 12.04/12.18 [135]~E(x1351,x1352)+E(f6(x1351,x1353),f6(x1352,x1353))
% 12.04/12.18 [136]~E(x1361,x1362)+E(f6(x1363,x1361),f6(x1363,x1362))
% 12.04/12.18 [137]~E(x1371,x1372)+E(f53(x1371,x1373,x1374),f53(x1372,x1373,x1374))
% 12.04/12.18 [138]~E(x1381,x1382)+E(f53(x1383,x1381,x1384),f53(x1383,x1382,x1384))
% 12.04/12.18 [139]~E(x1391,x1392)+E(f53(x1393,x1394,x1391),f53(x1393,x1394,x1392))
% 12.04/12.18 [140]~E(x1401,x1402)+E(f36(x1401,x1403),f36(x1402,x1403))
% 12.04/12.18 [141]~E(x1411,x1412)+E(f36(x1413,x1411),f36(x1413,x1412))
% 12.04/12.18 [142]~E(x1421,x1422)+E(f55(x1421,x1423,x1424),f55(x1422,x1423,x1424))
% 12.04/12.18 [143]~E(x1431,x1432)+E(f55(x1433,x1431,x1434),f55(x1433,x1432,x1434))
% 12.04/12.18 [144]~E(x1441,x1442)+E(f55(x1443,x1444,x1441),f55(x1443,x1444,x1442))
% 12.04/12.18 [145]~E(x1451,x1452)+E(f37(x1451),f37(x1452))
% 12.04/12.18 [146]~E(x1461,x1462)+E(f18(x1461,x1463,x1464,x1465),f18(x1462,x1463,x1464,x1465))
% 12.04/12.18 [147]~E(x1471,x1472)+E(f18(x1473,x1471,x1474,x1475),f18(x1473,x1472,x1474,x1475))
% 12.04/12.18 [148]~E(x1481,x1482)+E(f18(x1483,x1484,x1481,x1485),f18(x1483,x1484,x1482,x1485))
% 12.04/12.18 [149]~E(x1491,x1492)+E(f18(x1493,x1494,x1495,x1491),f18(x1493,x1494,x1495,x1492))
% 12.04/12.18 [150]~E(x1501,x1502)+E(f44(x1501,x1503),f44(x1502,x1503))
% 12.04/12.18 [151]~E(x1511,x1512)+E(f44(x1513,x1511),f44(x1513,x1512))
% 12.04/12.18 [152]~E(x1521,x1522)+E(f47(x1521),f47(x1522))
% 12.04/12.18 [153]~E(x1531,x1532)+E(f33(x1531),f33(x1532))
% 12.04/12.18 [154]~P1(x1541)+P1(x1542)+~E(x1541,x1542)
% 12.04/12.18 [155]P12(x1552,x1553,x1554)+~E(x1551,x1552)+~P12(x1551,x1553,x1554)
% 12.04/12.18 [156]P12(x1563,x1562,x1564)+~E(x1561,x1562)+~P12(x1563,x1561,x1564)
% 12.04/12.18 [157]P12(x1573,x1574,x1572)+~E(x1571,x1572)+~P12(x1573,x1574,x1571)
% 12.04/12.18 [158]~P2(x1581)+P2(x1582)+~E(x1581,x1582)
% 12.04/12.18 [159]~P47(x1591)+P47(x1592)+~E(x1591,x1592)
% 12.04/12.18 [160]P11(x1602,x1603,x1604)+~E(x1601,x1602)+~P11(x1601,x1603,x1604)
% 12.04/12.18 [161]P11(x1613,x1612,x1614)+~E(x1611,x1612)+~P11(x1613,x1611,x1614)
% 12.04/12.18 [162]P11(x1623,x1624,x1622)+~E(x1621,x1622)+~P11(x1623,x1624,x1621)
% 12.04/12.18 [163]~P37(x1631)+P37(x1632)+~E(x1631,x1632)
% 12.04/12.18 [164]~P53(x1641)+P53(x1642)+~E(x1641,x1642)
% 12.04/12.18 [165]P13(x1652,x1653,x1654)+~E(x1651,x1652)+~P13(x1651,x1653,x1654)
% 12.04/12.18 [166]P13(x1663,x1662,x1664)+~E(x1661,x1662)+~P13(x1663,x1661,x1664)
% 12.04/12.18 [167]P13(x1673,x1674,x1672)+~E(x1671,x1672)+~P13(x1673,x1674,x1671)
% 12.04/12.18 [168]~P60(x1681)+P60(x1682)+~E(x1681,x1682)
% 12.04/12.18 [169]~P41(x1691)+P41(x1692)+~E(x1691,x1692)
% 12.04/12.18 [170]~P3(x1701)+P3(x1702)+~E(x1701,x1702)
% 12.04/12.18 [171]~P4(x1711)+P4(x1712)+~E(x1711,x1712)
% 12.04/12.18 [172]~P30(x1721)+P30(x1722)+~E(x1721,x1722)
% 12.04/12.18 [173]P14(x1732,x1733)+~E(x1731,x1732)+~P14(x1731,x1733)
% 12.04/12.18 [174]P14(x1743,x1742)+~E(x1741,x1742)+~P14(x1743,x1741)
% 12.04/12.18 [175]~P17(x1751)+P17(x1752)+~E(x1751,x1752)
% 12.04/12.18 [176]~P23(x1761)+P23(x1762)+~E(x1761,x1762)
% 12.04/12.18 [177]~P33(x1771)+P33(x1772)+~E(x1771,x1772)
% 12.04/12.18 [178]~P18(x1781)+P18(x1782)+~E(x1781,x1782)
% 12.04/12.18 [179]~P43(x1791)+P43(x1792)+~E(x1791,x1792)
% 12.04/12.18 [180]~P42(x1801)+P42(x1802)+~E(x1801,x1802)
% 12.04/12.18 [181]~P26(x1811)+P26(x1812)+~E(x1811,x1812)
% 12.04/12.18 [182]~P31(x1821)+P31(x1822)+~E(x1821,x1822)
% 12.04/12.18 [183]~P38(x1831)+P38(x1832)+~E(x1831,x1832)
% 12.04/12.18 [184]~P40(x1841)+P40(x1842)+~E(x1841,x1842)
% 12.04/12.18 [185]~P19(x1851)+P19(x1852)+~E(x1851,x1852)
% 12.04/12.18 [186]~P51(x1861)+P51(x1862)+~E(x1861,x1862)
% 12.04/12.18 [187]~P7(x1871)+P7(x1872)+~E(x1871,x1872)
% 12.04/12.18 [188]~P65(x1881)+P65(x1882)+~E(x1881,x1882)
% 12.04/12.18 [189]~P20(x1891)+P20(x1892)+~E(x1891,x1892)
% 12.04/12.18 [190]~P68(x1901)+P68(x1902)+~E(x1901,x1902)
% 12.04/12.18 [191]~P29(x1911)+P29(x1912)+~E(x1911,x1912)
% 12.04/12.18 [192]~P61(x1921)+P61(x1922)+~E(x1921,x1922)
% 12.04/12.18 [193]~P49(x1931)+P49(x1932)+~E(x1931,x1932)
% 12.04/12.18 [194]~P52(x1941)+P52(x1942)+~E(x1941,x1942)
% 12.04/12.18 [195]~P34(x1951)+P34(x1952)+~E(x1951,x1952)
% 12.04/12.18 [196]~P9(x1961)+P9(x1962)+~E(x1961,x1962)
% 12.04/12.18 [197]~P27(x1971)+P27(x1972)+~E(x1971,x1972)
% 12.04/12.18 [198]~P8(x1981)+P8(x1982)+~E(x1981,x1982)
% 12.04/12.18 [199]~P10(x1991)+P10(x1992)+~E(x1991,x1992)
% 12.04/12.18 [200]~P32(x2001)+P32(x2002)+~E(x2001,x2002)
% 12.04/12.18 [201]~P46(x2011)+P46(x2012)+~E(x2011,x2012)
% 12.04/12.18 [202]~P45(x2021)+P45(x2022)+~E(x2021,x2022)
% 12.04/12.18 [203]~P55(x2031)+P55(x2032)+~E(x2031,x2032)
% 12.04/12.18 [204]~P21(x2041)+P21(x2042)+~E(x2041,x2042)
% 12.04/12.18 [205]~P6(x2051)+P6(x2052)+~E(x2051,x2052)
% 12.04/12.18 [206]~P25(x2061)+P25(x2062)+~E(x2061,x2062)
% 12.04/12.18 [207]~P66(x2071)+P66(x2072)+~E(x2071,x2072)
% 12.04/12.18 [208]~P62(x2081)+P62(x2082)+~E(x2081,x2082)
% 12.04/12.18 [209]~P24(x2091)+P24(x2092)+~E(x2091,x2092)
% 12.04/12.18 [210]~P63(x2101)+P63(x2102)+~E(x2101,x2102)
% 12.04/12.18 [211]~P48(x2111)+P48(x2112)+~E(x2111,x2112)
% 12.04/12.18 [212]~P58(x2121)+P58(x2122)+~E(x2121,x2122)
% 12.04/12.18 [213]~P16(x2131)+P16(x2132)+~E(x2131,x2132)
% 12.04/12.18 [214]~P54(x2141)+P54(x2142)+~E(x2141,x2142)
% 12.04/12.18 [215]~P5(x2151)+P5(x2152)+~E(x2151,x2152)
% 12.04/12.18 [216]~P57(x2161)+P57(x2162)+~E(x2161,x2162)
% 12.04/12.18 [217]~P22(x2171)+P22(x2172)+~E(x2171,x2172)
% 12.04/12.18 [218]~P59(x2181)+P59(x2182)+~E(x2181,x2182)
% 12.04/12.18 [219]~P56(x2191)+P56(x2192)+~E(x2191,x2192)
% 12.04/12.18 [220]~P44(x2201)+P44(x2202)+~E(x2201,x2202)
% 12.04/12.18 [221]~P64(x2211)+P64(x2212)+~E(x2211,x2212)
% 12.04/12.18 [222]~P39(x2221)+P39(x2222)+~E(x2221,x2222)
% 12.04/12.18 [223]~P36(x2231)+P36(x2232)+~E(x2231,x2232)
% 12.04/12.18 [224]~P28(x2241)+P28(x2242)+~E(x2241,x2242)
% 12.04/12.18 [225]~P67(x2251)+P67(x2252)+~E(x2251,x2252)
% 12.04/12.18 [226]~P50(x2261)+P50(x2262)+~E(x2261,x2262)
% 12.04/12.18 [227]~P35(x2271)+P35(x2272)+~E(x2271,x2272)
% 12.04/12.18 [228]~P15(x2281)+P15(x2282)+~E(x2281,x2282)
% 12.04/12.18
% 12.04/12.18 %-------------------------------------------
% 12.04/12.20 cnf(1826,plain,
% 12.04/12.20 (P13(a69,f3(a69),x18261)),
% 12.04/12.20 inference(rename_variables,[],[449])).
% 12.04/12.20 cnf(1829,plain,
% 12.04/12.20 (~P12(a69,f11(a69,x18291,x18292),x18292)),
% 12.04/12.20 inference(rename_variables,[],[565])).
% 12.04/12.20 cnf(1832,plain,
% 12.04/12.20 (E(f11(a69,x18321,x18322),f11(a69,x18322,x18321))),
% 12.04/12.20 inference(rename_variables,[],[470])).
% 12.04/12.20 cnf(1835,plain,
% 12.04/12.20 (P11(a69,x18351,f11(a69,x18352,x18351))),
% 12.04/12.20 inference(rename_variables,[],[482])).
% 12.04/12.20 cnf(1840,plain,
% 12.04/12.20 (P11(a70,x18401,x18401)),
% 12.04/12.20 inference(rename_variables,[],[439])).
% 12.04/12.20 cnf(1843,plain,
% 12.04/12.20 (P11(a69,x18431,f11(a69,x18432,x18431))),
% 12.04/12.20 inference(rename_variables,[],[482])).
% 12.04/12.20 cnf(1846,plain,
% 12.04/12.20 (P11(a70,x18461,x18461)),
% 12.04/12.20 inference(rename_variables,[],[439])).
% 12.04/12.20 cnf(1851,plain,
% 12.04/12.20 (E(f11(a69,x18511,x18512),f11(a69,x18512,x18511))),
% 12.04/12.20 inference(rename_variables,[],[470])).
% 12.04/12.20 cnf(1854,plain,
% 12.04/12.20 (P12(a69,x18541,f11(a69,f11(a69,x18542,x18541),f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[525])).
% 12.04/12.20 cnf(1857,plain,
% 12.04/12.20 (P11(a69,x18571,f11(a69,x18572,x18571))),
% 12.04/12.20 inference(rename_variables,[],[482])).
% 12.04/12.20 cnf(1860,plain,
% 12.04/12.20 (P11(a69,x18601,f11(a69,x18602,x18601))),
% 12.04/12.20 inference(rename_variables,[],[482])).
% 12.04/12.20 cnf(1863,plain,
% 12.04/12.20 (~P12(a69,f11(a69,x18631,x18632),x18631)),
% 12.04/12.20 inference(rename_variables,[],[566])).
% 12.04/12.20 cnf(1868,plain,
% 12.04/12.20 (~P12(a69,f11(a69,x18681,x18682),x18682)),
% 12.04/12.20 inference(rename_variables,[],[565])).
% 12.04/12.20 cnf(1871,plain,
% 12.04/12.20 (~P12(a69,f11(a69,x18711,x18712),x18712)),
% 12.04/12.20 inference(rename_variables,[],[565])).
% 12.04/12.20 cnf(1874,plain,
% 12.04/12.20 (~P11(a69,f11(a69,x18741,f3(a69)),x18741)),
% 12.04/12.20 inference(rename_variables,[],[567])).
% 12.04/12.20 cnf(1877,plain,
% 12.04/12.20 (~P11(a69,f11(a69,x18771,f3(a69)),x18771)),
% 12.04/12.20 inference(rename_variables,[],[567])).
% 12.04/12.20 cnf(1886,plain,
% 12.04/12.20 (E(f12(f26(a69,x18861)),x18861)),
% 12.04/12.20 inference(rename_variables,[],[431])).
% 12.04/12.20 cnf(1889,plain,
% 12.04/12.20 (~E(f11(a69,x18891,f3(a69)),x18891)),
% 12.04/12.20 inference(rename_variables,[],[556])).
% 12.04/12.20 cnf(1903,plain,
% 12.04/12.20 (P11(a68,x19031,f26(a69,f13(x19031)))),
% 12.04/12.20 inference(rename_variables,[],[466])).
% 12.04/12.20 cnf(1906,plain,
% 12.04/12.20 (P12(a68,x19061,f11(a68,f26(a69,f12(x19061)),f3(a68)))),
% 12.04/12.20 inference(rename_variables,[],[500])).
% 12.04/12.20 cnf(1909,plain,
% 12.04/12.20 (P11(a69,x19091,x19091)),
% 12.04/12.20 inference(rename_variables,[],[438])).
% 12.04/12.20 cnf(1916,plain,
% 12.04/12.20 (P11(a68,x19161,f26(a69,f13(x19161)))),
% 12.04/12.20 inference(rename_variables,[],[466])).
% 12.04/12.20 cnf(1919,plain,
% 12.04/12.20 (P11(a68,x19191,x19191)),
% 12.04/12.20 inference(rename_variables,[],[437])).
% 12.04/12.20 cnf(1922,plain,
% 12.04/12.20 (P11(a68,x19221,f26(a69,f13(x19221)))),
% 12.04/12.20 inference(rename_variables,[],[466])).
% 12.04/12.20 cnf(1925,plain,
% 12.04/12.20 (~E(f11(a69,x19251,f3(a69)),f2(a69))),
% 12.04/12.20 inference(rename_variables,[],[563])).
% 12.04/12.20 cnf(1928,plain,
% 12.04/12.20 (E(f4(a69,f11(a69,x19281,x19282),x19282),x19281)),
% 12.04/12.20 inference(rename_variables,[],[485])).
% 12.04/12.20 cnf(1933,plain,
% 12.04/12.20 (~E(f11(a69,x19331,f3(a69)),f2(a69))),
% 12.04/12.20 inference(rename_variables,[],[563])).
% 12.04/12.20 cnf(1936,plain,
% 12.04/12.20 (~E(f11(a69,x19361,f3(a69)),f2(a69))),
% 12.04/12.20 inference(rename_variables,[],[563])).
% 12.04/12.20 cnf(1939,plain,
% 12.04/12.20 (P12(a68,x19391,f11(a68,f26(a69,f12(x19391)),f3(a68)))),
% 12.04/12.20 inference(rename_variables,[],[500])).
% 12.04/12.20 cnf(1942,plain,
% 12.04/12.20 (~P12(a69,x19421,x19421)),
% 12.04/12.20 inference(rename_variables,[],[551])).
% 12.04/12.20 cnf(1945,plain,
% 12.04/12.20 (~P12(a69,x19451,x19451)),
% 12.04/12.20 inference(rename_variables,[],[551])).
% 12.04/12.20 cnf(1948,plain,
% 12.04/12.20 (~P11(a69,f11(a69,x19481,f3(a69)),x19481)),
% 12.04/12.20 inference(rename_variables,[],[567])).
% 12.04/12.20 cnf(1951,plain,
% 12.04/12.20 (E(f12(f26(a69,x19511)),x19511)),
% 12.04/12.20 inference(rename_variables,[],[431])).
% 12.04/12.20 cnf(1953,plain,
% 12.04/12.20 (E(f12(f26(a69,x19531)),x19531)),
% 12.04/12.20 inference(rename_variables,[],[431])).
% 12.04/12.20 cnf(1955,plain,
% 12.04/12.20 (E(f12(f26(a69,x19551)),x19551)),
% 12.04/12.20 inference(rename_variables,[],[431])).
% 12.04/12.20 cnf(1958,plain,
% 12.04/12.20 (E(f11(a69,x19581,x19582),f11(a69,x19582,x19581))),
% 12.04/12.20 inference(rename_variables,[],[470])).
% 12.04/12.20 cnf(1960,plain,
% 12.04/12.20 (P11(a68,x19601,x19601)),
% 12.04/12.20 inference(rename_variables,[],[437])).
% 12.04/12.20 cnf(1962,plain,
% 12.04/12.20 (P11(a68,x19621,x19621)),
% 12.04/12.20 inference(rename_variables,[],[437])).
% 12.04/12.20 cnf(1965,plain,
% 12.04/12.20 (~P12(a69,x19651,x19651)),
% 12.04/12.20 inference(rename_variables,[],[551])).
% 12.04/12.20 cnf(1967,plain,
% 12.04/12.20 (~E(f11(a69,x19671,f3(a69)),x19671)),
% 12.04/12.20 inference(rename_variables,[],[556])).
% 12.04/12.20 cnf(1978,plain,
% 12.04/12.20 (P11(a69,f2(a69),x19781)),
% 12.04/12.20 inference(rename_variables,[],[448])).
% 12.04/12.20 cnf(1985,plain,
% 12.04/12.20 (P11(a69,f2(a69),x19851)),
% 12.04/12.20 inference(rename_variables,[],[448])).
% 12.04/12.20 cnf(1992,plain,
% 12.04/12.20 (~P12(a69,x19921,f2(a69))),
% 12.04/12.20 inference(rename_variables,[],[554])).
% 12.04/12.20 cnf(2005,plain,
% 12.04/12.20 (P12(a69,x20051,f11(a69,x20051,f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[488])).
% 12.04/12.20 cnf(2006,plain,
% 12.04/12.20 (P12(a69,x20061,f11(a69,f11(a69,x20062,x20061),f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[525])).
% 12.04/12.20 cnf(2009,plain,
% 12.04/12.20 (P12(a69,x20091,f11(a69,x20091,f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[488])).
% 12.04/12.20 cnf(2010,plain,
% 12.04/12.20 (~P11(a69,f11(a69,x20101,f3(a69)),x20101)),
% 12.04/12.20 inference(rename_variables,[],[567])).
% 12.04/12.20 cnf(2013,plain,
% 12.04/12.20 (P12(a69,x20131,f11(a69,x20131,f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[488])).
% 12.04/12.20 cnf(2014,plain,
% 12.04/12.20 (~P12(a69,x20141,x20141)),
% 12.04/12.20 inference(rename_variables,[],[551])).
% 12.04/12.20 cnf(2020,plain,
% 12.04/12.20 (E(f12(f26(a69,x20201)),x20201)),
% 12.04/12.20 inference(rename_variables,[],[431])).
% 12.04/12.20 cnf(2025,plain,
% 12.04/12.20 (P12(a69,x20251,f11(a69,x20251,f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[488])).
% 12.04/12.20 cnf(2028,plain,
% 12.04/12.20 (~E(f11(a69,x20281,f3(a69)),f2(a69))),
% 12.04/12.20 inference(rename_variables,[],[563])).
% 12.04/12.20 cnf(2031,plain,
% 12.04/12.20 (P12(a69,x20311,f11(a69,x20311,f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[488])).
% 12.04/12.20 cnf(2032,plain,
% 12.04/12.20 (~P12(a69,x20321,x20321)),
% 12.04/12.20 inference(rename_variables,[],[551])).
% 12.04/12.20 cnf(2039,plain,
% 12.04/12.20 (E(f12(f26(a69,x20391)),x20391)),
% 12.04/12.20 inference(rename_variables,[],[431])).
% 12.04/12.20 cnf(2042,plain,
% 12.04/12.20 (P11(a68,x20421,x20421)),
% 12.04/12.20 inference(rename_variables,[],[437])).
% 12.04/12.20 cnf(2045,plain,
% 12.04/12.20 (P11(a68,x20451,x20451)),
% 12.04/12.20 inference(rename_variables,[],[437])).
% 12.04/12.20 cnf(2046,plain,
% 12.04/12.20 (P11(a69,x20461,x20461)),
% 12.04/12.20 inference(rename_variables,[],[438])).
% 12.04/12.20 cnf(2052,plain,
% 12.04/12.20 (P12(a69,x20521,f11(a69,x20521,f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[488])).
% 12.04/12.20 cnf(2057,plain,
% 12.04/12.20 (P12(a69,x20571,f11(a69,x20571,f3(a69)))),
% 12.04/12.20 inference(rename_variables,[],[488])).
% 12.04/12.20 cnf(2058,plain,
% 12.04/12.20 (~E(f11(a69,x20581,f3(a69)),x20581)),
% 12.04/12.20 inference(rename_variables,[],[556])).
% 12.04/12.20 cnf(2073,plain,
% 12.04/12.20 (E(f12(f26(a69,x20731)),x20731)),
% 12.04/12.20 inference(rename_variables,[],[431])).
% 12.04/12.20 cnf(2078,plain,
% 12.04/12.20 (P12(a68,x20781,f11(a68,f26(a69,f12(x20781)),f3(a68)))),
% 12.04/12.20 inference(rename_variables,[],[500])).
% 12.04/12.20 cnf(2085,plain,
% 12.04/12.20 (~P12(a69,x20851,f2(a69))),
% 12.04/12.20 inference(rename_variables,[],[554])).
% 12.04/12.20 cnf(2092,plain,
% 12.04/12.20 (~E(f11(a69,x20921,f3(a69)),x20921)),
% 12.04/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2102,plain,
% 12.38/12.20 (~E(f11(a69,x21021,f3(a69)),x21021)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2103,plain,
% 12.38/12.20 (P11(a69,f2(a69),x21031)),
% 12.38/12.20 inference(rename_variables,[],[448])).
% 12.38/12.20 cnf(2148,plain,
% 12.38/12.20 (~E(f11(a69,x21481,f3(a69)),x21481)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2151,plain,
% 12.38/12.20 (~E(f11(a69,x21511,f3(a69)),x21511)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2160,plain,
% 12.38/12.20 (~E(f11(a69,x21601,f3(a69)),x21601)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2163,plain,
% 12.38/12.20 (P11(a69,x21631,x21631)),
% 12.38/12.20 inference(rename_variables,[],[438])).
% 12.38/12.20 cnf(2168,plain,
% 12.38/12.20 (~P12(a69,x21681,x21681)),
% 12.38/12.20 inference(rename_variables,[],[551])).
% 12.38/12.20 cnf(2175,plain,
% 12.38/12.20 (P11(a69,x21751,x21751)),
% 12.38/12.20 inference(rename_variables,[],[438])).
% 12.38/12.20 cnf(2176,plain,
% 12.38/12.20 (P11(a69,f2(a69),x21761)),
% 12.38/12.20 inference(rename_variables,[],[448])).
% 12.38/12.20 cnf(2187,plain,
% 12.38/12.20 (E(f11(a69,x21871,x21872),f11(a69,x21872,x21871))),
% 12.38/12.20 inference(rename_variables,[],[470])).
% 12.38/12.20 cnf(2190,plain,
% 12.38/12.20 (E(f11(a69,x21901,x21902),f11(a69,x21902,x21901))),
% 12.38/12.20 inference(rename_variables,[],[470])).
% 12.38/12.20 cnf(2198,plain,
% 12.38/12.20 (~E(f11(a69,x21981,f3(a69)),x21981)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2203,plain,
% 12.38/12.20 (P12(a69,x22031,f11(a69,f11(a69,x22031,x22032),f3(a69)))),
% 12.38/12.20 inference(rename_variables,[],[526])).
% 12.38/12.20 cnf(2211,plain,
% 12.38/12.20 (P12(a68,x22111,f11(a68,f26(a69,f12(x22111)),f3(a68)))),
% 12.38/12.20 inference(rename_variables,[],[500])).
% 12.38/12.20 cnf(2217,plain,
% 12.38/12.20 (P12(a68,x22171,f11(a68,f26(a69,f12(x22171)),f3(a68)))),
% 12.38/12.20 inference(rename_variables,[],[500])).
% 12.38/12.20 cnf(2222,plain,
% 12.38/12.20 (P11(a69,x22221,f11(a69,x22222,x22221))),
% 12.38/12.20 inference(rename_variables,[],[482])).
% 12.38/12.20 cnf(2228,plain,
% 12.38/12.20 (~P12(a69,x22281,f2(a69))),
% 12.38/12.20 inference(rename_variables,[],[554])).
% 12.38/12.20 cnf(2231,plain,
% 12.38/12.20 (~P12(a69,x22311,f2(a69))),
% 12.38/12.20 inference(rename_variables,[],[554])).
% 12.38/12.20 cnf(2242,plain,
% 12.38/12.20 (P11(a69,f2(a69),x22421)),
% 12.38/12.20 inference(rename_variables,[],[448])).
% 12.38/12.20 cnf(2243,plain,
% 12.38/12.20 (P11(a69,x22431,x22431)),
% 12.38/12.20 inference(rename_variables,[],[438])).
% 12.38/12.20 cnf(2246,plain,
% 12.38/12.20 (P12(a69,x22461,f11(a69,x22461,f3(a69)))),
% 12.38/12.20 inference(rename_variables,[],[488])).
% 12.38/12.20 cnf(2249,plain,
% 12.38/12.20 (P11(a69,f2(a69),x22491)),
% 12.38/12.20 inference(rename_variables,[],[448])).
% 12.38/12.20 cnf(2253,plain,
% 12.38/12.20 (P12(a69,x22531,f11(a69,x22531,f3(a69)))),
% 12.38/12.20 inference(rename_variables,[],[488])).
% 12.38/12.20 cnf(2256,plain,
% 12.38/12.20 (P11(a69,x22561,x22561)),
% 12.38/12.20 inference(rename_variables,[],[438])).
% 12.38/12.20 cnf(2259,plain,
% 12.38/12.20 (P11(a69,x22591,x22591)),
% 12.38/12.20 inference(rename_variables,[],[438])).
% 12.38/12.20 cnf(2262,plain,
% 12.38/12.20 (P12(a69,x22621,f11(a69,x22621,f3(a69)))),
% 12.38/12.20 inference(rename_variables,[],[488])).
% 12.38/12.20 cnf(2273,plain,
% 12.38/12.20 (E(f12(f26(a69,x22731)),x22731)),
% 12.38/12.20 inference(rename_variables,[],[431])).
% 12.38/12.20 cnf(2279,plain,
% 12.38/12.20 (~E(f11(a69,x22791,f3(a69)),x22791)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2282,plain,
% 12.38/12.20 (~E(f11(a69,x22821,f3(a69)),x22821)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2285,plain,
% 12.38/12.20 (~E(f11(a69,x22851,f3(a69)),x22851)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2289,plain,
% 12.38/12.20 (~E(f11(a69,x22891,f3(a69)),x22891)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2293,plain,
% 12.38/12.20 (~E(f11(a69,x22931,f3(a69)),x22931)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2294,plain,
% 12.38/12.20 (P13(a69,f11(a69,f2(a69),f3(a69)),x22941)),
% 12.38/12.20 inference(rename_variables,[],[491])).
% 12.38/12.20 cnf(2301,plain,
% 12.38/12.20 (~E(f11(a69,x23011,f3(a69)),x23011)),
% 12.38/12.20 inference(rename_variables,[],[556])).
% 12.38/12.20 cnf(2333,plain,
% 12.38/12.20 (P11(a68,x23331,f29(a1,f61(x23331)))),
% 12.38/12.20 inference(scs_inference,[],[543,437,1919,1960,1962,2042,2045,438,1909,2046,2163,2175,2243,2256,2259,439,1840,1846,440,551,1942,1945,1965,2014,2032,2168,231,232,233,234,235,243,244,247,249,257,258,262,266,268,269,270,271,275,276,292,293,295,296,297,301,302,316,317,318,319,320,356,358,359,371,411,415,417,446,448,1978,1985,2103,2176,2242,2249,449,1826,554,1992,2085,2228,2231,544,458,459,546,547,491,2294,424,425,426,557,482,1835,1843,1857,1860,2222,484,565,1829,1868,1871,566,1863,470,1832,1851,1958,2187,2190,465,464,564,431,1886,1951,1953,1955,2020,2039,2073,2273,466,1903,1916,1922,488,2005,2009,2013,2025,2031,2052,2057,2246,2253,2262,567,1874,1877,1948,2010,485,1928,486,453,556,1889,1967,2058,2092,2102,2148,2151,2160,2198,2279,2282,2285,2289,2293,2301,525,1854,2006,526,2203,502,480,487,563,1925,1933,1936,2028,434,500,1906,1939,2078,2211,2217,503,568,468,2,787,760,759,754,773,1296,941,895,1332,1331,1262,1260,1256,1255,1251,1241,1240,1239,1147,1132,1130,1128,1126,1124,1065,936,876,763,671,1165,28,1563,1548,1547,1458,1457,1355,1345,1047,1046,972,971,944,885,1140,1138,783,1300,1434,1432,1431,225,204,187,167,166,162,161,157,156,3,982,981,980,948,947,899,897,883,880,840,826,800,799,688,686,1175,1174,1080,1090,1337,1320,1318,1317,695,1392,1253,1252,894,1192,1178,1488,1244,823,1330,1490,1026,1024,1023,809,649,648,640,1571,1569,1294,1181,1062,1058,651,1575,1574,1076,1075,1045,1043,1042,1020,1018,854,853,646,645,637,636,1312,1311,1310,1309,1308,1016,967,815,837,836,835,772,771,1551,1424,1801,1800,1799,1798,1791,1790,1789,1788,1758,1757,1745,1744,1808,1743,1742,1105,1104,1103,1102,1101,1100,1099,1098,1097,996,913,907,905,855,1335,1319,1354,1353,1352,1351,1350,1511,1510,1509,1508,1139,1225,1323,1322,860,1600,1115,1202,1549,873,872,867,822,821,680,679,669,665,662,786,785,673,1194,765])).
% 12.38/12.20 cnf(2334,plain,
% 12.38/12.20 (~P11(a68,f11(a68,a78,f29(a1,a76)),f29(a1,f27(f21(a1,f16(a1,a74,a73)),f61(x23341))))),
% 12.38/12.20 inference(scs_inference,[],[543,437,1919,1960,1962,2042,2045,438,1909,2046,2163,2175,2243,2256,2259,439,1840,1846,440,551,1942,1945,1965,2014,2032,2168,231,232,233,234,235,243,244,247,249,257,258,262,266,268,269,270,271,275,276,292,293,295,296,297,301,302,316,317,318,319,320,356,358,359,371,411,415,417,446,448,1978,1985,2103,2176,2242,2249,449,1826,554,1992,2085,2228,2231,544,458,459,546,547,491,2294,424,425,426,557,482,1835,1843,1857,1860,2222,484,565,1829,1868,1871,566,1863,470,1832,1851,1958,2187,2190,465,464,564,431,1886,1951,1953,1955,2020,2039,2073,2273,466,1903,1916,1922,488,2005,2009,2013,2025,2031,2052,2057,2246,2253,2262,567,1874,1877,1948,2010,485,1928,486,453,556,1889,1967,2058,2092,2102,2148,2151,2160,2198,2279,2282,2285,2289,2293,2301,525,1854,2006,526,2203,502,480,487,563,1925,1933,1936,2028,434,500,1906,1939,2078,2211,2217,503,568,468,2,787,760,759,754,773,1296,941,895,1332,1331,1262,1260,1256,1255,1251,1241,1240,1239,1147,1132,1130,1128,1126,1124,1065,936,876,763,671,1165,28,1563,1548,1547,1458,1457,1355,1345,1047,1046,972,971,944,885,1140,1138,783,1300,1434,1432,1431,225,204,187,167,166,162,161,157,156,3,982,981,980,948,947,899,897,883,880,840,826,800,799,688,686,1175,1174,1080,1090,1337,1320,1318,1317,695,1392,1253,1252,894,1192,1178,1488,1244,823,1330,1490,1026,1024,1023,809,649,648,640,1571,1569,1294,1181,1062,1058,651,1575,1574,1076,1075,1045,1043,1042,1020,1018,854,853,646,645,637,636,1312,1311,1310,1309,1308,1016,967,815,837,836,835,772,771,1551,1424,1801,1800,1799,1798,1791,1790,1789,1788,1758,1757,1745,1744,1808,1743,1742,1105,1104,1103,1102,1101,1100,1099,1098,1097,996,913,907,905,855,1335,1319,1354,1353,1352,1351,1350,1511,1510,1509,1508,1139,1225,1323,1322,860,1600,1115,1202,1549,873,872,867,822,821,680,679,669,665,662,786,785,673,1194,765,1781])).
% 12.38/12.20 cnf(4038,plain,
% 12.38/12.20 (~P11(a68,f49(x40381,x40382),f29(a1,x40383))+P11(a68,x40382,f29(a1,f27(f21(a1,f16(a1,x40381,a73)),x40383)))),
% 12.38/12.20 inference(scs_inference,[],[548,1752])).
% 12.38/12.20 cnf(4039,plain,
% 12.38/12.20 ($false),
% 12.38/12.20 inference(scs_inference,[],[2333,2334,4038]),
% 12.38/12.20 ['proof']).
% 12.38/12.20 % SZS output end Proof
% 12.38/12.20 % Total time :10.920000s
%------------------------------------------------------------------------------