TSTP Solution File: SWW229+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:14 EDT 2023
% Result : Theorem 1.20s 1.55s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 21:23:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 1.10/1.50 %-------------------------------------------
% 1.10/1.50 % File :CSE---1.6
% 1.10/1.50 % Problem :theBenchmark
% 1.10/1.50 % Transform :cnf
% 1.10/1.50 % Format :tptp:raw
% 1.10/1.50 % Command :java -jar mcs_scs.jar %d %s
% 1.10/1.50
% 1.10/1.50 % Result :Theorem 0.230000s
% 1.10/1.50 % Output :CNFRefutation 0.230000s
% 1.10/1.50 %-------------------------------------------
% 1.10/1.50 %------------------------------------------------------------------------------
% 1.10/1.50 % File : SWW229+1 : TPTP v8.1.2. Released v5.2.0.
% 1.10/1.50 % Domain : Software Verification
% 1.10/1.50 % Problem : Fundamental Theorem of Algebra 437418, 1000 axioms selected
% 1.10/1.50 % Version : Especial.
% 1.10/1.50 % English :
% 1.10/1.50
% 1.10/1.50 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 1.10/1.50 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 1.10/1.50 % Source : [Bla11]
% 1.10/1.50 % Names : fta_437418.1000.p [Bla11]
% 1.10/1.50
% 1.10/1.50 % Status : Theorem
% 1.10/1.50 % Rating : 0.31 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.23 v7.3.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0, 0.48 v5.2.0
% 1.10/1.50 % Syntax : Number of formulae : 1254 ( 392 unt; 0 def)
% 1.10/1.50 % Number of atoms : 2834 ( 743 equ)
% 1.10/1.50 % Maximal formula atoms : 8 ( 2 avg)
% 1.10/1.50 % Number of connectives : 1769 ( 189 ~; 50 |; 123 &)
% 1.10/1.50 % ( 254 <=>;1153 =>; 0 <=; 0 <~>)
% 1.10/1.50 % Maximal formula depth : 12 ( 4 avg)
% 1.10/1.50 % Maximal term depth : 8 ( 1 avg)
% 1.10/1.50 % Number of predicates : 72 ( 71 usr; 0 prp; 1-3 aty)
% 1.10/1.50 % Number of functors : 42 ( 42 usr; 16 con; 0-3 aty)
% 1.10/1.50 % Number of variables : 2381 (2349 !; 32 ?)
% 1.10/1.50 % SPC : FOF_THM_RFO_SEQ
% 1.10/1.50
% 1.10/1.50 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 1.10/1.50 % 2011-03-01 11:40:29
% 1.10/1.50 %------------------------------------------------------------------------------
% 1.10/1.50 %----Relevant facts (995)
% 1.10/1.50 fof(fact_ext,axiom,
% 1.10/1.50 ! [V_ga_2,V_fa_2] :
% 1.10/1.50 ( ! [B_x] : hAPP(V_fa_2,B_x) = hAPP(V_ga_2,B_x)
% 1.10/1.50 => V_fa_2 = V_ga_2 ) ).
% 1.10/1.50
% 1.10/1.50 fof(fact_fz_I1_J,axiom,
% 1.10/1.50 c_SEQ_Osubseq(v_f____) ).
% 1.10/1.50
% 1.10/1.50 fof(fact_g_I1_J,axiom,
% 1.10/1.50 ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(B_n)),v_r) ).
% 1.10/1.50
% 1.10/1.50 fof(fact_wr,axiom,
% 1.10/1.50 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r) ).
% 1.10/1.51
% 1.10/1.51 fof(fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096,axiom,
% 1.10/1.51 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_norm__triangle__ineq3,axiom,
% 1.10/1.51 ! [V_b,V_a,T_a] :
% 1.10/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_norm__triangle__ineq2,axiom,
% 1.10/1.51 ! [V_b,V_a,T_a] :
% 1.10/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_norm__diff__ineq,axiom,
% 1.10/1.51 ! [V_b,V_a,T_a] :
% 1.10/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.10/1.51 => 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))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_norm__diff__triangle__ineq,axiom,
% 1.10/1.51 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.10/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.10/1.51 => 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)))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_abs__triangle__ineq4,axiom,
% 1.10/1.51 ! [V_b,V_a,T_a] :
% 1.10/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_abs__diff__triangle__ineq,axiom,
% 1.10/1.51 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.10/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_norm__triangle__ineq,axiom,
% 1.10/1.51 ! [V_y,V_x,T_a] :
% 1.10/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_abs__triangle__ineq3,axiom,
% 1.10/1.51 ! [V_b,V_a,T_a] :
% 1.10/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_abs__triangle__ineq2,axiom,
% 1.10/1.51 ! [V_b,V_a,T_a] :
% 1.10/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_abs__triangle__ineq2__sym,axiom,
% 1.10/1.51 ! [V_b,V_a,T_a] :
% 1.10/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_ath2,axiom,
% 1.10/1.51 ! [V_m,V_c,V_b,V_a] :
% 1.10/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_b)),V_c)
% 1.10/1.51 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_m)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_m)),V_c)) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_rp,axiom,
% 1.10/1.51 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_real__norm__def,axiom,
% 1.10/1.51 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_complex__mod__triangle__sub,axiom,
% 1.10/1.51 ! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_norm__triangle__ineq4,axiom,
% 1.10/1.51 ! [V_b,V_a,T_a] :
% 1.10/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.10/1.51 => 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))) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_add__right__imp__eq,axiom,
% 1.10/1.51 ! [V_c,V_a,V_b,T_a] :
% 1.10/1.51 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.10/1.51 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 1.10/1.51 => V_b = V_c ) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_add__imp__eq,axiom,
% 1.10/1.51 ! [V_c,V_b,V_a,T_a] :
% 1.10/1.51 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 1.10/1.51 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.10/1.51 => V_b = V_c ) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_add__left__imp__eq,axiom,
% 1.10/1.51 ! [V_c,V_b,V_a,T_a] :
% 1.10/1.51 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.10/1.51 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.10/1.51 => V_b = V_c ) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_add__right__cancel,axiom,
% 1.10/1.51 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 1.10/1.51 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.10/1.51 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
% 1.10/1.51 <=> V_b_2 = V_c_2 ) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_add__left__cancel,axiom,
% 1.10/1.51 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 1.10/1.51 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.10/1.51 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
% 1.10/1.51 <=> V_b_2 = V_c_2 ) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.10/1.51 ! [V_c,V_b,V_a,T_a] :
% 1.10/1.51 ( class_Groups_Oab__semigroup__add(T_a)
% 1.10/1.51 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_diff__eq__diff__eq,axiom,
% 1.10/1.51 ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
% 1.10/1.51 ( class_Groups_Oab__group__add(T_a)
% 1.10/1.51 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
% 1.10/1.51 => ( V_a_2 = V_b_2
% 1.10/1.51 <=> V_c_2 = V_da_2 ) ) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_abs__idempotent,axiom,
% 1.10/1.51 ! [V_a,T_a] :
% 1.10/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.10/1.51 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 1.10/1.51
% 1.10/1.51 fof(fact_add__le__imp__le__left,axiom,
% 1.10/1.51 ! [V_b,V_a,V_c,T_a] :
% 1.10/1.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.10/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_add__le__imp__le__right,axiom,
% 1.11/1.51 ! [V_b,V_c,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_add__mono,axiom,
% 1.11/1.51 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_add__left__mono,axiom,
% 1.11/1.51 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_add__right__mono,axiom,
% 1.11/1.51 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_add__le__cancel__left,axiom,
% 1.11/1.51 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 1.11/1.51 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_add__le__cancel__right,axiom,
% 1.11/1.51 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 1.11/1.51 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_diff__eq__diff__less__eq,axiom,
% 1.11/1.51 ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.51 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 1.11/1.51 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_da_2) ) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_add__diff__cancel,axiom,
% 1.11/1.51 ! [V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.51 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_diff__add__cancel,axiom,
% 1.11/1.51 ! [V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.51 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_abs__le__D1,axiom,
% 1.11/1.51 ! [V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_abs__ge__self,axiom,
% 1.11/1.51 ! [V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_abs__add__abs,axiom,
% 1.11/1.51 ! [V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_norm__minus__commute,axiom,
% 1.11/1.51 ! [V_b,V_a,T_a] :
% 1.11/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.51 => 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)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_abs__minus__commute,axiom,
% 1.11/1.51 ! [V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_abs__norm__cancel,axiom,
% 1.11/1.51 ! [V_a,T_a] :
% 1.11/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_abs__triangle__ineq,axiom,
% 1.11/1.51 ! [V_b,V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_N1,axiom,
% 1.11/1.51 ! [B_n] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,B_n)
% 1.11/1.51 => 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_g____(hAPP(v_f____,B_n)),v_z____)),v_d____) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_ath,axiom,
% 1.11/1.51 ! [V_e,V_x,V_m] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_m,V_x)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_m,V_e))
% 1.11/1.51 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_m)),V_e) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_complex__mod__triangle__ineq2,axiom,
% 1.11/1.51 ! [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)) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_seq__suble,axiom,
% 1.11/1.51 ! [V_n_2,V_fa_2] :
% 1.11/1.51 ( c_SEQ_Osubseq(V_fa_2)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_order__refl,axiom,
% 1.11/1.51 ! [V_x,T_a] :
% 1.11/1.51 ( class_Orderings_Opreorder(T_a)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_th31,axiom,
% 1.11/1.51 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_poly__diff,axiom,
% 1.11/1.51 ! [V_x,V_q,V_p,T_a] :
% 1.11/1.51 ( class_Rings_Ocomm__ring(T_a)
% 1.11/1.51 => 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)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_poly__add,axiom,
% 1.11/1.51 ! [V_x,V_q,V_p,T_a] :
% 1.11/1.51 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.11/1.51 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_real__add__left__mono,axiom,
% 1.11/1.51 ! [V_z,V_y,V_x] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_diff__diff__right,axiom,
% 1.11/1.51 ! [V_i,V_j,V_k] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.11/1.51 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_le__diff__conv,axiom,
% 1.11/1.51 ! [V_i_2,V_k_2,V_j_2] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
% 1.11/1.51 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_le__add__diff,axiom,
% 1.11/1.51 ! [V_m,V_n,V_k] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_d_I1_J,axiom,
% 1.11/1.51 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_e,axiom,
% 1.11/1.51 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_s1m,axiom,
% 1.11/1.51 ! [V_z] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z),v_r)
% 1.11/1.51 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_z))) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact__096_B_Bn_O_A_N_As_A_060_061_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_096,axiom,
% 1.11/1.51 ! [V_n_1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(V_n_1)))) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_s,axiom,
% 1.11/1.51 ! [B_y] :
% 1.11/1.51 ( ? [B_x] :
% 1.11/1.51 ( ? [B_z] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.11/1.51 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) )
% 1.11/1.51 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
% 1.11/1.51 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,v_s____) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_fz_I2_J,axiom,
% 1.11/1.51 ! [B_e] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
% 1.11/1.51 => ? [B_N] :
% 1.11/1.51 ! [B_n] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n)
% 1.11/1.51 => 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_g____(hAPP(v_f____,B_n)),v_z____)),B_e) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_minus__zero,axiom,
% 1.11/1.51 ! [T_a] :
% 1.11/1.51 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.51 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_abs__if,axiom,
% 1.11/1.51 ! [V_a,T_a] :
% 1.11/1.51 ( class_Groups_Oabs__if(T_a)
% 1.11/1.51 => ( ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) )
% 1.11/1.51 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_abs__real__def,axiom,
% 1.11/1.51 ! [V_a] :
% 1.11/1.51 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) )
% 1.11/1.51 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_real__abs__def,axiom,
% 1.11/1.51 ! [V_r] :
% 1.11/1.51 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) )
% 1.11/1.51 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.11/1.51 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_minus__minus,axiom,
% 1.11/1.51 ! [V_a,T_a] :
% 1.11/1.51 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.51 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_zero__reorient,axiom,
% 1.11/1.51 ! [V_x_2,T_a] :
% 1.11/1.51 ( class_Groups_Ozero(T_a)
% 1.11/1.51 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 1.11/1.51 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_zero__less__norm__iff,axiom,
% 1.11/1.51 ! [V_x_2,T_a] :
% 1.11/1.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
% 1.11/1.51 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_neg__0__equal__iff__equal,axiom,
% 1.11/1.51 ! [V_a_2,T_a] :
% 1.11/1.51 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.51 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
% 1.11/1.51 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_neg__0__less__iff__less,axiom,
% 1.11/1.51 ! [V_a_2,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.51 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.11/1.51 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_real__0__less__add__iff,axiom,
% 1.11/1.51 ! [V_y_2,V_x_2] :
% 1.11/1.51 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.11/1.51 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_equal__neg__zero,axiom,
% 1.11/1.51 ! [V_a_2,T_a] :
% 1.11/1.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.51 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
% 1.11/1.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_equation__minus__iff,axiom,
% 1.11/1.51 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.51 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.51 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.11/1.51 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) ) ).
% 1.11/1.51
% 1.11/1.51 fof(fact_less__minus__iff,axiom,
% 1.11/1.51 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.51 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__less__0__iff__less,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__equal__0__iff__equal,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.11/1.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__less__nonneg,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__equal__zero,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
% 1.11/1.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__equation__iff,axiom,
% 1.11/1.52 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
% 1.11/1.52 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2 ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__less__iff,axiom,
% 1.11/1.52 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__equal__iff__equal,axiom,
% 1.11/1.52 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.11/1.52 <=> V_a_2 = V_b_2 ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__less__iff__less,axiom,
% 1.11/1.52 ! [V_a_2,V_b_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__eq__0__iff,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.11/1.52 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_real__add__eq__0__iff,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2] :
% 1.11/1.52 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.11/1.52 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_real__add__less__0__iff,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2] :
% 1.11/1.52 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_diff__commute,axiom,
% 1.11/1.52 ! [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) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_real__add__minus__iff,axiom,
% 1.11/1.52 ! [V_a_2,V_x_2] :
% 1.11/1.52 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.11/1.52 <=> V_x_2 = V_a_2 ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_abs__of__neg,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__cases,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => ( V_x != V_y
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__asym,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_xt1_I10_J,axiom,
% 1.11/1.52 ! [V_z,V_x,V_y,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__trans,axiom,
% 1.11/1.52 ! [V_z,V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_xt1_I2_J,axiom,
% 1.11/1.52 ! [V_c,V_a,V_b,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.11/1.52 => ( V_b = V_c
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_ord__less__eq__trans,axiom,
% 1.11/1.52 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.52 ( class_Orderings_Oord(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.11/1.52 => ( V_b = V_c
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_xt1_I1_J,axiom,
% 1.11/1.52 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( V_a = V_b
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_ord__eq__less__trans,axiom,
% 1.11/1.52 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.52 ( class_Orderings_Oord(T_a)
% 1.11/1.52 => ( V_a = V_b
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_xt1_I9_J,axiom,
% 1.11/1.52 ! [V_a,V_b,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__asym_H,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__imp__not__eq2,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => V_y != V_x ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__imp__not__eq,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => V_x != V_y ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__imp__not__less,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__not__sym,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_less__imp__neq,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => V_x != V_y ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__neqE,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( V_x != V_y
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__antisym__conv3,axiom,
% 1.11/1.52 ! [V_x_2,V_y_2,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_poly__minus,axiom,
% 1.11/1.52 ! [V_x,V_p,T_a] :
% 1.11/1.52 ( class_Rings_Ocomm__ring(T_a)
% 1.11/1.52 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__less__linear,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 | V_x = V_y
% 1.11/1.52 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_poly__0,axiom,
% 1.11/1.52 ! [V_x,T_a] :
% 1.11/1.52 ( class_Rings_Ocomm__semiring__0(T_a)
% 1.11/1.52 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_not__less__iff__gr__or__eq,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.11/1.52 | V_x_2 = V_y_2 ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__neq__iff,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( V_x_2 != V_y_2
% 1.11/1.52 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__irrefl,axiom,
% 1.11/1.52 ! [V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__le__self__iff,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__le__0__iff__le,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_le__minus__self__iff,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__0__le__iff__le,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__unique,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.11/1.52 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_ab__left__minus,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oab__group__add(T_a)
% 1.11/1.52 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_left__minus,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 1.11/1.52 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.11/1.52 <=> c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_right__minus,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_diff__0,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => 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) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__neg__neg,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__pos__pos,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_less__iff__diff__less__0,axiom,
% 1.11/1.52 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_abs__of__pos,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.52 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_zero__less__abs__iff,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
% 1.11/1.52 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_abs__not__less__zero,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_norm__not__less__zero,axiom,
% 1.11/1.52 ! [V_x,T_a] :
% 1.11/1.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__not__less,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__not__le,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__le__less__linear,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.11/1.52 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__le,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.11/1.52 & V_x_2 != V_y_2 ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_less__le__not__le,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.11/1.52 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__le__less,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 | V_x_2 = V_y_2 ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_leI,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_not__leE,axiom,
% 1.11/1.52 ! [V_x,V_y,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__antisym__conv1,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__neq__le__trans,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( V_a != V_b
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_xt1_I12_J,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( V_a != V_b
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_leD,axiom,
% 1.11/1.52 ! [V_x,V_y,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.11/1.52 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__imp__le,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_linorder__antisym__conv2,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.52 ( class_Orderings_Olinorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.11/1.52 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.11/1.52 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__le__imp__less__or__eq,axiom,
% 1.11/1.52 ! [V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 | V_x = V_y ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__le__neq__trans,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.52 => ( V_a != V_b
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_xt1_I11_J,axiom,
% 1.11/1.52 ! [V_a,V_b,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.11/1.52 => ( V_a != V_b
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__less__le__trans,axiom,
% 1.11/1.52 ! [V_z,V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_xt1_I7_J,axiom,
% 1.11/1.52 ! [V_z,V_x,V_y,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_order__le__less__trans,axiom,
% 1.11/1.52 ! [V_z,V_y,V_x,T_a] :
% 1.11/1.52 ( class_Orderings_Opreorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_xt1_I8_J,axiom,
% 1.11/1.52 ! [V_z,V_x,V_y,T_a] :
% 1.11/1.52 ( class_Orderings_Oorder(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_norm__eq__zero,axiom,
% 1.11/1.52 ! [V_x_2,T_a] :
% 1.11/1.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.52 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.11/1.52 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_norm__zero,axiom,
% 1.11/1.52 ! [T_a] :
% 1.11/1.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.52 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_real__less__def,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2] :
% 1.11/1.52 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.11/1.52 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.11/1.52 & V_x_2 != V_y_2 ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_less__eq__real__def,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2] :
% 1.11/1.52 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.11/1.52 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.11/1.52 | V_x_2 = V_y_2 ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_real__add__le__0__iff,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2] :
% 1.11/1.52 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_real__0__le__add__iff,axiom,
% 1.11/1.52 ! [V_y_2,V_x_2] :
% 1.11/1.52 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__pos__nonneg,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__nonneg__pos,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__strict__increasing,axiom,
% 1.11/1.52 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__strict__increasing2,axiom,
% 1.11/1.52 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__neg__nonpos,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__nonpos__neg,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_abs__minus__le__zero,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.52 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_abs__of__nonpos,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.52 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_norm__le__zero__iff,axiom,
% 1.11/1.52 ! [V_x_2,T_a] :
% 1.11/1.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.11/1.52 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_le__minus__iff,axiom,
% 1.11/1.52 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__le__iff,axiom,
% 1.11/1.52 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_neg__le__iff__le,axiom,
% 1.11/1.52 ! [V_a_2,V_b_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_le__imp__neg__le,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.52 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__add__distrib,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oab__group__add(T_a)
% 1.11/1.52 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__add,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__minus__cancel,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__add__cancel,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.52 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_minus__diff__eq,axiom,
% 1.11/1.52 ! [V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oab__group__add(T_a)
% 1.11/1.52 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__less__cancel__right,axiom,
% 1.11/1.52 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__less__cancel__left,axiom,
% 1.11/1.52 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__strict__right__mono,axiom,
% 1.11/1.52 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__strict__left__mono,axiom,
% 1.11/1.52 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__strict__mono,axiom,
% 1.11/1.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__less__imp__less__right,axiom,
% 1.11/1.52 ! [V_b,V_c,V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__less__imp__less__left,axiom,
% 1.11/1.52 ! [V_b,V_a,V_c,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 1.11/1.52 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_norm__minus__cancel,axiom,
% 1.11/1.52 ! [V_x,T_a] :
% 1.11/1.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.52 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_abs__minus__cancel,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.52 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_diff__eq__diff__less,axiom,
% 1.11/1.52 ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_da_2)
% 1.11/1.52 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 1.11/1.52 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_da_2) ) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__0__left,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Omonoid__add(T_a)
% 1.11/1.52 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__0,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.11/1.52 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_double__zero__sym,axiom,
% 1.11/1.52 ! [V_a_2,T_a] :
% 1.11/1.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.52 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 1.11/1.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add__0__right,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Omonoid__add(T_a)
% 1.11/1.52 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.11/1.52
% 1.11/1.52 fof(fact_add_Ocomm__neutral,axiom,
% 1.11/1.52 ! [V_a,T_a] :
% 1.11/1.52 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.11/1.53 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__0__right,axiom,
% 1.11/1.53 ! [V_a,T_a] :
% 1.11/1.53 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__self,axiom,
% 1.11/1.53 ! [V_a,T_a] :
% 1.11/1.53 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_eq__iff__diff__eq__0,axiom,
% 1.11/1.53 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.53 ( class_Groups_Oab__group__add(T_a)
% 1.11/1.53 => ( V_a_2 = V_b_2
% 1.11/1.53 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_right__minus__eq,axiom,
% 1.11/1.53 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.53 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.53 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.11/1.53 <=> V_a_2 = V_b_2 ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__zero,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__eq__0,axiom,
% 1.11/1.53 ! [V_a_2,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.11/1.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_complex__mod__minus__le__complex__mod,axiom,
% 1.11/1.53 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__le__interval__iff,axiom,
% 1.11/1.53 ! [V_ra_2,V_x_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2)
% 1.11/1.53 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_minus__real__def,axiom,
% 1.11/1.53 ! [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)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_real__diff__def,axiom,
% 1.11/1.53 ! [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)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__minus__add__cancel,axiom,
% 1.11/1.53 ! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_real__le__eq__diff,axiom,
% 1.11/1.53 ! [V_y_2,V_x_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.11/1.53 <=> 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)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__def,axiom,
% 1.11/1.53 ! [V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.53 => 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)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_ab__diff__minus,axiom,
% 1.11/1.53 ! [V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oab__group__add(T_a)
% 1.11/1.53 => 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)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__minus__eq__add,axiom,
% 1.11/1.53 ! [V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Ogroup__add(T_a)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__ge__minus__self,axiom,
% 1.11/1.53 ! [V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__le__iff,axiom,
% 1.11/1.53 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 1.11/1.53 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__leI,axiom,
% 1.11/1.53 ! [V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__le__D2,axiom,
% 1.11/1.53 ! [V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__less__le__mono,axiom,
% 1.11/1.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__le__less__mono,axiom,
% 1.11/1.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__sum__triangle__ineq,axiom,
% 1.11/1.53 ! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.11/1.53 ! [V_a_2,T_a] :
% 1.11/1.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.11/1.53 ! [V_a_2,T_a] :
% 1.11/1.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__nonneg__nonneg,axiom,
% 1.11/1.53 ! [V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__nonneg__eq__0__iff,axiom,
% 1.11/1.53 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 1.11/1.53 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.11/1.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.11/1.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__increasing,axiom,
% 1.11/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__increasing2,axiom,
% 1.11/1.53 ! [V_a,V_b,V_c,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__nonpos__nonpos,axiom,
% 1.11/1.53 ! [V_b,V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__iff__diff__le__0,axiom,
% 1.11/1.53 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__ge__zero,axiom,
% 1.11/1.53 ! [V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__le__zero__iff,axiom,
% 1.11/1.53 ! [V_a_2,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__of__nonneg,axiom,
% 1.11/1.53 ! [V_a,T_a] :
% 1.11/1.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.53 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_norm__ge__zero,axiom,
% 1.11/1.53 ! [V_x,T_a] :
% 1.11/1.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__fun__def,axiom,
% 1.11/1.53 ! [V_ga_2,V_fa_2,T_a,T_b] :
% 1.11/1.53 ( class_Orderings_Oord(T_b)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 1.11/1.53 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_ga_2,B_x)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_linorder__linear,axiom,
% 1.11/1.53 ! [V_y,V_x,T_a] :
% 1.11/1.53 ( class_Orderings_Olinorder(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.11/1.53 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_order__eq__iff,axiom,
% 1.11/1.53 ! [V_y_2,V_x_2,T_a] :
% 1.11/1.53 ( class_Orderings_Oorder(T_a)
% 1.11/1.53 => ( V_x_2 = V_y_2
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.11/1.53 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_order__eq__refl,axiom,
% 1.11/1.53 ! [V_y,V_x,T_a] :
% 1.11/1.53 ( class_Orderings_Opreorder(T_a)
% 1.11/1.53 => ( V_x = V_y
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__funD,axiom,
% 1.11/1.53 ! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
% 1.11/1.53 ( class_Orderings_Oord(T_b)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_order__antisym__conv,axiom,
% 1.11/1.53 ! [V_x_2,V_y_2,T_a] :
% 1.11/1.53 ( class_Orderings_Oorder(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.11/1.53 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_ord__eq__le__trans,axiom,
% 1.11/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.53 ( class_Orderings_Oord(T_a)
% 1.11/1.53 => ( V_a = V_b
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_xt1_I3_J,axiom,
% 1.11/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.53 ( class_Orderings_Oorder(T_a)
% 1.11/1.53 => ( V_a = V_b
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_ord__le__eq__trans,axiom,
% 1.11/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.53 ( class_Orderings_Oord(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.11/1.53 => ( V_b = V_c
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_xt1_I4_J,axiom,
% 1.11/1.53 ! [V_c,V_a,V_b,T_a] :
% 1.11/1.53 ( class_Orderings_Oorder(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.11/1.53 => ( V_b = V_c
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_order__antisym,axiom,
% 1.11/1.53 ! [V_y,V_x,T_a] :
% 1.11/1.53 ( class_Orderings_Oorder(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.11/1.53 => V_x = V_y ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_order__trans,axiom,
% 1.11/1.53 ! [V_z,V_y,V_x,T_a] :
% 1.11/1.53 ( class_Orderings_Opreorder(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_xt1_I5_J,axiom,
% 1.11/1.53 ! [V_x,V_y,T_a] :
% 1.11/1.53 ( class_Orderings_Oorder(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.11/1.53 => V_x = V_y ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_xt1_I6_J,axiom,
% 1.11/1.53 ! [V_z,V_x,V_y,T_a] :
% 1.11/1.53 ( class_Orderings_Oorder(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__funE,axiom,
% 1.11/1.53 ! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
% 1.11/1.53 ( class_Orderings_Oord(T_b)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_linorder__le__cases,axiom,
% 1.11/1.53 ! [V_y,V_x,T_a] :
% 1.11/1.53 ( class_Orderings_Olinorder(T_a)
% 1.11/1.53 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_norm__add__less,axiom,
% 1.11/1.53 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.11/1.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_real__le__refl,axiom,
% 1.11/1.53 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_real__le__linear,axiom,
% 1.11/1.53 ! [V_w,V_z] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.11/1.53 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_real__le__trans,axiom,
% 1.11/1.53 ! [V_k,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_real__le__antisym,axiom,
% 1.11/1.53 ! [V_w,V_z] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 1.11/1.53 => V_z = V_w ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__add__commute,axiom,
% 1.11/1.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__add__left__commute,axiom,
% 1.11/1.53 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__add__assoc,axiom,
% 1.11/1.53 ! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__add__left__cancel,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2,V_k_2] :
% 1.11/1.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
% 1.11/1.53 <=> V_m_2 = V_n_2 ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__add__right__cancel,axiom,
% 1.11/1.53 ! [V_n_2,V_k_2,V_m_2] :
% 1.11/1.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
% 1.11/1.53 <=> V_m_2 = V_n_2 ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__add__inverse2,axiom,
% 1.11/1.53 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__add__inverse,axiom,
% 1.11/1.53 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__diff__left,axiom,
% 1.11/1.53 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__cancel,axiom,
% 1.11/1.53 ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__cancel2,axiom,
% 1.11/1.53 ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__diff__iff,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2,V_k_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_Nat_Odiff__diff__eq,axiom,
% 1.11/1.53 ! [V_n,V_m,V_k] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_eq__diff__iff,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2,V_k_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 1.11/1.53 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
% 1.11/1.53 <=> V_m_2 = V_n_2 ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__antisym,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.11/1.53 => V_m = V_n ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__trans,axiom,
% 1.11/1.53 ! [V_k,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__diff__cancel,axiom,
% 1.11/1.53 ! [V_n,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__le__mono,axiom,
% 1.11/1.53 ! [V_l,V_n,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__le__mono2,axiom,
% 1.11/1.53 ! [V_l,V_n,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_eq__imp__le,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( V_m = V_n
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__le__linear,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__le__self,axiom,
% 1.11/1.53 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__refl,axiom,
% 1.11/1.53 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_poly__eq__iff,axiom,
% 1.11/1.53 ! [V_q_2,V_pa_2,T_a] :
% 1.11/1.53 ( ( class_Int_Oring__char__0(T_a)
% 1.11/1.53 & class_Rings_Oidom(T_a) )
% 1.11/1.53 => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
% 1.11/1.53 <=> V_pa_2 = V_q_2 ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__add2,axiom,
% 1.11/1.53 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__add1,axiom,
% 1.11/1.53 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__iff__add,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.11/1.53 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__add__left__cancel__le,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2,V_k_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_trans__le__add1,axiom,
% 1.11/1.53 ! [V_m,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_trans__le__add2,axiom,
% 1.11/1.53 ! [V_m,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__le__mono1,axiom,
% 1.11/1.53 ! [V_k,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__le__mono,axiom,
% 1.11/1.53 ! [V_l,V_k,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__leD2,axiom,
% 1.11/1.53 ! [V_n,V_k,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__leD1,axiom,
% 1.11/1.53 ! [V_n,V_k,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__leE,axiom,
% 1.11/1.53 ! [V_n,V_k,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.11/1.53 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__add__assoc2,axiom,
% 1.11/1.53 ! [V_i,V_j,V_k] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__diff__assoc2,axiom,
% 1.11/1.53 ! [V_i,V_j,V_k] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.11/1.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__add__assoc,axiom,
% 1.11/1.53 ! [V_i,V_j,V_k] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__imp__diff__is__add,axiom,
% 1.11/1.53 ! [V_k_2,V_j_2,V_i_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.11/1.53 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 1.11/1.53 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__add__diff__inverse2,axiom,
% 1.11/1.53 ! [V_m,V_n] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.11/1.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__diff__conv2,axiom,
% 1.11/1.53 ! [V_i_2,V_j_2,V_k_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__diff__assoc,axiom,
% 1.11/1.53 ! [V_i,V_j,V_k] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.11/1.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__add__diff__inverse,axiom,
% 1.11/1.53 ! [V_m,V_n] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.11/1.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096,axiom,
% 1.11/1.53 ? [B_N] :
% 1.11/1.53 ! [B_n] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n)
% 1.11/1.53 => 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_g____(hAPP(v_f____,B_n)),v_z____)),v_d____) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096,axiom,
% 1.11/1.53 ! [V_y_2] :
% 1.11/1.53 ( ? [B_z] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.11/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)))),V_y_2) )
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_s1,axiom,
% 1.11/1.53 ! [V_y_2] :
% 1.11/1.53 ( ? [B_z] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.11/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),V_y_2) )
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),V_y_2) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096,axiom,
% 1.11/1.53 ( ? [B_z] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.11/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) )
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_mth2,axiom,
% 1.11/1.53 ? [B_z] :
% 1.11/1.53 ! [B_x] :
% 1.11/1.53 ( ? [B_za] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_za),v_r)
% 1.11/1.53 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_za)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) )
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_z) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_calculation,axiom,
% 1.11/1.53 ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r)
% 1.11/1.53 => ? [B_z] :
% 1.11/1.53 ! [B_w] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_w),v_r)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_w))) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096,axiom,
% 1.11/1.53 ! [V_x_2,V_z_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r)
% 1.11/1.53 => ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),V_z_2)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096,axiom,
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_r)
% 1.11/1.53 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__diff__less__iff,axiom,
% 1.11/1.53 ! [V_ra_2,V_a_2,V_x_2,T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__idom(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2)
% 1.11/1.53 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.11/1.53 ~ ! [B_N1] :
% 1.11/1.53 ~ ! [B_n] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N1,B_n)
% 1.11/1.53 => 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_g____(hAPP(v_f____,B_n)),v_z____)),v_d____) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__less__iff,axiom,
% 1.11/1.53 ! [V_b_2,V_a_2,T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__idom(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 1.11/1.53 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_th000_I2_J,axiom,
% 1.11/1.53 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_th000_I1_J,axiom,
% 1.11/1.53 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le0,axiom,
% 1.11/1.53 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__poly__def,axiom,
% 1.11/1.53 ! [V_x,T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__idom(T_a)
% 1.11/1.53 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.11/1.53 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x) )
% 1.11/1.53 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.11/1.53 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__fun__def,axiom,
% 1.11/1.53 ! [V_ga_2,V_fa_2,T_a,T_b] :
% 1.11/1.53 ( class_Orderings_Oord(T_b)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 1.11/1.53 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2,V_fa_2) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_minus__poly__code_I1_J,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Groups_Oab__group__add(T_a)
% 1.11/1.53 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_one__reorient,axiom,
% 1.11/1.53 ! [V_x_2,T_a] :
% 1.11/1.53 ( class_Groups_Oone(T_a)
% 1.11/1.53 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 1.11/1.53 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_norm__one,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.11/1.53 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__gr__0,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.11/1.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__less,axiom,
% 1.11/1.53 ! [V_m,V_n] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_zero__less__diff,axiom,
% 1.11/1.53 ! [V_m_2,V_n_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_poly__1,axiom,
% 1.11/1.53 ! [V_x,T_a] :
% 1.11/1.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.11/1.53 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_one__neq__zero,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Rings_Ozero__neq__one(T_a)
% 1.11/1.53 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_zero__neq__one,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Rings_Ozero__neq__one(T_a)
% 1.11/1.53 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__one,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__idom(T_a)
% 1.11/1.53 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__poly__code_I1_J,axiom,
% 1.11/1.53 ! [V_q,T_a] :
% 1.11/1.53 ( class_Groups_Oab__group__add(T_a)
% 1.11/1.53 => 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) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__diff__split,axiom,
% 1.11/1.53 ! [V_b_2,V_a_2,V_P_2] :
% 1.11/1.53 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 1.11/1.53 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
% 1.11/1.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.11/1.53 & ! [B_d] :
% 1.11/1.53 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 1.11/1.53 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__diff__split__asm,axiom,
% 1.11/1.53 ! [V_b_2,V_a_2,V_P_2] :
% 1.11/1.53 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 1.11/1.53 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
% 1.11/1.53 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.11/1.53 | ? [B_d] :
% 1.11/1.53 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 1.11/1.53 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__lessD1,axiom,
% 1.11/1.53 ! [V_k,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__add__eq__less,axiom,
% 1.11/1.53 ! [V_n,V_m,V_l,V_k] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.11/1.53 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__less__mono,axiom,
% 1.11/1.53 ! [V_l,V_k,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__less__mono1,axiom,
% 1.11/1.53 ! [V_k,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_trans__less__add2,axiom,
% 1.11/1.53 ! [V_m,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_trans__less__add1,axiom,
% 1.11/1.53 ! [V_m,V_j,V_i] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__add__left__cancel__less,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2,V_k_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_not__add__less2,axiom,
% 1.11/1.53 ! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_not__add__less1,axiom,
% 1.11/1.53 ! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_nat__less__le,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.11/1.53 & V_m_2 != V_n_2 ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__eq__less__or__eq,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.11/1.53 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.11/1.53 | V_m_2 = V_n_2 ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__imp__le__nat,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__neq__implies__less,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => ( V_m != V_n
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__or__eq__imp__le,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 | V_m = V_n )
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_real__zero__not__eq__one,axiom,
% 1.11/1.53 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__less__mono2,axiom,
% 1.11/1.53 ! [V_l,V_n,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__imp__diff__less,axiom,
% 1.11/1.53 ! [V_n,V_k,V_j] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_zero__le__one,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__semidom(T_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_not__one__le__zero,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__semidom(T_a)
% 1.11/1.53 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__eq__self__zero,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 1.11/1.53 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__is__0,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2] :
% 1.11/1.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.11/1.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.11/1.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_Nat_Oadd__0__right,axiom,
% 1.11/1.53 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.11/1.53
% 1.11/1.53 fof(fact_plus__nat_Oadd__0,axiom,
% 1.11/1.53 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 1.11/1.53 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_le__0__eq,axiom,
% 1.11/1.53 ! [V_n_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.11/1.53 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_not__one__less__zero,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__semidom(T_a)
% 1.11/1.53 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_zero__less__one,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__semidom(T_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__add__one,axiom,
% 1.11/1.53 ! [V_a,T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__semidom(T_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diffs0__imp__equal,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.11/1.53 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.11/1.53 => V_m = V_n ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__self__eq__0,axiom,
% 1.11/1.53 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_minus__nat_Odiff__0,axiom,
% 1.11/1.53 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__0__eq__0,axiom,
% 1.11/1.53 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_poly__zero,axiom,
% 1.11/1.53 ! [V_pa_2,T_a] :
% 1.11/1.53 ( ( class_Int_Oring__char__0(T_a)
% 1.11/1.53 & class_Rings_Oidom(T_a) )
% 1.11/1.53 => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 1.11/1.53 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__poly__code_I2_J,axiom,
% 1.11/1.53 ! [V_p,T_a] :
% 1.11/1.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.11/1.53 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__poly__code_I1_J,axiom,
% 1.11/1.53 ! [V_q,T_a] :
% 1.11/1.53 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.11/1.53 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__poly__code_I2_J,axiom,
% 1.11/1.53 ! [V_p,T_a] :
% 1.11/1.53 ( class_Groups_Oab__group__add(T_a)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_subseq__def,axiom,
% 1.11/1.53 ! [V_fa_2] :
% 1.11/1.53 ( c_SEQ_Osubseq(V_fa_2)
% 1.11/1.53 <=> ! [B_m,B_n] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_zero__less__two,axiom,
% 1.11/1.53 ! [T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__semidom(T_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__diff__conv,axiom,
% 1.11/1.53 ! [V_k_2,V_j_2,V_i_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_add__diff__inverse,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__less__mono,axiom,
% 1.11/1.53 ! [V_c,V_b,V_a] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__diff__iff,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2,V_k_2] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__add__0,axiom,
% 1.11/1.53 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__is__0__eq,axiom,
% 1.11/1.53 ! [V_n_2,V_m_2] :
% 1.11/1.53 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_diff__is__0__eq_H,axiom,
% 1.11/1.53 ! [V_n,V_m] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.11/1.53 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_complex__diff__def,axiom,
% 1.11/1.53 ! [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)) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_linorder__neqE__linordered__idom,axiom,
% 1.11/1.53 ! [V_y,V_x,T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__idom(T_a)
% 1.11/1.53 => ( V_x != V_y
% 1.11/1.53 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__add__one__not__less__self,axiom,
% 1.11/1.53 ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_abs__add__one__gt__zero,axiom,
% 1.11/1.53 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_pos__add__strict,axiom,
% 1.11/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__semidom(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.11/1.53 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_less__minus__self__iff,axiom,
% 1.11/1.53 ! [V_a_2,T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__idom(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 1.11/1.53 ! [V_y,V_x,T_a] :
% 1.11/1.53 ( class_Rings_Ocomm__ring__1(T_a)
% 1.11/1.53 => 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)) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact_even__less__0__iff,axiom,
% 1.11/1.53 ! [V_a_2,T_a] :
% 1.11/1.53 ( class_Rings_Olinordered__idom(T_a)
% 1.11/1.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096,axiom,
% 1.11/1.53 ? [B_s] :
% 1.11/1.53 ! [B_y] :
% 1.11/1.53 ( ? [B_x] :
% 1.11/1.53 ( ? [B_z] :
% 1.11/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.11/1.53 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) )
% 1.11/1.53 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_x) )
% 1.11/1.53 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,B_s) ) ).
% 1.11/1.53
% 1.11/1.53 fof(fact__096abs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_060_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096,axiom,
% 1.11/1.53 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_mth1,axiom,
% 1.20/1.53 ? [B_x,B_z] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.20/1.53 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B_x) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_lemmaCauchy,axiom,
% 1.20/1.53 ! [V_X_2,V_M_2,T_a,T_b] :
% 1.20/1.53 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 1.20/1.53 & class_Orderings_Oord(T_a) )
% 1.20/1.53 => ( ! [B_n] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 1.20/1.53 => 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)) )
% 1.20/1.53 => ! [B_n] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 1.20/1.53 => 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)))) ) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_g_I2_J,axiom,
% 1.20/1.53 ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(B_n))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__zeroE,axiom,
% 1.20/1.53 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__mono,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_lessI,axiom,
% 1.20/1.53 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_th000_I3_J,axiom,
% 1.20/1.53 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(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact__0961_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_A_060_061_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096,axiom,
% 1.20/1.53 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_zero__less__Suc,axiom,
% 1.20/1.53 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__ge__zero,axiom,
% 1.20/1.53 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_th00,axiom,
% 1.20/1.53 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact__096cmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_096,axiom,
% 1.20/1.53 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_th32,axiom,
% 1.20/1.53 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__diff__1,axiom,
% 1.20/1.53 ! [V_n] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.20/1.53 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_nat__less__cases,axiom,
% 1.20/1.53 ! [V_P_2,V_n_2,V_m_2] :
% 1.20/1.53 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.53 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 1.20/1.53 => ( ( V_m_2 = V_n_2
% 1.20/1.53 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 1.20/1.53 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 1.20/1.53 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 1.20/1.53 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_gr0I,axiom,
% 1.20/1.53 ! [V_n] :
% 1.20/1.53 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__less__SucD,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 1.20/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__lessD,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.20/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__neq__Zero,axiom,
% 1.20/1.53 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__SucE,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 1.20/1.53 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.53 => V_m = V_n ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__trans__Suc,axiom,
% 1.20/1.53 ! [V_k,V_j,V_i] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.20/1.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.20/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__lessI,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.53 => ( c_Nat_OSuc(V_m) != V_n
% 1.20/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__SucI,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__not__refl3,axiom,
% 1.20/1.53 ! [V_t,V_s] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 1.20/1.53 => V_s != V_t ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__not__refl2,axiom,
% 1.20/1.53 ! [V_m,V_n] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.20/1.53 => V_m != V_n ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_gr__implies__not0,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.53 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__irrefl__nat,axiom,
% 1.20/1.53 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Zero__neq__Suc,axiom,
% 1.20/1.53 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_linorder__neqE__nat,axiom,
% 1.20/1.53 ! [V_y,V_x] :
% 1.20/1.53 ( V_x != V_y
% 1.20/1.53 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.20/1.53 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__antisym,axiom,
% 1.20/1.53 ! [V_m,V_n] :
% 1.20/1.53 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.20/1.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 1.20/1.53 => V_m = V_n ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_not__less__less__Suc__eq,axiom,
% 1.20/1.53 ! [V_m_2,V_n_2] :
% 1.20/1.53 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 1.20/1.53 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 1.20/1.53 <=> V_n_2 = V_m_2 ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__less__eq,axiom,
% 1.20/1.53 ! [V_n_2,V_m_2] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
% 1.20/1.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__Suc__eq,axiom,
% 1.20/1.53 ! [V_n_2,V_m_2] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 1.20/1.53 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.53 | V_m_2 = V_n_2 ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__Suc__eq__0__disj,axiom,
% 1.20/1.53 ! [V_n_2,V_m_2] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 1.20/1.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.53 | ? [B_j] :
% 1.20/1.53 ( V_m_2 = c_Nat_OSuc(B_j)
% 1.20/1.53 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2) ) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__Suc0,axiom,
% 1.20/1.53 ! [V_n_2] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 1.20/1.53 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__nat__zero__code,axiom,
% 1.20/1.53 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_gr0__conv__Suc,axiom,
% 1.20/1.53 ! [V_n_2] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 1.20/1.53 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_nat__neq__iff,axiom,
% 1.20/1.53 ! [V_n_2,V_m_2] :
% 1.20/1.53 ( V_m_2 != V_n_2
% 1.20/1.53 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.53 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_not__less__eq,axiom,
% 1.20/1.53 ! [V_n_2,V_m_2] :
% 1.20/1.53 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_neq0__conv,axiom,
% 1.20/1.53 ! [V_n_2] :
% 1.20/1.53 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__one,axiom,
% 1.20/1.53 c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__1,axiom,
% 1.20/1.53 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_One__nat__def,axiom,
% 1.20/1.53 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_nat_Osimps_I3_J,axiom,
% 1.20/1.53 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__not__Zero,axiom,
% 1.20/1.53 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__not__refl,axiom,
% 1.20/1.53 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_not__less0,axiom,
% 1.20/1.53 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_nat_Osimps_I2_J,axiom,
% 1.20/1.53 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Zero__not__Suc,axiom,
% 1.20/1.53 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_norm__divide,axiom,
% 1.20/1.53 ! [V_b,V_a,T_a] :
% 1.20/1.53 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.53 & class_RealVector_Oreal__normed__field(T_a) )
% 1.20/1.53 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_diff__Suc__1,axiom,
% 1.20/1.53 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 1.20/1.53
% 1.20/1.53 fof(fact_nonzero__norm__divide,axiom,
% 1.20/1.53 ! [V_a,V_b,T_a] :
% 1.20/1.53 ( class_RealVector_Oreal__normed__field(T_a)
% 1.20/1.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.53 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__Suc__gt__zero,axiom,
% 1.20/1.53 ! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_n__not__Suc__n,axiom,
% 1.20/1.53 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__n__not__n,axiom,
% 1.20/1.53 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 1.20/1.53
% 1.20/1.53 fof(fact_nat_Oinject,axiom,
% 1.20/1.53 ! [V_nat_H_2,V_nat_2] :
% 1.20/1.53 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 1.20/1.53 <=> V_nat_2 = V_nat_H_2 ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__inject,axiom,
% 1.20/1.53 ! [V_m_2,V_n_2] :
% 1.20/1.53 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
% 1.20/1.53 <=> V_n_2 = V_m_2 ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__inject,axiom,
% 1.20/1.53 ! [V_y,V_x] :
% 1.20/1.53 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 1.20/1.53 => V_x = V_y ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__Suc,axiom,
% 1.20/1.53 ! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_divide_Ozero,axiom,
% 1.20/1.53 ! [V_y,T_a] :
% 1.20/1.53 ( class_RealVector_Oreal__normed__field(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_divide__zero,axiom,
% 1.20/1.53 ! [V_a,T_a] :
% 1.20/1.53 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_divide__zero__left,axiom,
% 1.20/1.53 ! [V_a,T_a] :
% 1.20/1.53 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_divide_Oadd,axiom,
% 1.20/1.53 ! [V_ya,V_y,V_x,T_a] :
% 1.20/1.53 ( class_RealVector_Oreal__normed__field(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_add__divide__distrib,axiom,
% 1.20/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.53 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_divide_Odiff,axiom,
% 1.20/1.53 ! [V_ya,V_y,V_x,T_a] :
% 1.20/1.53 ( class_RealVector_Oreal__normed__field(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_diff__divide__distrib,axiom,
% 1.20/1.53 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.53 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_divide__1,axiom,
% 1.20/1.53 ! [V_a,T_a] :
% 1.20/1.53 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__less__iff,axiom,
% 1.20/1.53 ! [V_m_2,V_n_2] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
% 1.20/1.53 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__zero__iff,axiom,
% 1.20/1.53 ! [V_n_2] :
% 1.20/1.53 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.20/1.53 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_real__of__nat__zero,axiom,
% 1.20/1.53 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_divide_Ominus,axiom,
% 1.20/1.53 ! [V_y,V_x,T_a] :
% 1.20/1.53 ( class_RealVector_Oreal__normed__field(T_a)
% 1.20/1.53 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_minus__divide__left,axiom,
% 1.20/1.53 ! [V_b,V_a,T_a] :
% 1.20/1.53 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.53 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_abs__real__of__nat__cancel,axiom,
% 1.20/1.53 ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_add__Suc__right,axiom,
% 1.20/1.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_add__Suc,axiom,
% 1.20/1.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_add__Suc__shift,axiom,
% 1.20/1.53 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_one__is__add,axiom,
% 1.20/1.53 ! [V_n_2,V_m_2] :
% 1.20/1.53 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.53 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.20/1.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.20/1.53 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.53 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_add__is__1,axiom,
% 1.20/1.53 ! [V_n_2,V_m_2] :
% 1.20/1.53 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.20/1.53 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.20/1.53 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.20/1.53 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.53 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__add__Suc1,axiom,
% 1.20/1.53 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__add__Suc2,axiom,
% 1.20/1.53 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_less__iff__Suc__add,axiom,
% 1.20/1.53 ! [V_n_2,V_m_2] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.53 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__leD,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.20/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_le__SucE,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 1.20/1.53 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.20/1.53 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_le__SucI,axiom,
% 1.20/1.53 ! [V_n,V_m] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.20/1.53 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.20/1.53
% 1.20/1.53 fof(fact_Suc__le__mono,axiom,
% 1.20/1.53 ! [V_m_2,V_n_2] :
% 1.20/1.53 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__Suc__eq,axiom,
% 1.20/1.54 ! [V_n_2,V_m_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 1.20/1.54 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.54 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_not__less__eq__eq,axiom,
% 1.20/1.54 ! [V_n_2,V_m_2] :
% 1.20/1.54 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__n__not__le__n,axiom,
% 1.20/1.54 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__eq__Suc__le,axiom,
% 1.20/1.54 ! [V_m_2,V_n_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__Suc__eq__le,axiom,
% 1.20/1.54 ! [V_n_2,V_m_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__le__eq,axiom,
% 1.20/1.54 ! [V_n_2,V_m_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__imp__less__Suc,axiom,
% 1.20/1.54 ! [V_n,V_m] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__leI,axiom,
% 1.20/1.54 ! [V_n,V_m] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__less__Suc__eq,axiom,
% 1.20/1.54 ! [V_n_2,V_m_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 1.20/1.54 <=> V_n_2 = V_m_2 ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__le__lessD,axiom,
% 1.20/1.54 ! [V_n,V_m] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__Suc__Suc,axiom,
% 1.20/1.54 ! [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) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__diff__diff,axiom,
% 1.20/1.54 ! [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) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__less__Suc,axiom,
% 1.20/1.54 ! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__Suc__less,axiom,
% 1.20/1.54 ! [V_i,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.20/1.54 => 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) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__pred,axiom,
% 1.20/1.54 ! [V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.20/1.54 => 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 ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_subseq__Suc__iff,axiom,
% 1.20/1.54 ! [V_fa_2] :
% 1.20/1.54 ( c_SEQ_Osubseq(V_fa_2)
% 1.20/1.54 <=> ! [B_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_lemma__NBseq__def2,axiom,
% 1.20/1.54 ! [V_X_2,T_b] :
% 1.20/1.54 ( class_RealVector_Oreal__normed__vector(T_b)
% 1.20/1.54 => ( ? [B_K] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.20/1.54 & ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K) )
% 1.20/1.54 <=> ? [B_N] :
% 1.20/1.54 ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_lemma__NBseq__def,axiom,
% 1.20/1.54 ! [V_X_2,T_b] :
% 1.20/1.54 ( class_RealVector_Oreal__normed__vector(T_b)
% 1.20/1.54 => ( ? [B_K] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 1.20/1.54 & ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K) )
% 1.20/1.54 <=> ? [B_N] :
% 1.20/1.54 ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__self__if,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.20/1.54 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.20/1.54 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__self,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.54 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_right__inverse__eq,axiom,
% 1.20/1.54 ! [V_a_2,V_b_2,T_a] :
% 1.20/1.54 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.54 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 1.20/1.54 <=> V_a_2 = V_b_2 ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_nonzero__minus__divide__divide,axiom,
% 1.20/1.54 ! [V_a,V_b,T_a] :
% 1.20/1.54 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_nonzero__minus__divide__right,axiom,
% 1.20/1.54 ! [V_a,V_b,T_a] :
% 1.20/1.54 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 1.20/1.54 ! [V_n_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.20/1.54 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_not__real__of__nat__less__zero,axiom,
% 1.20/1.54 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 1.20/1.54 ! [V_n_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__of__nat__le__iff,axiom,
% 1.20/1.54 ! [V_m_2,V_n_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__of__nat__add,axiom,
% 1.20/1.54 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__0__le__divide__iff,axiom,
% 1.20/1.54 ! [V_y_2,V_x_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.20/1.54 <=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.20/1.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) )
% 1.20/1.54 & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.20/1.54 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__diff__le,axiom,
% 1.20/1.54 ! [V_m,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.20/1.54 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_nat__less__real__le,axiom,
% 1.20/1.54 ! [V_m_2,V_n_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__of__nat__diff,axiom,
% 1.20/1.54 ! [V_m,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.20/1.54 => 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)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__Suc__diff__eq2,axiom,
% 1.20/1.54 ! [V_m,V_j,V_k] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.20/1.54 => 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)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__Suc__diff__eq1,axiom,
% 1.20/1.54 ! [V_m,V_j,V_k] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.20/1.54 => 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)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 1.20/1.54 ! [V_c,V_a,T_a] :
% 1.20/1.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 1.20/1.54 ! [V_d,V_c,V_a,T_a] :
% 1.20/1.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 1.20/1.54 ! [V_d,V_c,V_a,T_a] :
% 1.20/1.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 1.20/1.54 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 1.20/1.54 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 1.20/1.54 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.20/1.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_nat__le__real__less,axiom,
% 1.20/1.54 ! [V_m_2,V_n_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__0__iff,axiom,
% 1.20/1.54 ! [V_a_2,V_b_2,T_a] :
% 1.20/1.54 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.20/1.54 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
% 1.20/1.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_double__eq__0__iff,axiom,
% 1.20/1.54 ! [V_a_2,T_a] :
% 1.20/1.54 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.20/1.54 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096,axiom,
% 1.20/1.54 ! [V_n_2] :
% 1.20/1.54 ? [B_z] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.20/1.54 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n_2))))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096,axiom,
% 1.20/1.54 ? [B_f] :
% 1.20/1.54 ! [B_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B_f,B_x)),v_r)
% 1.20/1.54 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(B_f,B_x))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_x))))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_th,axiom,
% 1.20/1.54 ! [B_n] :
% 1.20/1.54 ? [B_z] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 1.20/1.54 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_z)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__eq__if,axiom,
% 1.20/1.54 ! [V_n,V_m] :
% 1.20/1.54 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n )
% 1.20/1.54 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.54 => 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)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__pred_H,axiom,
% 1.20/1.54 ! [V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.20/1.54 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__eq__plus1,axiom,
% 1.20/1.54 ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Suc__eq__plus1__left,axiom,
% 1.20/1.54 ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 1.20/1.54 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_abs__div__pos,axiom,
% 1.20/1.54 ! [V_x,V_y,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_gt__half__sum,axiom,
% 1.20/1.54 ! [V_b,V_a,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__half__sum,axiom,
% 1.20/1.54 ! [V_b,V_a,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__nonpos__neg,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_minus__divide__right,axiom,
% 1.20/1.54 ! [V_b,V_a,T_a] :
% 1.20/1.54 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.54 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_minus__divide__divide,axiom,
% 1.20/1.54 ! [V_b,V_a,T_a] :
% 1.20/1.54 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_abs__divide,axiom,
% 1.20/1.54 ! [V_b,V_a,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zero__le__divide__iff,axiom,
% 1.20/1.54 ! [V_b_2,V_a_2,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
% 1.20/1.54 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.20/1.54 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.20/1.54 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__le__0__iff,axiom,
% 1.20/1.54 ! [V_b_2,V_a_2,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.20/1.54 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.20/1.54 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__right__mono,axiom,
% 1.20/1.54 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__right__mono__neg,axiom,
% 1.20/1.54 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__strict__right__mono__neg,axiom,
% 1.20/1.54 ! [V_c,V_a,V_b,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__strict__right__mono,axiom,
% 1.20/1.54 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__neg__neg,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__neg__pos,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__pos__neg,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__pos__pos,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__less__0__iff,axiom,
% 1.20/1.54 ! [V_b_2,V_a_2,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.20/1.54 & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.20/1.54 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zero__less__divide__iff,axiom,
% 1.20/1.54 ! [V_b_2,V_a_2,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
% 1.20/1.54 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.20/1.54 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.20/1.54 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_nonzero__abs__divide,axiom,
% 1.20/1.54 ! [V_a,V_b,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__nonneg__pos,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__nonneg__neg,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_frac__less2,axiom,
% 1.20/1.54 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_frac__less,axiom,
% 1.20/1.54 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_frac__le,axiom,
% 1.20/1.54 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__nonpos__pos,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 1.20/1.54 ! [V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 1.20/1.54 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.54 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__eq,axiom,
% 1.20/1.54 ! [V_x,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 1.20/1.54 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_psize__eq__0__iff,axiom,
% 1.20/1.54 ! [V_pa_2,T_a] :
% 1.20/1.54 ( class_Groups_Ozero(T_a)
% 1.20/1.54 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.54 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_order__root,axiom,
% 1.20/1.54 ! [V_a_2,V_pa_2,T_a] :
% 1.20/1.54 ( class_Rings_Oidom(T_a)
% 1.20/1.54 => ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 <=> ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.20/1.54 | c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__real__of__nat,axiom,
% 1.20/1.54 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__zero,axiom,
% 1.20/1.54 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zero__le__natceiling,axiom,
% 1.20/1.54 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__mono,axiom,
% 1.20/1.54 ! [V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__natceiling__ge,axiom,
% 1.20/1.54 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__one,axiom,
% 1.20/1.54 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__neg,axiom,
% 1.20/1.54 ! [V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.20/1.54 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__le,axiom,
% 1.20/1.54 ! [V_a,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__le__eq,axiom,
% 1.20/1.54 ! [V_a_2,V_x_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__le__eq__one,axiom,
% 1.20/1.54 ! [V_x_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__subtract,axiom,
% 1.20/1.54 ! [V_x,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 1.20/1.54 => 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) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__add,axiom,
% 1.20/1.54 ! [V_a,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.54 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natceiling__add__one,axiom,
% 1.20/1.54 ! [V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.54 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_AALL_An_O_Acmod_A_Ig_An_J_A_060_061_Ar_059_AALL_An_O_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.20/1.54 ~ ! [B_g] :
% 1.20/1.54 ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(B_g,B_n)),v_r)
% 1.20/1.54 => ~ ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(B_g,B_n))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_reals__Archimedean6,axiom,
% 1.20/1.54 ! [V_r] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 1.20/1.54 => ? [B_n] :
% 1.20/1.54 ( 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)
% 1.20/1.54 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_unimodular__reduce__norm,axiom,
% 1.20/1.54 ! [V_z] :
% 1.20/1.54 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 1.20/1.54 => ( 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))
% 1.20/1.54 | 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))
% 1.20/1.54 | 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))
% 1.20/1.54 | 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)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__add__one,axiom,
% 1.20/1.54 ! [V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.54 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_complex__i__not__one,axiom,
% 1.20/1.54 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__real__of__nat,axiom,
% 1.20/1.54 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 1.20/1.54
% 1.20/1.54 fof(fact_complex__i__not__zero,axiom,
% 1.20/1.54 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__zero,axiom,
% 1.20/1.54 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zero__le__natfloor,axiom,
% 1.20/1.54 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__mono,axiom,
% 1.20/1.54 ! [V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__one,axiom,
% 1.20/1.54 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__neg,axiom,
% 1.20/1.54 ! [V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.20/1.54 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__natfloor__le,axiom,
% 1.20/1.54 ! [V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__natfloor,axiom,
% 1.20/1.54 ! [V_a,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__natfloor__eq,axiom,
% 1.20/1.54 ! [V_a_2,V_x_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__natfloor__eq__one,axiom,
% 1.20/1.54 ! [V_x_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__natfloor__add__one__gt,axiom,
% 1.20/1.54 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__subtract,axiom,
% 1.20/1.54 ! [V_x,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 1.20/1.54 => 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) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__natfloor__gt__diff__one,axiom,
% 1.20/1.54 ! [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))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__natfloor,axiom,
% 1.20/1.54 ! [V_n,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__add,axiom,
% 1.20/1.54 ! [V_a,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.54 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 1.20/1.54 ! [V_n,V_z] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__eq,axiom,
% 1.20/1.54 ! [V_x,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 1.20/1.54 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__Suc__ex__iff,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 1.20/1.54 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_termination__basic__simps_I3_J,axiom,
% 1.20/1.54 ! [V_z,V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_termination__basic__simps_I4_J,axiom,
% 1.20/1.54 ! [V_y,V_z,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_termination__basic__simps_I2_J,axiom,
% 1.20/1.54 ! [V_y,V_z,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_termination__basic__simps_I1_J,axiom,
% 1.20/1.54 ! [V_z,V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_termination__basic__simps_I5_J,axiom,
% 1.20/1.54 ! [V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Limits_Ominus__diff__minus,axiom,
% 1.20/1.54 ! [V_b,V_a,T_a] :
% 1.20/1.54 ( class_Groups_Oab__group__add(T_a)
% 1.20/1.54 => 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)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_natfloor__div__nat,axiom,
% 1.20/1.54 ! [V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y)
% 1.20/1.54 => c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_decseq__def,axiom,
% 1.20/1.54 ! [V_X_2,T_a] :
% 1.20/1.54 ( class_Orderings_Oorder(T_a)
% 1.20/1.54 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 1.20/1.54 <=> ! [B_m,B_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__of__nat__div4,axiom,
% 1.20/1.54 ! [V_x,V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__of__nat__div2,axiom,
% 1.20/1.54 ! [V_x,V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__of__nat__div3,axiom,
% 1.20/1.54 ! [V_x,V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__div__geq,axiom,
% 1.20/1.54 ! [V_m,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__if,axiom,
% 1.20/1.54 ! [V_m,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.20/1.54 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.20/1.54 & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__geq,axiom,
% 1.20/1.54 ! [V_m,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.20/1.54 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__0,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Divides_Osemiring__div(T_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__by__0,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Divides_Osemiring__div(T_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__by__1,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Divides_Osemiring__div(T_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__le__mono,axiom,
% 1.20/1.54 ! [V_k,V_n,V_m] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__le__dividend,axiom,
% 1.20/1.54 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__self,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Divides_Osemiring__div(T_a)
% 1.20/1.54 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__1,axiom,
% 1.20/1.54 ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__less,axiom,
% 1.20/1.54 ! [V_n,V_m] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__add__self1,axiom,
% 1.20/1.54 ! [V_a,V_b,T_a] :
% 1.20/1.54 ( class_Divides_Osemiring__div(T_a)
% 1.20/1.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__add__self2,axiom,
% 1.20/1.54 ! [V_a,V_b,T_a] :
% 1.20/1.54 ( class_Divides_Osemiring__div(T_a)
% 1.20/1.54 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__le__mono2,axiom,
% 1.20/1.54 ! [V_k,V_n,V_m] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__less__dividend,axiom,
% 1.20/1.54 ! [V_m,V_n] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Deriv_Oadd__diff__add,axiom,
% 1.20/1.54 ! [V_d,V_b,V_c,V_a,T_a] :
% 1.20/1.54 ( class_Groups_Oab__group__add(T_a)
% 1.20/1.54 => 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)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_compl__mono,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Lattices_Oboolean__algebra(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_compl__le__compl__iff,axiom,
% 1.20/1.54 ! [V_y_2,V_x_2,T_a] :
% 1.20/1.54 ( class_Lattices_Oboolean__algebra(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_poly__div__minus__right,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Ofield(T_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_poly__div__minus__left,axiom,
% 1.20/1.54 ! [V_y,V_x,T_a] :
% 1.20/1.54 ( class_Fields_Ofield(T_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_minus__apply,axiom,
% 1.20/1.54 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 1.20/1.54 ( class_Groups_Ominus(T_a)
% 1.20/1.54 => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_compl__eq__compl__iff,axiom,
% 1.20/1.54 ! [V_y_2,V_x_2,T_a] :
% 1.20/1.54 ( class_Lattices_Oboolean__algebra(T_a)
% 1.20/1.54 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
% 1.20/1.54 <=> V_x_2 = V_y_2 ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_uminus__apply,axiom,
% 1.20/1.54 ! [V_x_2,V_A_2,T_b,T_a] :
% 1.20/1.54 ( class_Groups_Ouminus(T_a)
% 1.20/1.54 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_double__compl,axiom,
% 1.20/1.54 ! [V_x,T_a] :
% 1.20/1.54 ( class_Lattices_Oboolean__algebra(T_a)
% 1.20/1.54 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_poly__cont,axiom,
% 1.20/1.54 ! [V_p,V_z,V_e] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)
% 1.20/1.54 => ? [B_d] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 1.20/1.54 & ! [B_w] :
% 1.20/1.54 ( ( 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)))
% 1.20/1.54 & 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) )
% 1.20/1.54 => 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) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__poly__def,axiom,
% 1.20/1.54 ! [V_x,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => ( ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 1.20/1.54 & ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 1.20/1.54 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) )
% 1.20/1.54 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) ) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_th2,axiom,
% 1.20/1.54 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),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_N2,axiom,
% 1.20/1.54 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,v_N2____)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_d_I2_J,axiom,
% 1.20/1.54 ! [B_w] :
% 1.20/1.54 ( ( 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____)))
% 1.20/1.54 & 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____)),v_d____) )
% 1.20/1.54 => 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____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_e2,axiom,
% 1.20/1.54 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_th1,axiom,
% 1.20/1.54 ! [V_wa_2] :
% 1.20/1.54 ( 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_wa_2,v_z____)),v_d____)
% 1.20/1.54 => 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),V_wa_2),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096,axiom,
% 1.20/1.54 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact__0961_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096,axiom,
% 1.20/1.54 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_thc1,axiom,
% 1.20/1.54 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__average__minus__second,axiom,
% 1.20/1.54 ! [V_a,V_b] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__average__minus__first,axiom,
% 1.20/1.54 ! [V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Bit1__def,axiom,
% 1.20/1.54 ! [V_k] : c_Int_OBit1(V_k) = 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_k),V_k) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_number__of__Bit1,axiom,
% 1.20/1.54 ! [V_w,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_one__add__one__is__two,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__special_I2_J,axiom,
% 1.20/1.54 ! [V_w,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__special_I1_J,axiom,
% 1.20/1.54 ! [V_w,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__special_I3_J,axiom,
% 1.20/1.54 ! [V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__special_I2_J,axiom,
% 1.20/1.54 ! [V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__special_I4_J,axiom,
% 1.20/1.54 ! [V_x_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__special_I2_J,axiom,
% 1.20/1.54 ! [V_y_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_semiring__norm_I110_J,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_numeral__1__eq__1,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__special_I4_J,axiom,
% 1.20/1.54 ! [V_x_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__special_I2_J,axiom,
% 1.20/1.54 ! [V_y_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__one,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I5_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I29_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__number__of__eq,axiom,
% 1.20/1.54 ! [V_w,V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I15_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__int__code_I14_J,axiom,
% 1.20/1.54 ! [V_k2_2,V_k1_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I33_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__eq__int__code_I15_J,axiom,
% 1.20/1.54 ! [V_k2_2,V_k1_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__int__code_I16_J,axiom,
% 1.20/1.54 ! [V_k2_2,V_k1_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__int__code_I15_J,axiom,
% 1.20/1.54 ! [V_k2_2,V_k1_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I17_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I16_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__int__code_I13_J,axiom,
% 1.20/1.54 ! [V_k2_2,V_k1_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I14_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_bin__less__0__simps_I4_J,axiom,
% 1.20/1.54 ! [V_wa_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I12_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_bin__less__0__simps_I3_J,axiom,
% 1.20/1.54 ! [V_wa_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I10_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I4_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_bin__less__0__simps_I1_J,axiom,
% 1.20/1.54 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I2_J,axiom,
% 1.20/1.54 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_minus__Bit0,axiom,
% 1.20/1.54 ! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_number__of__Pls,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_minus__Pls,axiom,
% 1.20/1.54 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Pls__def,axiom,
% 1.20/1.54 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__eq__int__code_I16_J,axiom,
% 1.20/1.54 ! [V_k2_2,V_k1_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I34_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__eq__int__code_I14_J,axiom,
% 1.20/1.54 ! [V_k2_2,V_k1_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__eq__int__code_I13_J,axiom,
% 1.20/1.54 ! [V_k2_2,V_k1_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I32_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I31_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I27_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I22_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I21_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I19_J,axiom,
% 1.20/1.54 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__number__of,axiom,
% 1.20/1.54 ! [V_y_2,V_x_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__number__of,axiom,
% 1.20/1.54 ! [V_y_2,V_x_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__number__of__left,axiom,
% 1.20/1.54 ! [V_z,V_w,V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__number__of__eq,axiom,
% 1.20/1.54 ! [V_w,V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_number__of__add,axiom,
% 1.20/1.54 ! [V_w,V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_number__of__diff,axiom,
% 1.20/1.54 ! [V_w,V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_arith__simps_I30_J,axiom,
% 1.20/1.54 ! [V_w,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_number__of__minus,axiom,
% 1.20/1.54 ! [V_w,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_number__of__Bit0,axiom,
% 1.20/1.54 ! [V_w,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__special_I3_J,axiom,
% 1.20/1.54 ! [V_x_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__special_I1_J,axiom,
% 1.20/1.54 ! [V_y_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__special_I1_J,axiom,
% 1.20/1.54 ! [V_y_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__special_I3_J,axiom,
% 1.20/1.54 ! [V_x_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_eq__number__of,axiom,
% 1.20/1.54 ! [V_y_2,V_x_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Int_Oring__char__0(T_a) )
% 1.20/1.54 => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
% 1.20/1.54 <=> V_x_2 = V_y_2 ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I51_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 1.20/1.54 <=> V_k_2 = V_l_2 ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I48_J,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 1.20/1.54 <=> V_k_2 = V_l_2 ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I50_J,axiom,
% 1.20/1.54 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I49_J,axiom,
% 1.20/1.54 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_number__of__reorient,axiom,
% 1.20/1.54 ! [V_x_2,V_wa_2,T_a] :
% 1.20/1.54 ( class_Int_Onumber(T_a)
% 1.20/1.54 => ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
% 1.20/1.54 <=> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I44_J,axiom,
% 1.20/1.54 ! [V_k_2] :
% 1.20/1.54 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 1.20/1.54 <=> V_k_2 = c_Int_OPls ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I46_J,axiom,
% 1.20/1.54 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I38_J,axiom,
% 1.20/1.54 ! [V_l_2] :
% 1.20/1.54 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 1.20/1.54 <=> c_Int_OPls = V_l_2 ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_rel__simps_I39_J,axiom,
% 1.20/1.54 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Bit0__Pls,axiom,
% 1.20/1.54 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__bin__simps_I10_J,axiom,
% 1.20/1.54 ! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__bin__simps_I9_J,axiom,
% 1.20/1.54 ! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__bin__simps_I7_J,axiom,
% 1.20/1.54 ! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__Bit1__Bit0,axiom,
% 1.20/1.54 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__Bit0__Bit1,axiom,
% 1.20/1.54 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__Bit0__Bit0,axiom,
% 1.20/1.54 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__numeral__0,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__numeral__0__right,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__bin__simps_I1_J,axiom,
% 1.20/1.54 ! [V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__Pls__right,axiom,
% 1.20/1.54 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__bin__simps_I3_J,axiom,
% 1.20/1.54 ! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,V_l)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__Pls,axiom,
% 1.20/1.54 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Bit0__def,axiom,
% 1.20/1.54 ! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_norm__number__of,axiom,
% 1.20/1.54 ! [V_w,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_RealVector_Oreal__normed__algebra__1(T_a) )
% 1.20/1.54 => c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__sgn,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__minus,axiom,
% 1.20/1.54 ! [V_x,T_a] :
% 1.20/1.54 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn0,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( class_Groups_Osgn__if(T_a)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__zero,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__zero__iff,axiom,
% 1.20/1.54 ! [V_x_2,T_a] :
% 1.20/1.54 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.20/1.54 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__0__0,axiom,
% 1.20/1.54 ! [V_a_2,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__numeral__1,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( ( class_Fields_Ofield(T_a)
% 1.20/1.54 & class_Int_Onumber__ring(T_a) )
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__Numeral1,axiom,
% 1.20/1.54 ! [V_x,T_a] :
% 1.20/1.54 ( ( class_Fields_Ofield(T_a)
% 1.20/1.54 & class_Int_Onumber__ring(T_a) )
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_semiring__norm_I112_J,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_half__gt__zero__iff,axiom,
% 1.20/1.54 ! [V_ra_2,T_a] :
% 1.20/1.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 & class_Int_Onumber__ring(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_ra_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ra_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_divide__Numeral0,axiom,
% 1.20/1.54 ! [V_x,T_a] :
% 1.20/1.54 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.54 & class_Int_Onumber__ring(T_a) )
% 1.20/1.54 => c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_half__gt__zero,axiom,
% 1.20/1.54 ! [V_r,T_a] :
% 1.20/1.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 & class_Int_Onumber__ring(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__gt__half__sum,axiom,
% 1.20/1.54 ! [V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__less__half__sum,axiom,
% 1.20/1.54 ! [V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_real__sum__of__halves,axiom,
% 1.20/1.54 ! [V_x] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x ).
% 1.20/1.54
% 1.20/1.54 fof(fact_half,axiom,
% 1.20/1.54 ! [T_a] :
% 1.20/1.54 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.54 & class_Int_Onumber__ring(T_a) )
% 1.20/1.54 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_le__number__of__eq__not__less,axiom,
% 1.20/1.54 ! [V_wa_2,V_v_2,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber(T_a)
% 1.20/1.54 & class_Orderings_Olinorder(T_a) )
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.20/1.54 <=> ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__number__of__diff2,axiom,
% 1.20/1.54 ! [V_w,V_c,V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,V_c,c_Int_Onumber__class_Onumber__of(T_a,V_w))) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_c) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_add__number__of__diff1,axiom,
% 1.20/1.54 ! [V_c,V_w,V_v,T_a] :
% 1.20/1.54 ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__greater,axiom,
% 1.20/1.54 ! [V_a_2,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__less,axiom,
% 1.20/1.54 ! [V_a_2,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__1__pos,axiom,
% 1.20/1.54 ! [V_a_2,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__pos,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_abs__number__of,axiom,
% 1.20/1.54 ! [V_x,T_a] :
% 1.20/1.54 ( ( class_Int_Onumber__ring(T_a)
% 1.20/1.54 & class_Rings_Olinordered__idom(T_a) )
% 1.20/1.54 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) )
% 1.20/1.54 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x)) = c_Int_Onumber__class_Onumber__of(T_a,V_x) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__1__neg,axiom,
% 1.20/1.54 ! [V_a_2,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__neg,axiom,
% 1.20/1.54 ! [V_a,T_a] :
% 1.20/1.54 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_sgn__if,axiom,
% 1.20/1.54 ! [V_x,T_a] :
% 1.20/1.54 ( class_Groups_Osgn__if(T_a)
% 1.20/1.54 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.20/1.54 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 1.20/1.54 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_norm__sgn,axiom,
% 1.20/1.54 ! [V_x,T_a] :
% 1.20/1.54 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.20/1.54 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 1.20/1.54 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.54 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096,axiom,
% 1.20/1.54 ? [B_d] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 1.20/1.54 & ! [B_w] :
% 1.20/1.54 ( ( 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____)))
% 1.20/1.54 & 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) )
% 1.20/1.54 => 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____))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact__096_B_Bthesis_O_A_I_B_BN2_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_AN2_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.20/1.54 ~ ! [B_N2] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,B_N2)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact__096EX_An_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_An_096,axiom,
% 1.20/1.54 ? [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,B_n)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__number__of__Bit0,axiom,
% 1.20/1.54 ! [V_w,V_v] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__zero,axiom,
% 1.20/1.54 ! [V_b] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__zminus2,axiom,
% 1.20/1.54 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__zminus__zminus,axiom,
% 1.20/1.54 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 1.20/1.54 ! [V_a_2,V_b_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 1.20/1.54 ! [V_a_2,V_b_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__neg__pos__less0,axiom,
% 1.20/1.54 ! [V_b,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__mono1__neg,axiom,
% 1.20/1.54 ! [V_b,V_a_H,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__mono1,axiom,
% 1.20/1.54 ! [V_b,V_a_H,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__neg__neg__trivial,axiom,
% 1.20/1.54 ! [V_b,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__mono2__neg,axiom,
% 1.20/1.54 ! [V_b,V_b_H,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__nonpos__pos__le0,axiom,
% 1.20/1.54 ! [V_b,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 1.20/1.54 ! [V_a_2,V_b_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__pos__pos__trivial,axiom,
% 1.20/1.54 ! [V_b,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_div__nonneg__neg__le0,axiom,
% 1.20/1.54 ! [V_b,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__mono2,axiom,
% 1.20/1.54 ! [V_b,V_b_H,V_a] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 1.20/1.54 ! [V_y,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 1.20/1.54 ! [V_b_2,V_a_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
% 1.20/1.54 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_a_2)
% 1.20/1.54 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 1.20/1.54 ! [V_i_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 1.20/1.54 ! [V_a_2,V_b_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__eq__0__iff,axiom,
% 1.20/1.54 ! [V_k_2,V_i_2] :
% 1.20/1.54 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.20/1.54 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.20/1.54 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)
% 1.20/1.54 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) )
% 1.20/1.54 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zdiv__self,axiom,
% 1.20/1.54 ! [V_a] :
% 1.20/1.54 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.20/1.54 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_int__div__less__self,axiom,
% 1.20/1.54 ! [V_k,V_x] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
% 1.20/1.54 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zle__diff1__eq,axiom,
% 1.20/1.54 ! [V_za_2,V_wa_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zsgn__def,axiom,
% 1.20/1.54 ! [V_i] :
% 1.20/1.54 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 1.20/1.54 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.20/1.54 => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 1.20/1.54 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)
% 1.20/1.54 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_complex__i__not__number__of,axiom,
% 1.20/1.54 ! [V_w] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zabs__def,axiom,
% 1.20/1.54 ! [V_i] :
% 1.20/1.54 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) )
% 1.20/1.54 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.54 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zminus__zadd__distrib,axiom,
% 1.20/1.54 ! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__int__def,axiom,
% 1.20/1.54 ! [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)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__bin__lemma,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
% 1.20/1.54 <=> 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)) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_diff__int__def__symmetric,axiom,
% 1.20/1.54 ! [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) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zadd__zminus__inverse2,axiom,
% 1.20/1.54 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_minus__numeral__code_I6_J,axiom,
% 1.20/1.54 ! [V_w,V_v] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__number__of__int__code,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_minus__numeral__code_I5_J,axiom,
% 1.20/1.54 ! [V_w] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zminus__zminus,axiom,
% 1.20/1.54 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zminus__0,axiom,
% 1.20/1.54 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zero__is__num__zero,axiom,
% 1.20/1.54 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_less__eq__number__of__int__code,axiom,
% 1.20/1.54 ! [V_l_2,V_k_2] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
% 1.20/1.54 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_plus__numeral__code_I9_J,axiom,
% 1.20/1.54 ! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zadd__commute,axiom,
% 1.20/1.54 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zadd__left__commute,axiom,
% 1.20/1.54 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zadd__assoc,axiom,
% 1.20/1.54 ! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zle__refl,axiom,
% 1.20/1.54 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zle__linear,axiom,
% 1.20/1.54 ! [V_w,V_z] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.20/1.54 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zle__trans,axiom,
% 1.20/1.54 ! [V_k,V_j,V_i] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 1.20/1.54 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 1.20/1.54
% 1.20/1.54 fof(fact_zle__antisym,axiom,
% 1.20/1.54 ! [V_w,V_z] :
% 1.20/1.54 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.20/1.54 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 1.20/1.54 => V_z = V_w ) ) ).
% 1.20/1.54
% 1.20/1.55 fof(fact_zless__linear,axiom,
% 1.20/1.55 ! [V_y,V_x] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 1.20/1.55 | V_x = V_y
% 1.20/1.55 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zadd__zless__mono,axiom,
% 1.20/1.55 ! [V_z,V_z_H,V_w,V_w_H] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zadd__left__mono,axiom,
% 1.20/1.55 ! [V_k,V_j,V_i] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zadd__strict__right__mono,axiom,
% 1.20/1.55 ! [V_k,V_j,V_i] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zless__le,axiom,
% 1.20/1.55 ! [V_wa_2,V_za_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
% 1.20/1.55 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2)
% 1.20/1.55 & V_za_2 != V_wa_2 ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zadd__0__right,axiom,
% 1.20/1.55 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zadd__0,axiom,
% 1.20/1.55 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 1.20/1.55
% 1.20/1.55 fof(fact_int__0__neq__1,axiom,
% 1.20/1.55 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_int__0__less__1,axiom,
% 1.20/1.55 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zless__imp__add1__zle,axiom,
% 1.20/1.55 ! [V_z,V_w] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_le__imp__0__less,axiom,
% 1.20/1.55 ! [V_z] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_odd__less__0,axiom,
% 1.20/1.55 ! [V_za_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_add1__zle__eq,axiom,
% 1.20/1.55 ! [V_za_2,V_wa_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zabs__less__one__iff,axiom,
% 1.20/1.55 ! [V_za_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
% 1.20/1.55 <=> V_za_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zless__add1__eq,axiom,
% 1.20/1.55 ! [V_za_2,V_wa_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.20/1.55 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
% 1.20/1.55 | V_wa_2 = V_za_2 ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zle__add1__eq__le,axiom,
% 1.20/1.55 ! [V_za_2,V_wa_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_int__one__le__iff__zero__less,axiom,
% 1.20/1.55 ! [V_za_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_odd__nonzero,axiom,
% 1.20/1.55 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_one__is__num__one,axiom,
% 1.20/1.55 c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zdiv__number__of__Bit1,axiom,
% 1.20/1.55 ! [V_v,V_w] :
% 1.20/1.55 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))
% 1.20/1.55 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) )
% 1.20/1.55 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))
% 1.20/1.55 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w))) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_eq__0__number__of,axiom,
% 1.20/1.55 ! [V_v_2] :
% 1.20/1.55 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_eq__number__of__0,axiom,
% 1.20/1.55 ! [V_v_2] :
% 1.20/1.55 ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nat__number__of__Pls,axiom,
% 1.20/1.55 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_semiring__norm_I113_J,axiom,
% 1.20/1.55 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_less__nat__number__of,axiom,
% 1.20/1.55 ! [V_v_H_2,V_v_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
% 1.20/1.55 <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) )
% 1.20/1.55 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_add__nat__number__of,axiom,
% 1.20/1.55 ! [V_v_H,V_v] :
% 1.20/1.55 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H) )
% 1.20/1.55 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.20/1.55 => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) )
% 1.20/1.55 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_le__nat__number__of,axiom,
% 1.20/1.55 ! [V_v_H_2,V_v_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
% 1.20/1.55 <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_natfloor__number__of__eq,axiom,
% 1.20/1.55 ! [V_n] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_natceiling__number__of__eq,axiom,
% 1.20/1.55 ! [V_n] : c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_real__sgn__eq,axiom,
% 1.20/1.55 ! [V_x] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
% 1.20/1.55 ! [V_x] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 1.20/1.55 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.20/1.55 | V_x = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_less__0__number__of,axiom,
% 1.20/1.55 ! [V_v_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nat__numeral__1__eq__1,axiom,
% 1.20/1.55 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_Numeral1__eq1__nat,axiom,
% 1.20/1.55 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_real__sgn__pos,axiom,
% 1.20/1.55 ! [V_x] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_numeral__3__eq__3,axiom,
% 1.20/1.55 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_numeral__1__eq__Suc__0,axiom,
% 1.20/1.55 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_Suc3__eq__add__3,axiom,
% 1.20/1.55 ! [V_n] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),V_n) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_real__sgn__def,axiom,
% 1.20/1.55 ! [V_x] :
% 1.20/1.55 ( ( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 1.20/1.55 & ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.20/1.55 => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
% 1.20/1.55 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_sgn__real__def,axiom,
% 1.20/1.55 ! [V_a] :
% 1.20/1.55 ( ( V_a = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 1.20/1.55 & ( V_a != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.20/1.55 => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
% 1.20/1.55 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_numeral__2__eq__2,axiom,
% 1.20/1.55 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_semiring__norm_I115_J,axiom,
% 1.20/1.55 c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_add__2__eq__Suc,axiom,
% 1.20/1.55 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n) = c_Nat_OSuc(c_Nat_OSuc(V_n)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_add__2__eq__Suc_H,axiom,
% 1.20/1.55 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(V_n)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 1.20/1.55 ! [V_m,V_n] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),V_n)
% 1.20/1.55 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nat__1__add__1,axiom,
% 1.20/1.55 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_expand__Suc,axiom,
% 1.20/1.55 ! [V_v] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))
% 1.20/1.55 => c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_div2__Suc__Suc,axiom,
% 1.20/1.55 ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(V_m)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 1.20/1.55 ! [V_v,V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(V_m))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),V_m),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_Suc__div__eq__add3__div,axiom,
% 1.20/1.55 ! [V_n,V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(V_m))),V_n) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),V_m),V_n) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_div__Suc__eq__div__add3,axiom,
% 1.20/1.55 ! [V_n,V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(V_n)))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),V_n)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_add__self__div__2,axiom,
% 1.20/1.55 ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_m),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m ).
% 1.20/1.55
% 1.20/1.55 fof(fact_less__2__cases,axiom,
% 1.20/1.55 ! [V_n] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 1.20/1.55 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.20/1.55 | V_n = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_div__2__gt__zero,axiom,
% 1.20/1.55 ! [V_n] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 1.20/1.55 ! [V_n] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096,axiom,
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_th0,axiom,
% 1.20/1.55 ! [V_m_2,V_b_2,V_e2_2,V_a_2] :
% 1.20/1.55 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a_2,V_e2_2)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_m_2)),V_e2_2)
% 1.20/1.55 => ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_e2_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_m_2)),V_a_2)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_DERIV__inverse__lemma,axiom,
% 1.20/1.55 ! [V_h,V_b,V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__field(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)),V_h) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_h)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_Deriv_Oinverse__diff__inverse,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_division__ring__inverse__diff,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__number__of__left,axiom,
% 1.20/1.55 ! [V_z,V_w,V_v,T_a] :
% 1.20/1.55 ( class_Int_Onumber__ring(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_arith__simps_I32_J,axiom,
% 1.20/1.55 ! [V_w,V_v,T_a] :
% 1.20/1.55 ( class_Int_Onumber__ring(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_number__of__mult,axiom,
% 1.20/1.55 ! [V_w,V_v,T_a] :
% 1.20/1.55 ( class_Int_Onumber__ring(T_a)
% 1.20/1.55 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_number__of__is__id,axiom,
% 1.20/1.55 ! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__minus__eq,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_sgn__mult,axiom,
% 1.20/1.55 ! [V_y,V_x,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x),c_Groups_Osgn__class_Osgn(T_a,V_y)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_sgn__times,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_a)
% 1.20/1.55 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Ominus__right,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__right_Ominus,axiom,
% 1.20/1.55 ! [V_x,V_xa,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Ominus__left,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__left_Ominus,axiom,
% 1.20/1.55 ! [V_y,V_x,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_square__eq__iff,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Rings_Oidom(T_a)
% 1.20/1.55 => ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_a_2) = c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2)
% 1.20/1.55 <=> ( V_a_2 = V_b_2
% 1.20/1.55 | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_minus__mult__minus,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oring(T_a)
% 1.20/1.55 => 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)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_minus__mult__commute,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oring(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_minus__mult__left,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oring(T_a)
% 1.20/1.55 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_minus__mult__right,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oring(T_a)
% 1.20/1.55 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Odiff__right,axiom,
% 1.20/1.55 ! [V_b_H,V_b,V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__right_Odiff,axiom,
% 1.20/1.55 ! [V_y,V_x,V_xa,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Odiff__left,axiom,
% 1.20/1.55 ! [V_b,V_a_H,V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__left_Odiff,axiom,
% 1.20/1.55 ! [V_ya,V_y,V_x,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_real__mult__right__cancel,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,V_c_2] :
% 1.20/1.55 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.20/1.55 => ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)
% 1.20/1.55 <=> V_a_2 = V_b_2 ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_real__mult__left__cancel,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,V_c_2] :
% 1.20/1.55 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.20/1.55 => ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)
% 1.20/1.55 <=> V_a_2 = V_b_2 ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_real__add__mult__distrib,axiom,
% 1.20/1.55 ! [V_w,V_z2,V_z1] : 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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w)) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_combine__common__factor,axiom,
% 1.20/1.55 ! [V_c,V_b,V_e,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Osemiring(T_a)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__class_Odistrib,axiom,
% 1.20/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__left_Oadd,axiom,
% 1.20/1.55 ! [V_ya,V_y,V_x,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Oadd__left,axiom,
% 1.20/1.55 ! [V_b,V_a_H,V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__right_Oadd,axiom,
% 1.20/1.55 ! [V_y,V_x,V_xa,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Oadd__right,axiom,
% 1.20/1.55 ! [V_b_H,V_b,V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__zero__left,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Omult__zero(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__zero__right,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Omult__zero(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__eq__0__iff,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Rings_Oring__no__zero__divisors(T_a)
% 1.20/1.55 => ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_no__zero__divisors,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ono__zero__divisors(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_divisors__zero,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ono__zero__divisors(T_a)
% 1.20/1.55 => ( c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__right_Ozero,axiom,
% 1.20/1.55 ! [V_x,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Ozero__right,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__left_Ozero,axiom,
% 1.20/1.55 ! [V_y,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Ozero__left,axiom,
% 1.20/1.55 ! [V_b,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_INVERSE__ZERO,axiom,
% 1.20/1.55 c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__zero,axiom,
% 1.20/1.55 ! [T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__nonzero__iff__nonzero,axiom,
% 1.20/1.55 ! [V_a_2,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.20/1.55 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nonzero__imp__inverse__nonzero,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nonzero__inverse__inverse__eq,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__zero__imp__zero,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nonzero__inverse__eq__imp__eq,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => V_a = V_b ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_norm__mult__less,axiom,
% 1.20/1.55 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_s)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_norm__mult__ineq,axiom,
% 1.20/1.55 ! [V_y,V_x,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nonzero__norm__inverse,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_division__ring__inverse__add,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 1.20/1.55 ! [V_z,V_y,V_x,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_x,V_z)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_crossproduct__noteq,axiom,
% 1.20/1.55 ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.20/1.55 => ( ( V_a_2 != V_b_2
% 1.20/1.55 & V_c_2 != V_da_2 )
% 1.20/1.55 <=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_da_2)) != c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_da_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 1.20/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 1.20/1.55 ! [V_b,V_m,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),c_Groups_Otimes__class_Otimes(T_a,V_b,V_m)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_m) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_crossproduct__eq,axiom,
% 1.20/1.55 ! [V_za_2,V_x_2,V_y_2,V_wa_2,T_a] :
% 1.20/1.55 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.20/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_wa_2,V_y_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_wa_2,V_za_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_y_2))
% 1.20/1.55 <=> ( V_wa_2 = V_x_2
% 1.20/1.55 | V_y_2 = V_za_2 ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nonzero__inverse__mult__distrib,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_field__inverse__zero,axiom,
% 1.20/1.55 ! [T_a] :
% 1.20/1.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__add,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Fields_Ofield(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_field__inverse,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Fields_Ofield(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__eq__1__iff,axiom,
% 1.20/1.55 ! [V_x_2,T_a] :
% 1.20/1.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.55 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.20/1.55 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_real__mult__1,axiom,
% 1.20/1.55 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z) = V_z ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__1__left,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Groups_Omonoid__mult(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__1,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__1__right,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Groups_Omonoid__mult(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Ocomm__neutral,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__1,axiom,
% 1.20/1.55 ! [T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_real__mult__inverse__left,axiom,
% 1.20/1.55 ! [V_x] :
% 1.20/1.55 ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x),V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__unique,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Oone__class_Oone(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_right__inverse,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_left__inverse,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_Bseq__inverse__lemma,axiom,
% 1.20/1.55 ! [V_x,V_r,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_r,c_RealVector_Onorm__class_Onorm(T_a,V_x))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_r)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
% 1.20/1.55 ! [V_a_2,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
% 1.20/1.55 ! [V_a_2,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__positive__iff__positive,axiom,
% 1.20/1.55 ! [V_a_2,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__negative__iff__negative,axiom,
% 1.20/1.55 ! [V_a_2,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_positive__imp__inverse__positive,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__positive__imp__positive,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_negative__imp__inverse__negative,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_less__imp__inverse__less,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_less__imp__inverse__less__neg,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__negative__imp__negative,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__less__imp__less,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__less__imp__less__neg,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nonzero__inverse__minus__eq,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nonzero__abs__inverse,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Fields_Olinordered__field(T_a)
% 1.20/1.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_field__class_Onormalizing__field__rules_I2_J,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Fields_Ofield(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_inverse__eq__divide,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zero__le__square,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring(T_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zero__le__mult__iff,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2))
% 1.20/1.55 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.20/1.55 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.20/1.55 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__le__0__iff,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.20/1.55 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.20/1.55 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__nonneg__nonneg,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__nonneg__nonpos,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__nonneg__nonpos2,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__nonpos__nonneg,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__nonpos__nonpos,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__ring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__right__mono,axiom,
% 1.20/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__left__mono,axiom,
% 1.20/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__mult__left__mono,axiom,
% 1.20/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__comm__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__right__mono__neg,axiom,
% 1.20/1.55 ! [V_c,V_a,V_b,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__ring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__left__mono__neg,axiom,
% 1.20/1.55 ! [V_c,V_a,V_b,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__ring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__mono_H,axiom,
% 1.20/1.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__mono,axiom,
% 1.20/1.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__semiring(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_split__mult__pos__le,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__ring(T_a)
% 1.20/1.55 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 1.20/1.55 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_split__mult__neg__le,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.20/1.55 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.20/1.55 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 1.20/1.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__strict__left__mono__neg,axiom,
% 1.20/1.55 ! [V_c,V_a,V_b,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__strict__right__mono__neg,axiom,
% 1.20/1.55 ! [V_c,V_a,V_b,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__mult__strict__left__mono,axiom,
% 1.20/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__strict__left__mono,axiom,
% 1.20/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__strict__right__mono,axiom,
% 1.20/1.55 ! [V_c,V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__neg__neg,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__neg__pos,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__less__cancel__left__neg,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zero__less__mult__pos2,axiom,
% 1.20/1.55 ! [V_a,V_b,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_zero__less__mult__pos,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__pos__neg2,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__pos__neg,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__pos__pos,axiom,
% 1.20/1.55 ! [V_b,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__less__cancel__left__pos,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
% 1.20/1.55 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__less__cancel__left__disj,axiom,
% 1.20/1.55 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))
% 1.20/1.55 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.20/1.55 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 1.20/1.55 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__less__cancel__right__disj,axiom,
% 1.20/1.55 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))
% 1.20/1.55 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.20/1.55 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 1.20/1.55 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.20/1.55 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_not__square__less__zero,axiom,
% 1.20/1.55 ! [V_a,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring(T_a)
% 1.20/1.55 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_add__scale__eq__noteq,axiom,
% 1.20/1.55 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 1.20/1.55 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.20/1.55 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( ( V_a = V_b
% 1.20/1.55 & V_c != V_d )
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_r,V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,c_Groups_Otimes__class_Otimes(T_a,V_r,V_d)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_sum__squares__eq__zero__iff,axiom,
% 1.20/1.55 ! [V_y_2,V_x_2,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.20/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_less__1__mult,axiom,
% 1.20/1.55 ! [V_n,V_m,T_a] :
% 1.20/1.55 ( class_Rings_Olinordered__semidom(T_a)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 1.20/1.55 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 1.20/1.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_right__distrib__number__of,axiom,
% 1.20/1.55 ! [V_c,V_b,V_v,T_b] :
% 1.20/1.55 ( ( class_Int_Onumber(T_b)
% 1.20/1.55 & class_Rings_Osemiring(T_b) )
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_left__distrib__number__of,axiom,
% 1.20/1.55 ! [V_v,V_b,V_a,T_b] :
% 1.20/1.55 ( ( class_Int_Onumber(T_b)
% 1.20/1.55 & class_Rings_Osemiring(T_b) )
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__diff__mult,axiom,
% 1.20/1.55 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.20/1.55 ( class_Rings_Oring(T_a)
% 1.20/1.55 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult_Oprod__diff__prod,axiom,
% 1.20/1.55 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.20/1.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.20/1.55 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),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,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)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_eq__add__iff2,axiom,
% 1.20/1.55 ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Rings_Oring(T_a)
% 1.20/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_da_2)
% 1.20/1.55 <=> V_c_2 = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_da_2) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_eq__add__iff1,axiom,
% 1.20/1.55 ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Rings_Oring(T_a)
% 1.20/1.55 => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_da_2)
% 1.20/1.55 <=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),V_e_2),V_c_2) = V_da_2 ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 1.20/1.55 ! [V_m,V_a,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),V_m) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 1.20/1.55 ! [V_a,V_m,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(T_a,V_m,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 1.20/1.55 ! [V_m,T_a] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.20/1.55 => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)),V_m) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_right__diff__distrib__number__of,axiom,
% 1.20/1.55 ! [V_c,V_b,V_v,T_b] :
% 1.20/1.55 ( ( class_Int_Onumber(T_b)
% 1.20/1.55 & class_Rings_Oring(T_b) )
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_left__diff__distrib__number__of,axiom,
% 1.20/1.55 ! [V_v,V_b,V_a,T_b] :
% 1.20/1.55 ( ( class_Int_Onumber(T_b)
% 1.20/1.55 & class_Rings_Oring(T_b) )
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_eq__divide__eq,axiom,
% 1.20/1.55 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 1.20/1.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.55 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
% 1.20/1.55 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_b_2 )
% 1.20/1.55 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_divide__eq__eq,axiom,
% 1.20/1.55 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 1.20/1.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.55 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
% 1.20/1.55 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) )
% 1.20/1.55 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__divide__mult__cancel__right,axiom,
% 1.20/1.55 ! [V_b,V_a,V_c,T_a] :
% 1.20/1.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.55 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_mult__divide__mult__cancel__left,axiom,
% 1.20/1.55 ! [V_b,V_a,V_c,T_a] :
% 1.20/1.55 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.20/1.55 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_frac__eq__eq,axiom,
% 1.20/1.55 ! [V_wa_2,V_x_2,V_za_2,V_y_2,T_a] :
% 1.20/1.55 ( class_Fields_Ofield(T_a)
% 1.20/1.55 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_za_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)
% 1.20/1.55 <=> c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_za_2) = c_Groups_Otimes__class_Otimes(T_a,V_wa_2,V_y_2) ) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_eq__divide__imp,axiom,
% 1.20/1.55 ! [V_b,V_a,V_c,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) = V_b
% 1.20/1.55 => V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_divide__eq__imp,axiom,
% 1.20/1.55 ! [V_a,V_b,V_c,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( V_b = c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)
% 1.20/1.55 => c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a ) ) ) ).
% 1.20/1.55
% 1.20/1.55 fof(fact_nonzero__divide__eq__eq,axiom,
% 1.20/1.55 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 1.20/1.55 ( class_Rings_Odivision__ring(T_a)
% 1.20/1.55 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.20/1.55 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
% 1.20/1.55 <=> V_b_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) ) ) ) ).
% 1.20/1.55
% 1.20/1.55 %----Arity declarations (258)
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.20/1.55 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 1.20/1.55 ! [T_2,T_1] :
% 1.20/1.55 ( class_Lattices_Oboolean__algebra(T_1)
% 1.20/1.55 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_fun__Orderings_Opreorder,axiom,
% 1.20/1.55 ! [T_2,T_1] :
% 1.20/1.55 ( class_Orderings_Opreorder(T_1)
% 1.20/1.55 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_fun__Orderings_Oorder,axiom,
% 1.20/1.55 ! [T_2,T_1] :
% 1.20/1.55 ( class_Orderings_Oorder(T_1)
% 1.20/1.55 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_fun__Orderings_Oord,axiom,
% 1.20/1.55 ! [T_2,T_1] :
% 1.20/1.55 ( class_Orderings_Oord(T_1)
% 1.20/1.55 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_fun__Groups_Ouminus,axiom,
% 1.20/1.55 ! [T_2,T_1] :
% 1.20/1.55 ( class_Groups_Ouminus(T_1)
% 1.20/1.55 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_fun__Groups_Ominus,axiom,
% 1.20/1.55 ! [T_2,T_1] :
% 1.20/1.55 ( class_Groups_Ominus(T_1)
% 1.20/1.55 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.20/1.55 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.20/1.55 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 1.20/1.55 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 1.20/1.55 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 1.20/1.55 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 1.20/1.55 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 1.20/1.55 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 1.20/1.55 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 1.20/1.55 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 1.20/1.55 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 1.20/1.55 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 1.20/1.55 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 1.20/1.55 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 1.20/1.55 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 1.20/1.55 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 1.20/1.55 class_Orderings_Opreorder(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 1.20/1.55 class_Orderings_Olinorder(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 1.20/1.55 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 1.20/1.55 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 1.20/1.55 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 1.20/1.55 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 1.20/1.55 class_Rings_Omult__zero(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 1.20/1.55 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 1.20/1.55 class_Orderings_Oorder(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 1.20/1.55 class_Int_Oring__char__0(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 1.20/1.55 class_Int_Onumber__ring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 1.20/1.55 class_Rings_Osemiring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 1.20/1.55 class_Orderings_Oord(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 1.20/1.55 class_Groups_Ouminus(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 1.20/1.55 class_Groups_Osgn__if(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 1.20/1.55 class_Groups_Oabs__if(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 1.20/1.55 class_Groups_Ominus(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 1.20/1.55 class_Groups_Ozero(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Oring,axiom,
% 1.20/1.55 class_Rings_Oring(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 1.20/1.55 class_Rings_Oidom(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Int_Onumber,axiom,
% 1.20/1.55 class_Int_Onumber(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Int__Oint__Groups_Oone,axiom,
% 1.20/1.55 class_Groups_Oone(tc_Int_Oint) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.20/1.55 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.20/1.55 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 1.20/1.55 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 1.20/1.55 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 1.20/1.55 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 1.20/1.55 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 1.20/1.55 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 1.20/1.55 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 1.20/1.55 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 1.20/1.55 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 1.20/1.55 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 1.20/1.55 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 1.20/1.55 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 1.20/1.55 class_Orderings_Oorder(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 1.20/1.55 class_Rings_Osemiring(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 1.20/1.55 class_Orderings_Oord(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 1.20/1.55 class_Groups_Ominus(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 1.20/1.55 class_Groups_Ozero(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 1.20/1.55 class_Int_Onumber(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 1.20/1.55 class_Groups_Oone(tc_Nat_Onat) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 1.20/1.55 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 1.20/1.55 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 1.20/1.55 class_Orderings_Oorder(tc_HOL_Obool) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 1.20/1.55 class_Orderings_Oord(tc_HOL_Obool) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 1.20/1.55 class_Groups_Ouminus(tc_HOL_Obool) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 1.20/1.55 class_Groups_Ominus(tc_HOL_Obool) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.20/1.55 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.20/1.55 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 1.20/1.55 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 1.20/1.55 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 1.20/1.55 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 1.20/1.55 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 1.20/1.55 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 1.20/1.55 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 1.20/1.55 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 1.20/1.55 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 1.20/1.55 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 1.20/1.55 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 1.20/1.55 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 1.20/1.55 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 1.20/1.55 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 1.20/1.55 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 1.20/1.55 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 1.20/1.55 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 1.20/1.55 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 1.20/1.55 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 1.20/1.55 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 1.20/1.55 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 1.20/1.55 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 1.20/1.55 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 1.20/1.55 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 1.20/1.55 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 1.20/1.55 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 1.20/1.55 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 1.20/1.55 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 1.20/1.55 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 1.20/1.55 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
% 1.20/1.55 class_Int_Onumber__ring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 1.20/1.55 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 1.20/1.55 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
% 1.20/1.55 class_Groups_Ouminus(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
% 1.20/1.55 class_Groups_Osgn__if(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
% 1.20/1.55 class_Groups_Oabs__if(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
% 1.20/1.55 class_Groups_Ominus(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 1.20/1.55 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 1.20/1.55 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 1.20/1.55 class_Rings_Oring(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 1.20/1.55 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Int_Onumber,axiom,
% 1.20/1.55 class_Int_Onumber(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 1.20/1.55 class_Groups_Oone(tc_RealDef_Oreal) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.20/1.55 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 1.20/1.55 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
% 1.20/1.55 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 1.20/1.55 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 1.20/1.55 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 1.20/1.55 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 1.20/1.55 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 1.20/1.55 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 1.20/1.55 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 1.20/1.55 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 1.20/1.55 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 1.20/1.55 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 1.20/1.55 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 1.20/1.55 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 1.20/1.55 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 1.20/1.55 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 1.20/1.55 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 1.20/1.55 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 1.20/1.55 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 1.20/1.55 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
% 1.20/1.55 class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 1.20/1.55 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
% 1.20/1.55 class_Groups_Ouminus(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
% 1.20/1.55 class_Groups_Ominus(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 1.20/1.55 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 1.20/1.55 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 1.20/1.55 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 1.20/1.55 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
% 1.20/1.55 class_Int_Onumber(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 1.20/1.55 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Oidom(T_1)
% 1.20/1.55 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.20/1.55 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Oidom(T_1)
% 1.20/1.55 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 1.20/1.55 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.20/1.55 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.20/1.55 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Oidom(T_1)
% 1.20/1.55 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.20/1.55 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.20/1.55 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.20/1.55 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Fields_Ofield(T_1)
% 1.20/1.55 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.20/1.55 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Oab__group__add(T_1)
% 1.20/1.55 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.20/1.55 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.20/1.55 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__ring__1(T_1)
% 1.20/1.55 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Ocomm__monoid__add(T_1)
% 1.20/1.55 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Oab__group__add(T_1)
% 1.20/1.55 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.20/1.55 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__ring(T_1)
% 1.20/1.55 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Int_Onumber__ring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__ring__1(T_1)
% 1.20/1.55 => class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__0(T_1)
% 1.20/1.55 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Oab__group__add(T_1)
% 1.20/1.55 => class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Olinordered__idom(T_1)
% 1.20/1.55 => class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Oab__group__add(T_1)
% 1.20/1.55 => class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Groups_Ozero(T_1)
% 1.20/1.55 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__ring(T_1)
% 1.20/1.55 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Oidom(T_1)
% 1.20/1.55 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Int_Onumber,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__ring__1(T_1)
% 1.20/1.55 => class_Int_Onumber(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 1.20/1.55 ! [T_1] :
% 1.20/1.55 ( class_Rings_Ocomm__semiring__1(T_1)
% 1.20/1.55 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 1.20/1.55
% 1.20/1.55 %----Conjectures (1)
% 1.20/1.55 fof(conj_0,conjecture,
% 1.20/1.55 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))),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),v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),v_z____)))) ).
% 1.20/1.55
% 1.20/1.55 %------------------------------------------------------------------------------
% 1.20/1.55 %-------------------------------------------
% 1.20/1.55 % Proof found
% 1.20/1.55 % SZS status Theorem for theBenchmark
% 1.20/1.55 % SZS output start Proof
% 1.20/1.55 %ClaNum:1805(EqnAxiom:190)
% 1.20/1.55 %VarNum:7764(SingletonVarNum:2657)
% 1.20/1.55 %MaxLitNum:6
% 1.20/1.55 %MaxfuncDepth:7
% 1.20/1.55 %SharedTerms:374
% 1.20/1.55 %goalClause: 592
% 1.20/1.55 %singleGoalClaCount:1
% 1.20/1.55 [192]P1(a73)
% 1.20/1.55 [193]P5(a74)
% 1.20/1.55 [194]P5(a14)
% 1.20/1.55 [195]P6(a74)
% 1.20/1.55 [196]P6(a1)
% 1.20/1.55 [197]P7(a74)
% 1.20/1.55 [198]P7(a14)
% 1.20/1.55 [199]P7(a75)
% 1.20/1.55 [200]P7(a1)
% 1.20/1.55 [201]P8(a74)
% 1.20/1.55 [202]P8(a14)
% 1.20/1.55 [203]P8(a75)
% 1.20/1.55 [204]P8(a1)
% 1.20/1.55 [205]P9(a74)
% 1.20/1.55 [206]P9(a14)
% 1.20/1.55 [207]P9(a75)
% 1.20/1.55 [208]P9(a1)
% 1.20/1.55 [209]P10(a74)
% 1.20/1.55 [210]P10(a14)
% 1.20/1.55 [211]P10(a1)
% 1.20/1.55 [212]P27(a74)
% 1.20/1.55 [213]P27(a75)
% 1.20/1.55 [214]P27(a1)
% 1.20/1.55 [215]P28(a74)
% 1.20/1.55 [216]P28(a75)
% 1.20/1.55 [217]P28(a1)
% 1.20/1.55 [218]P18(a74)
% 1.20/1.55 [219]P18(a1)
% 1.20/1.55 [220]P19(a74)
% 1.20/1.55 [221]P19(a14)
% 1.20/1.55 [222]P19(a1)
% 1.20/1.55 [223]P29(a74)
% 1.20/1.55 [224]P29(a75)
% 1.20/1.55 [225]P29(a1)
% 1.20/1.55 [226]P29(a72)
% 1.20/1.55 [227]P46(a74)
% 1.20/1.55 [228]P46(a14)
% 1.20/1.55 [229]P46(a1)
% 1.20/1.55 [230]P47(a74)
% 1.20/1.55 [231]P47(a14)
% 1.20/1.55 [232]P47(a75)
% 1.20/1.55 [233]P47(a1)
% 1.20/1.55 [234]P16(a74)
% 1.20/1.55 [235]P16(a1)
% 1.20/1.55 [236]P30(a74)
% 1.20/1.55 [237]P30(a14)
% 1.20/1.55 [238]P30(a75)
% 1.20/1.55 [239]P30(a1)
% 1.20/1.55 [240]P22(a74)
% 1.20/1.55 [241]P22(a1)
% 1.20/1.55 [242]P35(a74)
% 1.20/1.55 [243]P35(a75)
% 1.20/1.55 [244]P35(a1)
% 1.20/1.55 [245]P40(a74)
% 1.20/1.55 [246]P40(a75)
% 1.20/1.55 [247]P40(a1)
% 1.20/1.55 [248]P40(a72)
% 1.20/1.55 [249]P41(a74)
% 1.20/1.55 [250]P41(a75)
% 1.20/1.55 [251]P41(a1)
% 1.20/1.55 [252]P41(a72)
% 1.20/1.55 [253]P31(a74)
% 1.20/1.55 [254]P31(a75)
% 1.20/1.55 [255]P31(a1)
% 1.20/1.55 [256]P32(a74)
% 1.20/1.55 [257]P32(a75)
% 1.20/1.55 [258]P32(a1)
% 1.20/1.55 [259]P23(a74)
% 1.20/1.55 [260]P23(a14)
% 1.20/1.55 [261]P23(a75)
% 1.20/1.55 [262]P23(a1)
% 1.20/1.55 [263]P20(a74)
% 1.20/1.55 [264]P20(a14)
% 1.20/1.55 [265]P20(a75)
% 1.20/1.55 [266]P20(a1)
% 1.20/1.55 [267]P36(a74)
% 1.20/1.55 [268]P36(a14)
% 1.20/1.55 [269]P36(a1)
% 1.20/1.55 [270]P50(a74)
% 1.20/1.55 [271]P50(a14)
% 1.20/1.55 [272]P50(a1)
% 1.20/1.55 [273]P54(a74)
% 1.20/1.55 [274]P54(a1)
% 1.20/1.55 [275]P25(a74)
% 1.20/1.55 [276]P25(a14)
% 1.20/1.55 [277]P25(a75)
% 1.20/1.55 [278]P25(a1)
% 1.20/1.55 [279]P42(a74)
% 1.20/1.55 [280]P42(a14)
% 1.20/1.55 [281]P51(a74)
% 1.20/1.55 [282]P51(a14)
% 1.20/1.55 [283]P51(a75)
% 1.20/1.55 [284]P51(a1)
% 1.20/1.55 [285]P56(a74)
% 1.20/1.55 [286]P56(a14)
% 1.20/1.55 [287]P56(a75)
% 1.20/1.55 [288]P56(a1)
% 1.20/1.55 [289]P57(a74)
% 1.20/1.55 [290]P57(a75)
% 1.20/1.55 [291]P57(a1)
% 1.20/1.55 [292]P48(a74)
% 1.20/1.55 [293]P48(a14)
% 1.20/1.55 [294]P48(a1)
% 1.20/1.55 [295]P11(a74)
% 1.20/1.55 [296]P11(a14)
% 1.20/1.55 [297]P44(a74)
% 1.20/1.55 [298]P44(a14)
% 1.20/1.55 [299]P52(a74)
% 1.20/1.55 [300]P52(a14)
% 1.20/1.55 [301]P53(a74)
% 1.20/1.55 [302]P53(a14)
% 1.20/1.55 [303]P70(a74)
% 1.20/1.55 [304]P70(a14)
% 1.20/1.55 [305]P70(a75)
% 1.20/1.55 [306]P70(a1)
% 1.20/1.55 [307]P14(a74)
% 1.20/1.55 [308]P15(a74)
% 1.20/1.55 [309]P12(a75)
% 1.20/1.55 [310]P12(a1)
% 1.20/1.55 [311]P39(a72)
% 1.20/1.55 [312]P13(a74)
% 1.20/1.55 [313]P13(a14)
% 1.20/1.55 [314]P24(a74)
% 1.20/1.55 [315]P24(a14)
% 1.20/1.55 [316]P24(a75)
% 1.20/1.55 [317]P24(a1)
% 1.20/1.55 [318]P24(a72)
% 1.20/1.55 [319]P33(a74)
% 1.20/1.55 [320]P33(a14)
% 1.20/1.55 [321]P33(a1)
% 1.20/1.55 [322]P33(a72)
% 1.20/1.55 [323]P37(a74)
% 1.20/1.55 [324]P37(a14)
% 1.20/1.55 [325]P37(a1)
% 1.20/1.55 [326]P38(a74)
% 1.20/1.55 [327]P38(a14)
% 1.20/1.55 [328]P38(a75)
% 1.20/1.55 [329]P38(a1)
% 1.20/1.55 [330]P34(a74)
% 1.20/1.55 [331]P34(a1)
% 1.20/1.55 [332]P45(a74)
% 1.20/1.55 [333]P45(a14)
% 1.20/1.55 [334]P43(a74)
% 1.20/1.55 [335]P43(a14)
% 1.20/1.55 [336]P60(a74)
% 1.20/1.55 [337]P60(a14)
% 1.20/1.55 [338]P60(a1)
% 1.20/1.55 [339]P68(a74)
% 1.20/1.55 [340]P68(a14)
% 1.20/1.55 [341]P68(a75)
% 1.20/1.55 [342]P68(a1)
% 1.20/1.55 [343]P49(a74)
% 1.20/1.55 [344]P49(a14)
% 1.20/1.55 [345]P49(a75)
% 1.20/1.55 [346]P49(a1)
% 1.20/1.55 [347]P61(a74)
% 1.20/1.55 [348]P61(a14)
% 1.20/1.55 [349]P61(a75)
% 1.20/1.55 [350]P61(a1)
% 1.20/1.55 [351]P69(a74)
% 1.20/1.55 [352]P69(a14)
% 1.20/1.55 [353]P69(a1)
% 1.20/1.55 [354]P63(a74)
% 1.20/1.55 [355]P63(a14)
% 1.20/1.55 [356]P63(a75)
% 1.20/1.55 [357]P63(a1)
% 1.20/1.55 [358]P26(a74)
% 1.20/1.55 [359]P26(a14)
% 1.20/1.55 [360]P26(a75)
% 1.20/1.55 [361]P26(a1)
% 1.20/1.55 [362]P21(a74)
% 1.20/1.55 [363]P21(a14)
% 1.20/1.55 [364]P21(a75)
% 1.20/1.55 [365]P21(a1)
% 1.20/1.55 [366]P58(a74)
% 1.20/1.55 [367]P58(a1)
% 1.20/1.55 [368]P59(a74)
% 1.20/1.55 [369]P59(a1)
% 1.20/1.55 [370]P64(a74)
% 1.20/1.55 [371]P64(a75)
% 1.20/1.55 [372]P64(a1)
% 1.20/1.55 [373]P65(a74)
% 1.20/1.55 [374]P65(a1)
% 1.20/1.55 [375]P67(a74)
% 1.20/1.55 [376]P67(a75)
% 1.20/1.55 [377]P67(a1)
% 1.20/1.55 [378]P66(a74)
% 1.20/1.55 [379]P66(a75)
% 1.20/1.55 [380]P66(a1)
% 1.20/1.55 [381]P55(a74)
% 1.20/1.55 [382]P55(a75)
% 1.20/1.55 [383]P55(a1)
% 1.20/1.55 [384]P62(a74)
% 1.20/1.55 [385]P62(a75)
% 1.20/1.55 [386]P62(a1)
% 1.20/1.55 [387]P17(a74)
% 1.20/1.55 [388]P17(a14)
% 1.20/1.55 [389]P17(a75)
% 1.20/1.55 [390]P17(a1)
% 1.20/1.55 [567]~P3(a1,a13,a13)
% 1.20/1.55 [191]E(f2(a1),a13)
% 1.20/1.55 [395]E(f9(a1,a13),a13)
% 1.20/1.55 [398]E(f16(a1,a13),f2(a1))
% 1.20/1.55 [399]E(f16(a75,a13),f2(a75))
% 1.20/1.55 [419]P2(a74,f2(a74),a81)
% 1.20/1.55 [420]P3(a74,f2(a74),a77)
% 1.20/1.55 [421]P3(a74,f2(a74),a24)
% 1.20/1.55 [433]P2(a74,f2(a74),f3(a74))
% 1.20/1.55 [435]P3(a1,f2(a1),f3(a1))
% 1.20/1.55 [440]P2(a74,f22(a14,a84),a81)
% 1.20/1.55 [441]P2(a74,f22(a14,a25),a81)
% 1.20/1.55 [562]~E(f2(a14),a6)
% 1.20/1.55 [563]~E(f3(a14),a6)
% 1.20/1.55 [564]~E(f3(a74),f2(a74))
% 1.20/1.55 [565]~E(f3(a1),f2(a1))
% 1.20/1.55 [570]~P3(a1,a13,f2(a1))
% 1.20/1.55 [391]E(f15(f2(a74)),f2(a75))
% 1.20/1.55 [392]E(f15(f3(a74)),f3(a75))
% 1.20/1.55 [393]E(f19(f2(a74)),f2(a75))
% 1.20/1.55 [394]E(f19(f3(a74)),f3(a75))
% 1.20/1.55 [400]E(f9(a1,f2(a1)),f2(a1))
% 1.20/1.55 [401]E(f20(a75,f2(a75)),f2(a74))
% 1.20/1.55 [402]E(f20(a75,f3(a75)),f3(a74))
% 1.20/1.55 [403]E(f21(a74,f2(a74)),f2(a74))
% 1.20/1.55 [444]P2(a74,f22(a14,f2(a14)),a81)
% 1.20/1.55 [505]P2(a75,f10(a75,a78,a80),f63(a73,f10(a75,a78,a80)))
% 1.20/1.55 [445]E(f22(a14,f63(f17(a14,a82),a25)),f9(a74,a26))
% 1.20/1.55 [461]E(f20(a75,f10(a75,f2(a75),f3(a75))),f3(a74))
% 1.20/1.55 [523]P3(a74,f2(a74),f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85))))
% 1.20/1.55 [503]E(f16(a1,f10(a1,f10(a1,f3(a1),a13),a13)),f3(a1))
% 1.20/1.55 [504]E(f16(a75,f10(a1,f10(a1,f3(a1),a13),a13)),f3(a75))
% 1.20/1.55 [508]E(f16(a75,f10(a1,f10(a1,f3(a1),a13),a13)),f10(a75,f2(a75),f3(a75)))
% 1.20/1.55 [541]P2(a74,f23(a74,f3(a74),f20(a75,f10(a75,f63(a73,f10(a75,a78,a80)),f3(a75)))),f23(a74,f3(a74),f20(a75,f10(a75,f10(a75,a78,a80),f3(a75)))))
% 1.20/1.55 [546]P3(a74,f23(a74,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85)))),f20(a75,a80))
% 1.20/1.55 [547]P3(a74,f23(a74,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85)))),f20(a75,a64))
% 1.20/1.55 [548]P3(a74,f23(a74,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85)))),f20(a75,a65))
% 1.20/1.55 [550]P3(a74,f23(a74,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85)))),f20(a75,f10(a75,f10(a75,a78,a80),f3(a75))))
% 1.20/1.55 [555]P3(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),f83(f63(a73,f10(a75,a78,a80))))),f9(a74,a85))),f23(a74,f3(a74),f20(a75,f10(a75,f10(a75,a78,a80),f3(a75)))))
% 1.20/1.55 [511]E(f9(a74,f9(a74,f22(a14,f63(f17(a14,a82),f2(a14))))),f22(a14,f63(f17(a14,a82),f2(a14))))
% 1.20/1.55 [527]E(f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f10(a75,f3(a75),f3(a75)))
% 1.20/1.55 [529]E(f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f10(a75,f10(a75,f2(a75),f3(a75)),f3(a75)))
% 1.20/1.55 [536]E(f16(a75,f10(a1,f10(a1,f3(a1),f10(a1,f10(a1,f3(a1),a13),a13)),f10(a1,f10(a1,f3(a1),a13),a13))),f10(a75,f10(a75,f10(a75,f2(a75),f3(a75)),f3(a75)),f3(a75)))
% 1.20/1.55 [542]P3(a74,f22(a14,f63(f17(a14,a82),f83(f63(a73,f10(a75,a78,a80))))),f10(a74,f9(a74,a85),f23(a74,f3(a74),f20(a75,f10(a75,f10(a75,a78,a80),f3(a75))))))
% 1.20/1.55 [549]P2(a74,f10(a74,f9(a74,a85),f23(a74,f3(a74),f20(a75,f10(a75,f63(a73,f10(a75,a78,a80)),f3(a75))))),f10(a74,f9(a74,a85),f23(a74,f3(a74),f20(a75,f10(a75,f10(a75,a78,a80),f3(a75))))))
% 1.20/1.55 [592]~P2(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),f83(f63(a73,f10(a75,a78,a80))))),f22(a14,f63(f17(a14,a82),a86)))),f22(a14,f8(a14,f63(f17(a14,a82),f83(f63(a73,f10(a75,a78,a80)))),f63(f17(a14,a82),a86))))
% 1.20/1.55 [545]P3(a74,f2(a74),f23(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85))),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [554]P3(a74,f23(a74,f3(a74),f20(a75,f10(a75,f10(a75,a78,a80),f3(a75)))),f23(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85))),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [560]P3(a74,f22(a14,f8(a14,f63(f17(a14,a82),f83(f63(a73,f10(a75,a78,a80)))),f63(f17(a14,a82),a86))),f23(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85))),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [561]P3(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),f83(f63(a73,f10(a75,a78,a80))))),f9(a74,a85))),f23(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85))),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [416]P2(a74,x4161,x4161)
% 1.20/1.55 [417]P2(a75,x4171,x4171)
% 1.20/1.55 [418]P2(a1,x4181,x4181)
% 1.20/1.55 [569]~P3(a75,x5691,x5691)
% 1.20/1.55 [396]E(f16(a1,x3961),x3961)
% 1.20/1.55 [404]E(f22(a74,x4041),f4(a74,x4041))
% 1.20/1.55 [413]E(f10(a1,x4131,a13),x4131)
% 1.20/1.55 [414]E(f8(a1,x4141,a13),x4141)
% 1.20/1.55 [415]E(f10(a1,a13,x4151),x4151)
% 1.20/1.55 [422]E(f8(a75,x4221,x4221),f2(a75))
% 1.20/1.55 [424]P2(a75,f2(a75),x4241)
% 1.20/1.55 [443]P2(a74,f2(a74),f20(a75,x4431))
% 1.20/1.55 [566]~E(f16(a14,x5661),a6)
% 1.20/1.55 [573]~P3(a75,x5731,f2(a75))
% 1.20/1.55 [582]~P3(a74,f20(a75,x5821),f2(a74))
% 1.20/1.55 [405]E(f15(f20(a75,x4051)),x4051)
% 1.20/1.55 [406]E(f19(f20(a75,x4061)),x4061)
% 1.20/1.55 [407]E(f9(a1,f9(a1,x4071)),x4071)
% 1.20/1.55 [408]E(f15(f16(a74,x4081)),f16(a75,x4081))
% 1.20/1.55 [409]E(f19(f16(a74,x4091)),f16(a75,x4091))
% 1.20/1.55 [410]E(f4(a74,f20(a75,x4101)),f20(a75,x4101))
% 1.20/1.55 [425]E(f10(a75,x4251,f2(a75)),x4251)
% 1.20/1.55 [426]E(f10(a1,x4261,f2(a1)),x4261)
% 1.20/1.55 [427]E(f8(a75,x4271,f2(a75)),x4271)
% 1.20/1.55 [428]E(f10(a75,f2(a75),x4281),x4281)
% 1.20/1.55 [429]E(f10(a1,f2(a1),x4291),x4291)
% 1.20/1.55 [430]E(f11(a74,f3(a74),x4301),x4301)
% 1.20/1.55 [431]E(f8(a75,f2(a75),x4311),f2(a75))
% 1.20/1.55 [432]E(f5(a1,f2(a1),x4321),f2(a1))
% 1.20/1.55 [439]E(f9(a1,f16(a1,x4391)),f16(a1,f9(a1,x4391)))
% 1.20/1.55 [442]E(f10(a1,f9(a1,x4421),x4421),f2(a1))
% 1.20/1.55 [446]P2(a74,f22(a14,f83(x4461)),a81)
% 1.20/1.55 [447]P2(a74,f22(a14,f39(x4471)),a81)
% 1.20/1.55 [448]P2(a74,f22(a14,f54(x4481)),a81)
% 1.20/1.55 [449]P2(a74,x4491,f20(a75,f15(x4491)))
% 1.20/1.55 [450]E(f23(a74,x4501,f4(a74,x4501)),f12(a74,x4501))
% 1.20/1.55 [454]P2(a74,f22(a14,f63(a55,x4541)),a81)
% 1.20/1.55 [455]P2(a74,f22(a14,f63(a56,x4551)),a81)
% 1.20/1.55 [462]P2(a74,f9(a74,f22(a14,x4621)),f22(a14,x4621))
% 1.20/1.55 [472]P3(a75,x4721,f10(a75,x4721,f3(a75)))
% 1.20/1.55 [473]P3(a75,f2(a75),f10(a75,x4731,f3(a75)))
% 1.20/1.55 [476]P3(a74,f8(a74,x4761,f3(a74)),f20(a75,f19(x4761)))
% 1.20/1.55 [478]P3(a74,f2(a74),f10(a74,f3(a74),f4(a74,x4781)))
% 1.20/1.55 [483]P3(a74,x4831,f10(a74,f20(a75,f19(x4831)),f3(a74)))
% 1.20/1.55 [509]E(f10(a1,f8(a1,a13,x5091),f8(a1,a13,x5091)),f8(a1,a13,f10(a1,x5091,x5091)))
% 1.20/1.55 [575]~E(f10(a75,x5751,f3(a75)),x5751)
% 1.20/1.55 [581]~E(f10(a75,x5811,f3(a75)),f2(a75))
% 1.20/1.55 [587]~P2(a75,f10(a75,x5871,f3(a75)),x5871)
% 1.20/1.55 [589]~P3(a74,f10(a74,f4(a74,x5891),f3(a74)),x5891)
% 1.20/1.55 [475]E(f5(a75,x4751,f10(a75,f2(a75),f3(a75))),x4751)
% 1.20/1.55 [477]E(f10(a74,f20(a75,x4771),f3(a74)),f20(a75,f10(a75,x4771,f3(a75))))
% 1.20/1.55 [484]P2(a74,f9(a74,a85),f22(a14,f63(f17(a14,a82),f83(x4841))))
% 1.20/1.55 [487]P3(a74,f2(a74),f20(a75,f10(a75,x4871,f3(a75))))
% 1.20/1.55 [586]~E(f10(a1,f10(a1,f3(a1),x5861),x5861),a13)
% 1.20/1.55 [588]~E(f10(a1,f10(a1,f3(a1),x5881),x5881),f2(a1))
% 1.20/1.55 [530]P3(a74,f22(a14,f63(f17(a14,a82),f83(x5301))),f10(a74,f9(a74,a85),f23(a74,f3(a74),f20(a75,f10(a75,x5301,f3(a75))))))
% 1.20/1.55 [531]P3(a74,f22(a14,f63(f17(a14,a82),f39(x5311))),f10(a74,f9(a74,a85),f23(a74,f3(a74),f20(a75,f10(a75,x5311,f3(a75))))))
% 1.20/1.55 [532]P3(a74,f22(a14,f63(f17(a14,a82),f54(x5321))),f10(a74,f9(a74,a85),f23(a74,f3(a74),f20(a75,f10(a75,x5321,f3(a75))))))
% 1.20/1.55 [533]P3(a74,f22(a14,f63(f17(a14,a82),f63(a55,x5331))),f10(a74,f9(a74,a85),f23(a74,f3(a74),f20(a75,f10(a75,x5331,f3(a75))))))
% 1.20/1.55 [534]P3(a74,f22(a14,f63(f17(a14,a82),f63(a56,x5341))),f10(a74,f9(a74,a85),f23(a74,f3(a74),f20(a75,f10(a75,x5341,f3(a75))))))
% 1.20/1.55 [538]E(f5(a75,f10(a75,x5381,x5381),f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))),x5381)
% 1.20/1.55 [539]E(f10(a75,x5391,f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))),f10(a75,f10(a75,x5391,f3(a75)),f3(a75)))
% 1.20/1.55 [540]E(f10(a75,f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),x5401),f10(a75,f10(a75,x5401,f3(a75)),f3(a75)))
% 1.20/1.55 [543]E(f10(a75,f16(a75,f10(a1,f10(a1,f3(a1),f10(a1,f10(a1,f3(a1),a13),a13)),f10(a1,f10(a1,f3(a1),a13),a13))),x5431),f10(a75,f10(a75,f10(a75,x5431,f3(a75)),f3(a75)),f3(a75)))
% 1.20/1.55 [553]E(f5(a75,f10(a75,f10(a75,x5531,f3(a75)),f3(a75)),f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))),f10(a75,f5(a75,x5531,f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))),f3(a75)))
% 1.20/1.55 [559]E(f10(a74,f23(a74,x5591,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))),f23(a74,x5591,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))))),x5591)
% 1.20/1.55 [451]E(f10(a75,x4511,x4512),f10(a75,x4512,x4511))
% 1.20/1.55 [452]E(f10(a1,x4521,x4522),f10(a1,x4522,x4521))
% 1.20/1.55 [465]P2(a75,x4651,f10(a75,x4652,x4651))
% 1.20/1.55 [466]P2(a75,x4661,f10(a75,x4661,x4662))
% 1.20/1.55 [467]P2(a75,f8(a75,x4671,x4672),x4671)
% 1.20/1.55 [468]P2(a75,f5(a75,x4681,x4682),x4681)
% 1.20/1.55 [583]~P3(a75,f10(a75,x5831,x5832),x5832)
% 1.20/1.55 [584]~P3(a75,f10(a75,x5841,x5842),x5841)
% 1.20/1.55 [457]E(f10(a74,x4571,f9(a74,x4572)),f8(a74,x4571,x4572))
% 1.20/1.55 [458]E(f10(a14,x4581,f9(a14,x4582)),f8(a14,x4581,x4582))
% 1.20/1.55 [460]E(f10(a1,x4601,f9(a1,x4602)),f8(a1,x4601,x4602))
% 1.20/1.55 [463]E(f5(a1,f9(a1,x4631),x4632),f5(a1,x4631,f9(a1,x4632)))
% 1.20/1.55 [464]E(f5(a1,f9(a1,x4641),f9(a1,x4642)),f5(a1,x4641,x4642))
% 1.20/1.55 [469]E(f8(a75,f10(a75,x4691,x4692),x4692),x4691)
% 1.20/1.55 [470]E(f8(a75,f10(a75,x4701,x4702),x4701),x4702)
% 1.20/1.55 [471]E(f8(a75,x4711,f10(a75,x4711,x4712)),f2(a75))
% 1.20/1.55 [479]E(f10(a1,f9(a1,x4791),f9(a1,x4792)),f9(a1,f10(a1,x4791,x4792)))
% 1.20/1.55 [481]E(f10(a74,f20(a75,x4811),f20(a75,x4812)),f20(a75,f10(a75,x4811,x4812)))
% 1.20/1.55 [482]E(f10(a1,f16(a1,x4821),f16(a1,x4822)),f16(a1,f10(a1,x4821,x4822)))
% 1.20/1.55 [486]P3(a75,f8(a75,x4861,x4862),f10(a75,x4861,f3(a75)))
% 1.20/1.55 [506]P3(a75,x5061,f10(a75,f10(a75,x5062,x5061),f3(a75)))
% 1.20/1.55 [507]P3(a75,x5071,f10(a75,f10(a75,x5071,x5072),f3(a75)))
% 1.20/1.55 [512]P2(a74,f20(a75,f5(a75,x5121,x5122)),f23(a74,f20(a75,x5121),f20(a75,x5122)))
% 1.20/1.55 [513]E(f10(a1,f10(a1,x5131,x5131),f10(a1,x5132,x5132)),f10(a1,f10(a1,x5131,x5132),f10(a1,x5131,x5132)))
% 1.20/1.55 [514]E(f8(a1,f10(a1,x5141,x5141),f10(a1,x5142,x5142)),f10(a1,f8(a1,x5141,x5142),f8(a1,x5141,x5142)))
% 1.20/1.55 [517]P2(a74,f22(a14,x5171),f10(a74,f22(a14,f10(a14,x5171,x5172)),f22(a14,x5172)))
% 1.20/1.55 [518]P2(a74,f8(a74,f22(a14,f10(a14,x5181,x5182)),f22(a14,x5181)),f22(a14,x5182))
% 1.20/1.55 [521]E(f10(a1,f10(a1,f10(a1,f3(a1),x5211),x5211),f10(a1,x5212,x5212)),f10(a1,f10(a1,f3(a1),f10(a1,x5211,x5212)),f10(a1,x5211,x5212)))
% 1.20/1.55 [522]E(f8(a1,f10(a1,f10(a1,f3(a1),x5221),x5221),f10(a1,x5222,x5222)),f10(a1,f10(a1,f3(a1),f8(a1,x5221,x5222)),f8(a1,x5221,x5222)))
% 1.20/1.55 [485]E(f8(a1,f16(a1,x4851),f16(a1,x4852)),f16(a1,f10(a1,x4851,f9(a1,x4852))))
% 1.20/1.55 [497]E(f10(a75,f10(a75,x4971,f3(a75)),x4972),f10(a75,f10(a75,x4971,x4972),f3(a75)))
% 1.20/1.55 [498]E(f4(a74,f10(a74,x4981,f9(a74,x4982))),f4(a74,f10(a74,x4982,f9(a74,x4981))))
% 1.20/1.55 [499]E(f8(a75,f8(a75,x4991,f3(a75)),x4992),f8(a75,x4991,f10(a75,x4992,f3(a75))))
% 1.20/1.55 [500]E(f10(a75,f10(a75,x5001,f3(a75)),x5002),f10(a75,x5001,f10(a75,x5002,f3(a75))))
% 1.20/1.55 [515]E(f5(a1,f16(a1,f10(a1,x5151,x5151)),f16(a1,f10(a1,x5152,x5152))),f5(a1,f16(a1,x5151),f16(a1,x5152)))
% 1.20/1.55 [525]P2(a74,f2(a74),f8(a74,f23(a74,f20(a75,x5251),f20(a75,x5252)),f20(a75,f5(a75,x5251,x5252))))
% 1.20/1.55 [526]P2(a74,f8(a74,f23(a74,f20(a75,x5261),f20(a75,x5262)),f20(a75,f5(a75,x5261,x5262))),f3(a74))
% 1.20/1.55 [591]~E(f10(a1,x5911,x5911),f10(a1,f10(a1,f3(a1),x5912),x5912))
% 1.20/1.55 [520]E(f10(a1,f10(a1,x5201,x5201),f10(a1,f10(a1,f3(a1),x5202),x5202)),f10(a1,f10(a1,f3(a1),f10(a1,x5201,x5202)),f10(a1,x5201,x5202)))
% 1.20/1.55 [524]E(f8(a1,f10(a1,f10(a1,f3(a1),x5241),x5241),f10(a1,f10(a1,f3(a1),x5242),x5242)),f10(a1,f8(a1,x5241,x5242),f8(a1,x5241,x5242)))
% 1.20/1.55 [551]E(f8(a74,f23(a74,f10(a74,x5511,x5512),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))),x5512),f23(a74,f8(a74,x5511,x5512),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [552]E(f8(a74,f23(a74,f10(a74,x5521,x5522),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))),x5521),f23(a74,f8(a74,x5522,x5521),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [556]E(f5(a75,x5561,f10(a75,f16(a75,f10(a1,f10(a1,f3(a1),f10(a1,f10(a1,f3(a1),a13),a13)),f10(a1,f10(a1,f3(a1),a13),a13))),x5562)),f5(a75,x5561,f10(a75,f10(a75,f10(a75,x5562,f3(a75)),f3(a75)),f3(a75))))
% 1.20/1.55 [557]E(f5(a75,f10(a75,f16(a75,f10(a1,f10(a1,f3(a1),f10(a1,f10(a1,f3(a1),a13),a13)),f10(a1,f10(a1,f3(a1),a13),a13))),x5571),x5572),f5(a75,f10(a75,f10(a75,f10(a75,x5571,f3(a75)),f3(a75)),f3(a75)),x5572))
% 1.20/1.55 [488]E(f10(a75,x4881,f10(a75,x4882,x4883)),f10(a75,x4882,f10(a75,x4881,x4883)))
% 1.20/1.55 [489]E(f10(a1,x4891,f10(a1,x4892,x4893)),f10(a1,x4892,f10(a1,x4891,x4893)))
% 1.20/1.55 [490]E(f10(a75,f10(a75,x4901,x4902),x4903),f10(a75,x4901,f10(a75,x4902,x4903)))
% 1.20/1.55 [491]E(f10(a1,f10(a1,x4911,x4912),x4913),f10(a1,x4911,f10(a1,x4912,x4913)))
% 1.20/1.55 [492]E(f8(a75,f8(a75,x4921,x4922),x4923),f8(a75,x4921,f10(a75,x4922,x4923)))
% 1.20/1.55 [493]E(f8(a75,f8(a75,x4931,x4932),x4933),f8(a75,f8(a75,x4931,x4933),x4932))
% 1.20/1.55 [494]E(f8(a75,f10(a75,x4941,x4942),f10(a75,x4943,x4942)),f8(a75,x4941,x4943))
% 1.20/1.55 [495]E(f8(a75,f10(a75,x4951,x4952),f10(a75,x4951,x4953)),f8(a75,x4952,x4953))
% 1.20/1.55 [510]E(f10(a74,f11(a74,x5101,x5102),f11(a74,x5103,x5102)),f11(a74,f10(a74,x5101,x5103),x5102))
% 1.20/1.55 [516]E(f8(a75,f8(a75,f10(a75,x5161,f3(a75)),x5162),f10(a75,x5163,f3(a75))),f8(a75,f8(a75,x5161,x5162),x5163))
% 1.20/1.55 [537]P2(a74,f4(a74,f10(a74,f10(a74,x5371,x5372),f10(a74,f9(a74,x5373),f9(a74,x5374)))),f10(a74,f4(a74,f10(a74,x5371,f9(a74,x5373))),f4(a74,f10(a74,x5372,f9(a74,x5374)))))
% 1.20/1.55 [1173]~P3(a74,f9(a74,a85),f9(a74,a85))+P2(a74,f22(a14,a28),a81)
% 1.20/1.55 [1495]~P3(a74,f9(a74,a85),f9(a74,a85))+P3(a74,f22(a14,f63(f17(a14,a82),a28)),f9(a74,a85))
% 1.20/1.55 [593]~P54(x5931)+P6(f76(x5931))
% 1.20/1.55 [594]~P17(x5941)+P7(f76(x5941))
% 1.20/1.55 [595]~P17(x5951)+P8(f76(x5951))
% 1.20/1.55 [596]~P20(x5961)+P9(f76(x5961))
% 1.20/1.55 [597]~P10(x5971)+P10(f76(x5971))
% 1.20/1.55 [598]~P54(x5981)+P27(f76(x5981))
% 1.20/1.55 [599]~P54(x5991)+P28(f76(x5991))
% 1.20/1.55 [600]~P54(x6001)+P18(f76(x6001))
% 1.20/1.55 [601]~P10(x6011)+P19(f76(x6011))
% 1.20/1.55 [602]~P54(x6021)+P29(f76(x6021))
% 1.20/1.55 [603]~P46(x6031)+P46(f76(x6031))
% 1.20/1.55 [604]~P47(x6041)+P47(f76(x6041))
% 1.20/1.55 [605]~P54(x6051)+P16(f76(x6051))
% 1.20/1.55 [606]~P30(x6061)+P30(f76(x6061))
% 1.20/1.55 [607]~P54(x6071)+P22(f76(x6071))
% 1.20/1.55 [608]~P54(x6081)+P35(f76(x6081))
% 1.20/1.55 [609]~P54(x6091)+P40(f76(x6091))
% 1.20/1.55 [610]~P54(x6101)+P41(f76(x6101))
% 1.20/1.55 [611]~P54(x6111)+P31(f76(x6111))
% 1.20/1.55 [612]~P54(x6121)+P32(f76(x6121))
% 1.20/1.55 [613]~P20(x6131)+P23(f76(x6131))
% 1.20/1.55 [614]~P20(x6141)+P20(f76(x6141))
% 1.20/1.55 [615]~P54(x6151)+P36(f76(x6151))
% 1.20/1.55 [616]~P50(x6161)+P50(f76(x6161))
% 1.20/1.55 [617]~P54(x6171)+P54(f76(x6171))
% 1.20/1.55 [618]~P51(x6181)+P25(f76(x6181))
% 1.20/1.55 [619]~P51(x6191)+P51(f76(x6191))
% 1.20/1.55 [620]~P51(x6201)+P56(f76(x6201))
% 1.20/1.55 [621]~P54(x6211)+P57(f76(x6211))
% 1.20/1.55 [622]~P48(x6221)+P48(f76(x6221))
% 1.20/1.55 [623]~P50(x6231)+P70(f76(x6231))
% 1.20/1.55 [624]~P13(x6241)+P12(f76(x6241))
% 1.20/1.55 [625]~P10(x6251)+P24(f76(x6251))
% 1.20/1.55 [626]~P10(x6261)+P33(f76(x6261))
% 1.20/1.55 [627]~P48(x6271)+P37(f76(x6271))
% 1.20/1.55 [628]~P48(x6281)+P38(f76(x6281))
% 1.20/1.55 [629]~P54(x6291)+P34(f76(x6291))
% 1.20/1.55 [630]~P46(x6301)+P60(f76(x6301))
% 1.20/1.55 [631]~P47(x6311)+P68(f76(x6311))
% 1.20/1.55 [632]~P47(x6321)+P49(f76(x6321))
% 1.20/1.55 [633]~P47(x6331)+P61(f76(x6331))
% 1.20/1.55 [634]~P50(x6341)+P69(f76(x6341))
% 1.20/1.55 [635]~P50(x6351)+P63(f76(x6351))
% 1.20/1.55 [636]~P51(x6361)+P26(f76(x6361))
% 1.20/1.55 [637]~P51(x6371)+P21(f76(x6371))
% 1.20/1.55 [638]~P54(x6381)+P58(f76(x6381))
% 1.20/1.55 [639]~P54(x6391)+P59(f76(x6391))
% 1.20/1.55 [640]~P54(x6401)+P64(f76(x6401))
% 1.20/1.55 [641]~P54(x6411)+P65(f76(x6411))
% 1.20/1.55 [642]~P54(x6421)+P67(f76(x6421))
% 1.20/1.55 [643]~P54(x6431)+P66(f76(x6431))
% 1.20/1.55 [644]~P54(x6441)+P55(f76(x6441))
% 1.20/1.55 [645]~P54(x6451)+P62(f76(x6451))
% 1.20/1.55 [646]~P17(x6461)+P17(f76(x6461))
% 1.20/1.55 [648]~P56(x6481)+~E(f3(x6481),f2(x6481))
% 1.20/1.55 [649]~E(x6491,f2(a75))+E(f20(a75,x6491),f2(a74))
% 1.20/1.55 [651]~E(x6511,f2(a74))+E(f12(a74,x6511),f2(a74))
% 1.20/1.55 [652]~E(x6521,f2(a1))+E(f12(a1,x6521),f2(a1))
% 1.20/1.55 [654]~P37(x6541)+E(f16(x6541,a13),f2(x6541))
% 1.20/1.55 [655]E(x6551,f2(a75))+~E(f20(a75,x6551),f2(a74))
% 1.20/1.55 [710]~E(a13,x7101)+E(f10(a1,x7101,x7101),a13)
% 1.20/1.55 [711]~E(x7111,a13)+E(f10(a1,x7111,x7111),a13)
% 1.20/1.55 [718]E(x7181,f2(a1))+E(f5(a1,x7181,x7181),f3(a1))
% 1.20/1.55 [722]E(x7221,f2(a75))+P3(a75,f2(a75),x7221)
% 1.20/1.55 [758]E(f4(a74,x7581),x7581)+P3(a74,x7581,f2(a74))
% 1.20/1.55 [759]E(f4(a1,x7591),x7591)+P3(a1,x7591,f2(a1))
% 1.20/1.55 [760]P1(x7601)+P3(a75,f27(x7601),f34(x7601))
% 1.20/1.55 [778]~P57(x7781)+P2(x7781,f2(x7781),f3(x7781))
% 1.20/1.55 [779]~P57(x7791)+P3(x7791,f2(x7791),f3(x7791))
% 1.20/1.55 [787]P2(a1,x7871,a13)+~E(f16(a75,x7871),f2(a75))
% 1.20/1.55 [799]~E(x7991,f2(a75))+P2(a74,f20(a75,x7991),f2(a74))
% 1.20/1.55 [800]~E(x8001,f2(a1))+P3(a1,f4(a1,x8001),f3(a1))
% 1.20/1.55 [801]E(x8011,a13)+~E(f10(a1,x8011,x8011),a13)
% 1.20/1.55 [802]E(a13,x8021)+~E(f10(a1,x8021,x8021),a13)
% 1.20/1.55 [836]E(x8361,f2(a75))+~P2(a75,x8361,f2(a75))
% 1.20/1.55 [843]E(f15(x8431),f2(a75))+~P2(a74,x8431,f2(a74))
% 1.20/1.55 [844]E(f19(x8441),f2(a75))+~P2(a74,x8441,f2(a74))
% 1.20/1.55 [847]~P2(a1,x8471,a13)+E(f16(a75,x8471),f2(a75))
% 1.20/1.55 [867]~P3(a74,f2(a74),x8671)+E(f12(a74,x8671),f3(a74))
% 1.20/1.55 [889]~P57(x8891)+~P2(x8891,f3(x8891),f2(x8891))
% 1.20/1.55 [890]~P57(x8901)+~P3(x8901,f3(x8901),f2(x8901))
% 1.20/1.55 [892]E(f4(a74,x8921),f9(a74,x8921))+~P3(a74,x8921,f2(a74))
% 1.20/1.55 [893]E(f4(a1,x8931),f9(a1,x8931))+~P3(a1,x8931,f2(a1))
% 1.20/1.55 [924]E(x9241,f2(a75))+~P2(a74,f20(a75,x9241),f2(a74))
% 1.20/1.55 [925]E(x9251,f2(a1))+~P3(a1,f4(a1,x9251),f3(a1))
% 1.20/1.55 [954]~P3(a74,x9541,a85)+P3(a74,x9541,f40(x9541))
% 1.20/1.55 [955]~P3(a74,x9551,a37)+P3(a74,x9551,f36(x9551))
% 1.20/1.55 [963]~P3(a1,f2(a1),x9631)+P2(a1,f3(a1),x9631)
% 1.20/1.55 [964]~P2(a1,f3(a1),x9641)+P3(a1,f2(a1),x9641)
% 1.20/1.55 [983]~P2(a74,x9831,f3(a74))+P2(a75,f15(x9831),f3(a75))
% 1.20/1.55 [984]~P2(a74,f3(a74),x9841)+P2(a75,f3(a75),f19(x9841))
% 1.20/1.55 [987]~P2(a75,f15(x9871),f3(a75))+P2(a74,x9871,f3(a74))
% 1.20/1.55 [988]~P2(a75,f3(a75),f19(x9881))+P2(a74,f3(a74),x9881)
% 1.20/1.55 [1001]~P3(a1,a13,x10011)+P3(a75,f2(a75),f16(a75,x10011))
% 1.20/1.55 [1006]~P3(a75,f2(a75),x10061)+P3(a74,f2(a74),f20(a75,x10061))
% 1.20/1.55 [1029]P3(a1,a13,x10291)+~P3(a75,f2(a75),f16(a75,x10291))
% 1.20/1.55 [1055]P3(a75,f2(a75),x10551)+~P3(a74,f2(a74),f20(a75,x10551))
% 1.20/1.55 [1213]~P2(a1,a13,x12131)+P2(a1,a13,f10(a1,x12131,x12131))
% 1.20/1.55 [1214]~P3(a1,a13,x12141)+P3(a1,a13,f10(a1,x12141,x12141))
% 1.20/1.55 [1215]~P2(a1,x12151,a13)+P2(a1,f10(a1,x12151,x12151),a13)
% 1.20/1.55 [1216]~P3(a1,x12161,a13)+P3(a1,f10(a1,x12161,x12161),a13)
% 1.20/1.55 [1263]~P3(a1,x12631,f2(a1))+P3(a1,f10(a1,x12631,x12631),f2(a1))
% 1.20/1.55 [1304]P2(a1,x13041,a13)+~P2(a1,f10(a1,x13041,x13041),a13)
% 1.20/1.55 [1305]P3(a1,x13051,a13)+~P3(a1,f10(a1,x13051,x13051),a13)
% 1.20/1.55 [1306]P2(a1,a13,x13061)+~P2(a1,a13,f10(a1,x13061,x13061))
% 1.20/1.55 [1307]P3(a1,a13,x13071)+~P3(a1,a13,f10(a1,x13071,x13071))
% 1.20/1.55 [1333]P3(a1,x13331,f2(a1))+~P3(a1,f10(a1,x13331,x13331),f2(a1))
% 1.20/1.55 [656]~P5(x6561)+E(f22(x6561,f2(x6561)),f2(a74))
% 1.20/1.55 [657]~P42(x6571)+E(f22(x6571,f3(x6571)),f3(a74))
% 1.20/1.55 [660]~P6(x6601)+E(f4(x6601,f2(x6601)),f2(x6601))
% 1.20/1.55 [661]~P54(x6611)+E(f4(x6611,f3(x6611)),f3(x6611))
% 1.20/1.55 [662]~P19(x6621)+E(f9(x6621,f2(x6621)),f2(x6621))
% 1.20/1.55 [663]~P5(x6631)+E(f12(x6631,f2(x6631)),f2(x6631))
% 1.20/1.55 [664]~P34(x6641)+E(f12(x6641,f2(x6641)),f2(x6641))
% 1.20/1.55 [665]~P42(x6651)+E(f12(x6651,f3(x6651)),f3(x6651))
% 1.20/1.55 [666]~P11(x6661)+E(f21(x6661,f2(x6661)),f2(x6661))
% 1.20/1.55 [667]~P52(x6671)+E(f21(x6671,f2(x6671)),f2(x6671))
% 1.20/1.55 [668]~P53(x6681)+E(f21(x6681,f3(x6681)),f3(x6681))
% 1.20/1.55 [795]E(x7951,f2(a74))+E(f11(a74,f21(a74,x7951),x7951),f3(a74))
% 1.20/1.55 [985]~P3(a75,f2(a75),x9851)+E(f10(a75,f41(x9851),f3(a75)),x9851)
% 1.20/1.55 [1010]~P3(a74,x10101,a85)+P2(a74,f22(a14,f59(x10101)),a81)
% 1.20/1.55 [1011]~P3(a74,x10111,a37)+P2(a74,f22(a14,f38(x10111)),a81)
% 1.20/1.55 [1030]~P2(a74,f2(a74),x10301)+P3(a74,x10301,f20(a75,f60(x10301)))
% 1.20/1.55 [1031]~P2(a74,f2(a74),x10311)+P2(a74,f20(a75,f19(x10311)),x10311)
% 1.20/1.55 [1107]~P57(x11071)+P3(x11071,f2(x11071),f10(x11071,f3(x11071),f3(x11071)))
% 1.20/1.55 [1115]~P3(a74,f9(a74,a85),x11151)+P2(a74,f22(a14,f69(x11151)),a81)
% 1.20/1.55 [1116]~P3(a74,f9(a74,a85),x11161)+P2(a74,f22(a14,f71(x11161)),a81)
% 1.20/1.55 [1135]P1(x11351)+~P3(a75,f63(x11351,f27(x11351)),f63(x11351,f34(x11351)))
% 1.20/1.55 [1269]~P2(a1,f2(a1),x12691)+P3(a1,f2(a1),f10(a1,f3(a1),x12691))
% 1.20/1.55 [1271]~P3(a75,f2(a75),x12711)+E(f10(a75,f8(a75,x12711,f3(a75)),f3(a75)),x12711)
% 1.20/1.55 [1284]E(x12841,f2(a75))+~P3(a75,x12841,f10(a75,f2(a75),f3(a75)))
% 1.20/1.55 [1619]~P3(a75,f2(a75),x16191)+E(f10(a75,f8(a75,x16191,f10(a75,f2(a75),f3(a75))),f3(a75)),x16191)
% 1.20/1.55 [712]~P10(x7121)+E(f9(f76(x7121),f2(f76(x7121))),f2(f76(x7121)))
% 1.20/1.55 [1094]~P3(a74,x10941,a85)+E(f22(a14,f63(f17(a14,a82),f59(x10941))),f9(a74,f40(x10941)))
% 1.20/1.55 [1095]~P3(a74,x10951,a37)+E(f22(a14,f63(f17(a14,a82),f38(x10951))),f9(a74,f36(x10951)))
% 1.20/1.55 [1279]~P2(a74,f2(a74),x12791)+E(f15(f10(a74,x12791,f3(a74))),f10(a75,f15(x12791),f3(a75)))
% 1.20/1.55 [1280]~P2(a74,f2(a74),x12801)+E(f19(f10(a74,x12801,f3(a74))),f10(a75,f19(x12801),f3(a75)))
% 1.20/1.55 [1425]~P2(a74,f22(a14,x14251),a81)+P2(a74,f9(a74,a85),f22(a14,f63(f17(a14,a82),x14251)))
% 1.20/1.55 [1426]~P3(a74,f9(a74,a85),x14261)+P3(a74,f22(a14,f63(f17(a14,a82),f71(x14261))),x14261)
% 1.20/1.55 [1542]~P2(a74,f2(a74),x15421)+P2(a74,f20(a75,f8(a75,f60(x15421),f3(a75))),x15421)
% 1.20/1.55 [1585]~P2(a1,a13,x15851)+P2(a1,a13,f10(a1,f10(a1,f3(a1),x15851),x15851))
% 1.20/1.55 [1586]~P2(a1,a13,x15861)+P3(a1,a13,f10(a1,f10(a1,f3(a1),x15861),x15861))
% 1.20/1.55 [1587]~P3(a1,x15871,a13)+P2(a1,f10(a1,f10(a1,f3(a1),x15871),x15871),a13)
% 1.20/1.55 [1588]~P3(a1,x15881,a13)+P3(a1,f10(a1,f10(a1,f3(a1),x15881),x15881),a13)
% 1.20/1.55 [1617]~P3(a1,x16171,f2(a1))+P3(a1,f10(a1,f10(a1,f3(a1),x16171),x16171),f2(a1))
% 1.20/1.55 [1690]P1(x16901)+~P3(a75,f63(x16901,f45(x16901)),f63(x16901,f10(a75,f45(x16901),f3(a75))))
% 1.20/1.55 [1713]P3(a1,x17131,a13)+~P2(a1,f10(a1,f10(a1,f3(a1),x17131),x17131),a13)
% 1.20/1.55 [1714]P3(a1,x17141,a13)+~P3(a1,f10(a1,f10(a1,f3(a1),x17141),x17141),a13)
% 1.20/1.55 [1715]P2(a1,a13,x17151)+~P2(a1,a13,f10(a1,f10(a1,f3(a1),x17151),x17151))
% 1.20/1.55 [1716]P2(a1,a13,x17161)+~P3(a1,a13,f10(a1,f10(a1,f3(a1),x17161),x17161))
% 1.20/1.55 [1720]P3(a1,x17201,f2(a1))+~P3(a1,f10(a1,f10(a1,f3(a1),x17201),x17201),f2(a1))
% 1.20/1.55 [1402]~P37(x14021)+E(f16(x14021,f10(a1,f10(a1,f3(a1),a13),a13)),f3(x14021))
% 1.20/1.55 [1686]~P2(a75,a78,x16861)+P3(a74,f22(a14,f8(a14,f83(f63(a73,x16861)),a86)),a77)
% 1.20/1.55 [1687]~P2(a75,a70,x16871)+P3(a74,f22(a14,f8(a14,f83(f63(a73,x16871)),a86)),a77)
% 1.20/1.55 [1688]~P2(a75,a32,x16881)+P3(a74,f22(a14,f8(a14,f83(f63(a73,x16881)),a86)),a77)
% 1.20/1.55 [1762]~P3(a74,f9(a74,a85),x17621)+P3(a74,f9(a74,f9(a74,f22(a14,f63(f17(a14,a82),f69(x17621))))),x17621)
% 1.20/1.55 [1779]~P37(x17791)+E(f10(x17791,f3(x17791),f3(x17791)),f16(x17791,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))))
% 1.20/1.55 [1793]~P3(a75,f3(a75),x17931)+P3(a75,f2(a75),f5(a75,x17931,f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [1798]~P3(a75,f2(a75),x17981)+P3(a75,f2(a75),f5(a75,f10(a75,x17981,f3(a75)),f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [1800]~P3(a74,f22(a14,f8(a14,x18001,a86)),a77)+P3(a74,f22(a14,f8(a14,f63(f17(a14,a82),x18001),f63(f17(a14,a82),a86))),f23(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85))),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.55 [713]~E(x7131,x7132)+P2(a74,x7131,x7132)
% 1.20/1.55 [716]~E(x7161,x7162)+P2(a75,x7161,x7162)
% 1.20/1.55 [730]~P29(x7301)+P2(x7301,x7302,x7302)
% 1.20/1.55 [811]~E(x8111,x8112)+~P3(a74,x8111,x8112)
% 1.20/1.55 [816]~E(x8161,x8162)+~P3(a75,x8161,x8162)
% 1.20/1.55 [817]~E(x8171,x8172)+~P3(a1,x8171,x8172)
% 1.20/1.55 [839]~P3(x8391,x8392,x8392)+~P29(x8391)
% 1.20/1.55 [871]P2(a74,x8712,x8711)+P2(a74,x8711,x8712)
% 1.20/1.55 [872]P2(a75,x8722,x8721)+P2(a75,x8721,x8722)
% 1.20/1.55 [873]P2(a1,x8732,x8731)+P2(a1,x8731,x8732)
% 1.20/1.55 [931]~P3(a74,x9311,x9312)+P2(a74,x9311,x9312)
% 1.20/1.55 [936]~P3(a75,x9361,x9362)+P2(a75,x9361,x9362)
% 1.20/1.55 [937]~P3(a1,x9371,x9372)+P2(a1,x9371,x9372)
% 1.20/1.55 [680]~P29(x6802)+P29(f79(x6801,x6802))
% 1.20/1.55 [681]~P40(x6812)+P40(f79(x6811,x6812))
% 1.20/1.55 [682]~P41(x6822)+P41(f79(x6821,x6822))
% 1.20/1.55 [683]~P39(x6832)+P39(f79(x6831,x6832))
% 1.20/1.55 [684]~P24(x6842)+P24(f79(x6841,x6842))
% 1.20/1.55 [685]~P33(x6852)+P33(f79(x6851,x6852))
% 1.20/1.55 [696]E(x6961,x6962)+~E(f20(a75,x6961),f20(a75,x6962))
% 1.20/1.55 [720]E(f10(a75,x7201,x7202),x7202)+~E(x7201,f2(a75))
% 1.20/1.55 [729]~E(x7292,f2(a1))+E(f5(a1,x7291,x7292),f2(a1))
% 1.20/1.55 [737]~P19(x7371)+E(f8(x7371,x7372,x7372),f2(x7371))
% 1.20/1.55 [788]~E(x7882,f9(a74,x7881))+E(f10(a74,x7881,x7882),f2(a74))
% 1.20/1.55 [805]~P1(x8052)+P2(a75,x8051,f63(x8052,x8051))
% 1.20/1.55 [818]~P6(x8181)+P2(x8181,x8182,f4(x8181,x8182))
% 1.20/1.55 [824]~E(f10(a75,x8242,x8241),x8242)+E(x8241,f2(a75))
% 1.20/1.55 [825]~P5(x8251)+P2(a74,f2(a74),f22(x8251,x8252))
% 1.20/1.55 [829]~P3(a75,x8292,x8291)+~E(x8291,f2(a75))
% 1.20/1.55 [831]E(x8311,f2(a75))+~E(f10(a75,x8312,x8311),f2(a75))
% 1.20/1.55 [832]E(x8321,f2(a75))+~E(f10(a75,x8321,x8322),f2(a75))
% 1.20/1.55 [840]~P6(x8401)+P2(x8401,f2(x8401),f4(x8401,x8402))
% 1.20/1.55 [863]E(x8631,f9(a74,x8632))+~E(f10(a74,x8632,x8631),f2(a74))
% 1.20/1.55 [894]~P6(x8941)+P2(x8941,f9(x8941,x8942),f4(x8941,x8942))
% 1.20/1.55 [929]~P5(x9291)+~P3(a74,f22(x9291,x9292),f2(a74))
% 1.20/1.55 [944]~P2(a75,x9441,x9442)+E(f8(a75,x9441,x9442),f2(a75))
% 1.20/1.55 [945]~P3(a75,x9451,x9452)+E(f5(a75,x9451,x9452),f2(a75))
% 1.20/1.55 [953]P2(a75,x9531,x9532)+~E(f8(a75,x9531,x9532),f2(a75))
% 1.20/1.55 [961]~P6(x9611)+~P3(x9611,f4(x9611,x9612),f2(x9611))
% 1.20/1.55 [972]~P2(a74,x9721,x9722)+P2(a75,f15(x9721),f15(x9722))
% 1.20/1.55 [973]~P2(a74,x9731,x9732)+P2(a75,f19(x9731),f19(x9732))
% 1.20/1.55 [1014]E(x10141,x10142)+~E(f10(a1,x10141,x10141),f10(a1,x10142,x10142))
% 1.20/1.55 [1024]P2(a74,x10241,x10242)+~P2(a74,f4(a74,x10241),x10242)
% 1.20/1.55 [1027]~P58(x10271)+P2(x10271,f2(x10271),f11(x10271,x10272,x10272))
% 1.20/1.55 [1036]P2(a75,x10361,f19(x10362))+~P2(a74,f20(a75,x10361),x10362)
% 1.20/1.55 [1037]P2(a75,f15(x10371),x10372)+~P2(a74,x10371,f20(a75,x10372))
% 1.20/1.55 [1048]~P2(a1,x10481,a13)+P2(a75,f16(a75,x10481),f16(a75,x10482))
% 1.20/1.55 [1065]~P2(a75,x10651,x10652)+P2(a74,f20(a75,x10651),f20(a75,x10652))
% 1.20/1.55 [1066]~P2(a1,x10661,x10662)+P2(a75,f16(a75,x10661),f16(a75,x10662))
% 1.20/1.56 [1067]~P2(a1,x10671,x10672)+P2(a1,f16(a1,x10671),f16(a1,x10672))
% 1.20/1.56 [1068]~P3(a75,x10681,x10682)+P3(a74,f20(a75,x10681),f20(a75,x10682))
% 1.20/1.56 [1069]~P3(a1,x10691,x10692)+P3(a1,f16(a1,x10691),f16(a1,x10692))
% 1.20/1.56 [1103]~P2(a74,f4(a74,x11032),x11031)+P2(a74,f9(a74,x11031),x11032)
% 1.20/1.56 [1145]P2(a75,x11451,x11452)+~P2(a74,f20(a75,x11451),f20(a75,x11452))
% 1.20/1.56 [1146]P2(a1,x11461,x11462)+~P2(a1,f16(a1,x11461),f16(a1,x11462))
% 1.20/1.56 [1147]P3(a75,x11471,x11472)+~P3(a74,f20(a75,x11471),f20(a75,x11472))
% 1.20/1.56 [1148]P3(a1,x11481,x11482)+~P3(a75,f16(a75,x11481),f16(a75,x11482))
% 1.20/1.56 [1149]P3(a1,x11491,x11492)+~P3(a1,f16(a1,x11491),f16(a1,x11492))
% 1.20/1.56 [1239]~P3(a75,x12392,x12391)+P3(a75,f2(a75),f8(a75,x12391,x12392))
% 1.20/1.56 [1240]~P2(a74,x12401,x12402)+P2(a74,f8(a74,x12401,x12402),f2(a74))
% 1.20/1.56 [1241]~P3(a1,x12411,x12412)+P3(a1,f8(a1,x12411,x12412),f2(a1))
% 1.20/1.56 [1290]~P58(x12901)+~P3(x12901,f11(x12901,x12902,x12902),f2(x12901))
% 1.20/1.56 [1293]~P2(a74,f9(a74,x12931),x12932)+P2(a74,f2(a74),f10(a74,x12931,x12932))
% 1.20/1.56 [1294]~P3(a74,f9(a74,x12941),x12942)+P3(a74,f2(a74),f10(a74,x12941,x12942))
% 1.20/1.56 [1295]~P2(a74,x12952,f9(a74,x12951))+P2(a74,f10(a74,x12951,x12952),f2(a74))
% 1.20/1.56 [1296]~P3(a74,x12962,f9(a74,x12961))+P3(a74,f10(a74,x12961,x12962),f2(a74))
% 1.20/1.56 [1329]P3(a75,x13291,x13292)+~P3(a75,f2(a75),f8(a75,x13292,x13291))
% 1.20/1.56 [1330]P2(a74,x13301,x13302)+~P2(a74,f8(a74,x13301,x13302),f2(a74))
% 1.20/1.56 [1331]P3(a1,x13311,x13312)+~P3(a1,f8(a1,x13311,x13312),f2(a1))
% 1.20/1.56 [1361]P2(a74,x13611,f9(a74,x13612))+~P2(a74,f10(a74,x13612,x13611),f2(a74))
% 1.20/1.56 [1362]P3(a74,x13621,f9(a74,x13622))+~P3(a74,f10(a74,x13622,x13621),f2(a74))
% 1.20/1.56 [1363]P2(a74,f9(a74,x13631),x13632)+~P2(a74,f2(a74),f10(a74,x13631,x13632))
% 1.20/1.56 [1364]P3(a74,f9(a74,x13641),x13642)+~P3(a74,f2(a74),f10(a74,x13641,x13642))
% 1.20/1.56 [1419]~P2(a1,x14191,x14192)+P2(a1,f10(a1,x14191,x14191),f10(a1,x14192,x14192))
% 1.20/1.56 [1424]~P3(a1,x14241,x14242)+P3(a1,f10(a1,x14241,x14241),f10(a1,x14242,x14242))
% 1.20/1.56 [1611]P2(a1,x16111,x16112)+~P2(a1,f10(a1,x16111,x16111),f10(a1,x16112,x16112))
% 1.20/1.56 [1614]P3(a1,x16141,x16142)+~P3(a1,f10(a1,x16141,x16141),f10(a1,x16142,x16142))
% 1.20/1.56 [703]~P19(x7031)+E(f9(x7031,f9(x7031,x7032)),x7032)
% 1.20/1.56 [704]~P39(x7041)+E(f9(x7041,f9(x7041,x7042)),x7042)
% 1.20/1.56 [719]~P5(x7191)+E(f4(a74,f22(x7191,x7192)),f22(x7191,x7192))
% 1.20/1.56 [725]~P5(x7251)+E(f22(x7251,f9(x7251,x7252)),f22(x7251,x7252))
% 1.20/1.56 [726]~P6(x7261)+E(f4(x7261,f4(x7261,x7262)),f4(x7261,x7262))
% 1.20/1.56 [727]~P6(x7271)+E(f4(x7271,f9(x7271,x7272)),f4(x7271,x7272))
% 1.20/1.56 [728]~P54(x7281)+E(f12(x7281,f12(x7281,x7282)),f12(x7281,x7282))
% 1.20/1.56 [739]~P23(x7391)+E(f10(x7391,x7392,f2(x7391)),x7392)
% 1.20/1.56 [740]~P20(x7401)+E(f10(x7401,x7402,f2(x7401)),x7402)
% 1.20/1.56 [741]~P51(x7411)+E(f10(x7411,x7412,f2(x7411)),x7412)
% 1.20/1.56 [742]~P19(x7421)+E(f8(x7421,x7422,f2(x7421)),x7422)
% 1.20/1.56 [743]~P53(x7431)+E(f23(x7431,x7432,f3(x7431)),x7432)
% 1.20/1.56 [744]~P12(x7441)+E(f5(x7441,x7442,f3(x7441)),x7442)
% 1.20/1.56 [745]~P51(x7451)+E(f11(x7451,x7452,f3(x7451)),x7452)
% 1.20/1.56 [746]~P26(x7461)+E(f11(x7461,x7462,f3(x7461)),x7462)
% 1.20/1.56 [747]~P21(x7471)+E(f11(x7471,x7472,f3(x7471)),x7472)
% 1.20/1.56 [748]~P23(x7481)+E(f10(x7481,f2(x7481),x7482),x7482)
% 1.20/1.56 [749]~P20(x7491)+E(f10(x7491,f2(x7491),x7492),x7492)
% 1.20/1.56 [750]~P51(x7501)+E(f10(x7501,f2(x7501),x7502),x7502)
% 1.20/1.56 [751]~P51(x7511)+E(f11(x7511,f3(x7511),x7512),x7512)
% 1.20/1.56 [752]~P26(x7521)+E(f11(x7521,f3(x7521),x7522),x7522)
% 1.20/1.56 [753]~P21(x7531)+E(f11(x7531,f3(x7531),x7532),x7532)
% 1.20/1.56 [765]~P52(x7651)+E(f23(x7651,x7652,f2(x7651)),f2(x7651))
% 1.20/1.56 [766]~P12(x7661)+E(f5(x7661,x7662,f2(x7661)),f2(x7661))
% 1.20/1.56 [767]~P51(x7671)+E(f11(x7671,x7672,f2(x7671)),f2(x7671))
% 1.20/1.56 [769]~P43(x7691)+E(f11(x7691,x7692,f2(x7691)),f2(x7691))
% 1.20/1.56 [770]~P61(x7701)+E(f11(x7701,x7702,f2(x7701)),f2(x7701))
% 1.20/1.56 [771]~P44(x7711)+E(f23(x7711,f2(x7711),x7712),f2(x7711))
% 1.20/1.56 [772]~P53(x7721)+E(f23(x7721,f2(x7721),x7722),f2(x7721))
% 1.20/1.56 [773]~P12(x7731)+E(f5(x7731,f2(x7731),x7732),f2(x7731))
% 1.20/1.56 [774]~P51(x7741)+E(f11(x7741,f2(x7741),x7742),f2(x7741))
% 1.20/1.56 [776]~P43(x7761)+E(f11(x7761,f2(x7761),x7762),f2(x7761))
% 1.20/1.56 [777]~P61(x7771)+E(f11(x7771,f2(x7771),x7772),f2(x7771))
% 1.20/1.56 [791]~P53(x7911)+E(f23(x7911,f3(x7911),x7912),f21(x7911,x7912))
% 1.20/1.56 [792]~P13(x7921)+E(f23(x7921,f3(x7921),x7922),f21(x7921,x7922))
% 1.20/1.56 [793]~P19(x7931)+E(f8(x7931,f2(x7931),x7932),f9(x7931,x7932))
% 1.20/1.56 [794]~E(x7941,x7942)+E(f10(a74,x7941,f9(a74,x7942)),f2(a74))
% 1.20/1.56 [798]~P37(x7981)+E(f9(x7981,f16(x7981,x7982)),f16(x7981,f9(a1,x7982)))
% 1.20/1.56 [803]~P37(x8031)+E(f10(x8031,x8032,f16(x8031,a13)),x8032)
% 1.20/1.56 [804]~P37(x8041)+E(f10(x8041,f16(x8041,a13),x8042),x8042)
% 1.20/1.56 [809]~P5(x8091)+E(f12(x8091,f9(x8091,x8092)),f9(x8091,f12(x8091,x8092)))
% 1.20/1.56 [810]~P52(x8101)+E(f21(x8101,f9(x8101,x8102)),f9(x8101,f21(x8101,x8102)))
% 1.20/1.56 [833]~P19(x8331)+E(f10(x8331,x8332,f9(x8331,x8332)),f2(x8331))
% 1.20/1.56 [834]~P10(x8341)+E(f10(x8341,f9(x8341,x8342),x8342),f2(x8341))
% 1.20/1.56 [835]~P19(x8351)+E(f10(x8351,f9(x8351,x8352),x8352),f2(x8351))
% 1.20/1.56 [920]E(x9201,x9202)+~E(f10(a74,x9201,f9(a74,x9202)),f2(a74))
% 1.20/1.56 [923]E(x9231,x9232)+~E(f63(x9231,f35(x9232,x9231)),f63(x9232,f35(x9232,x9231)))
% 1.20/1.56 [965]~P6(x9651)+P2(x9651,f9(x9651,f4(x9651,x9652)),f2(x9651))
% 1.20/1.56 [966]P3(a75,f2(a75),x9661)+~E(x9661,f10(a75,x9662,f3(a75)))
% 1.20/1.56 [1002]~P2(a75,x10021,x10022)+E(f10(a75,x10021,f66(x10022,x10021)),x10022)
% 1.20/1.56 [1003]~P2(a75,x10031,x10032)+E(f10(a75,x10031,f58(x10032,x10031)),x10032)
% 1.20/1.56 [1004]~E(x10041,x10042)+P3(a75,x10041,f10(a75,x10042,f3(a75)))
% 1.20/1.56 [1005]~E(x10051,x10052)+P3(a1,x10051,f10(a1,x10052,f3(a1)))
% 1.20/1.56 [1015]~E(x10151,f2(a75))+P3(a75,x10151,f10(a75,x10152,f3(a75)))
% 1.20/1.56 [1054]~P57(x10541)+P3(x10541,x10542,f10(x10541,x10542,f3(x10541)))
% 1.20/1.56 [1097]~P3(a1,x10971,a13)+E(f10(a75,f16(a75,x10971),f16(a75,x10972)),f16(a75,x10972))
% 1.20/1.56 [1152]P3(a75,x11522,x11521)+E(f10(a75,x11521,f8(a75,x11522,x11521)),x11522)
% 1.20/1.56 [1171]P3(a75,x11711,x11712)+P3(a75,x11712,f10(a75,x11711,f3(a75)))
% 1.20/1.56 [1172]P2(a75,x11721,x11722)+P2(a75,f10(a75,x11722,f3(a75)),x11721)
% 1.20/1.56 [1236]~P2(a75,x12361,x12362)+E(f10(a75,x12361,f8(a75,x12362,x12361)),x12362)
% 1.20/1.56 [1237]~P2(a75,x12372,x12371)+E(f8(a75,x12371,f8(a75,x12371,x12372)),x12372)
% 1.20/1.56 [1238]~P2(a75,x12382,x12381)+E(f10(a75,f8(a75,x12381,x12382),x12382),x12381)
% 1.20/1.56 [1248]~P3(a1,x12481,x12482)+P2(a1,x12481,f8(a1,x12482,f3(a1)))
% 1.20/1.56 [1250]~P2(a75,x12501,x12502)+P3(a75,x12501,f10(a75,x12502,f3(a75)))
% 1.20/1.56 [1253]~P2(a1,x12531,x12532)+P3(a1,x12531,f10(a1,x12532,f3(a1)))
% 1.20/1.56 [1254]~P3(a1,x12541,x12542)+P3(a1,x12541,f10(a1,x12542,f3(a1)))
% 1.20/1.56 [1257]~P3(a75,x12571,x12572)+P2(a75,f10(a75,x12571,f3(a75)),x12572)
% 1.20/1.56 [1259]~P3(a1,x12591,x12592)+P2(a1,f10(a1,x12591,f3(a1)),x12592)
% 1.20/1.56 [1310]~P3(a75,x13101,x13102)+E(f10(a75,f10(a75,x13101,f44(x13102,x13101)),f3(a75)),x13102)
% 1.20/1.56 [1315]~P2(a75,x13152,x13151)+E(f8(a74,f20(a75,x13151),f20(a75,x13152)),f20(a75,f8(a75,x13151,x13152)))
% 1.20/1.56 [1334]P2(a75,x13341,x13342)+~P3(a75,x13341,f10(a75,x13342,f3(a75)))
% 1.20/1.56 [1335]P2(a1,x13351,x13352)+~P3(a1,x13351,f10(a1,x13352,f3(a1)))
% 1.20/1.56 [1336]P3(a1,x13361,x13362)+~P2(a1,x13361,f8(a1,x13362,f3(a1)))
% 1.20/1.56 [1340]P3(a75,x13401,x13402)+~P2(a75,f10(a75,x13401,f3(a75)),x13402)
% 1.20/1.56 [1342]P3(a1,x13421,x13422)+~P2(a1,f10(a1,x13421,f3(a1)),x13422)
% 1.20/1.56 [1349]~P2(a75,x13491,x13492)+P3(a74,f20(a75,x13491),f10(a74,f20(a75,x13492),f3(a74)))
% 1.20/1.56 [1350]~P3(a75,x13501,x13502)+P2(a74,f10(a74,f20(a75,x13501),f3(a74)),f20(a75,x13502))
% 1.20/1.56 [1403]~P3(a75,x14031,x14032)+~P3(a75,x14032,f10(a75,x14031,f3(a75)))
% 1.20/1.56 [1404]~P2(a75,x14041,x14042)+~P2(a75,f10(a75,x14042,f3(a75)),x14041)
% 1.20/1.56 [1434]P3(a74,x14341,f20(a75,x14342))+~P2(a75,f10(a75,f19(x14341),f3(a75)),x14342)
% 1.20/1.56 [1497]~P37(x14971)+E(f10(x14971,f10(x14971,f2(x14971),f16(x14971,x14972)),f16(x14971,x14972)),f16(x14971,f10(a1,x14972,x14972)))
% 1.20/1.56 [1543]P2(a75,x15431,x15432)+~P3(a74,f20(a75,x15431),f10(a74,f20(a75,x15432),f3(a74)))
% 1.20/1.56 [1544]P3(a75,x15441,x15442)+~P2(a74,f10(a74,f20(a75,x15441),f3(a74)),f20(a75,x15442))
% 1.20/1.56 [1556]E(x15561,f2(a75))+E(f10(a75,f10(a75,f8(a75,x15561,f3(a75)),x15562),f3(a75)),f10(a75,x15561,x15562))
% 1.20/1.56 [1620]P2(a75,x16201,x16202)+~P2(a75,f10(a75,x16201,f3(a75)),f10(a75,x16202,f3(a75)))
% 1.20/1.56 [1622]P3(a75,x16221,x16222)+~P3(a75,f10(a75,x16221,f3(a75)),f10(a75,x16222,f3(a75)))
% 1.20/1.56 [806]~P20(x8061)+E(f10(f76(x8061),x8062,f2(f76(x8061))),x8062)
% 1.20/1.56 [807]~P10(x8071)+E(f8(f76(x8071),x8072,f2(f76(x8071))),x8072)
% 1.20/1.56 [808]~P20(x8081)+E(f10(f76(x8081),f2(f76(x8081)),x8082),x8082)
% 1.20/1.56 [870]~P10(x8701)+E(f8(f76(x8701),f2(f76(x8701)),x8702),f9(f76(x8701),x8702))
% 1.20/1.56 [1260]~P51(x12601)+E(f10(x12601,x12602,x12602),f11(x12601,f10(x12601,f3(x12601),f3(x12601)),x12602))
% 1.20/1.56 [1324]~P2(a74,f2(a74),x13241)+E(f15(f10(a74,x13241,f20(a75,x13242))),f10(a75,f15(x13241),x13242))
% 1.20/1.56 [1325]~P2(a74,f2(a74),x13251)+E(f19(f10(a74,x13251,f20(a75,x13252))),f10(a75,f19(x13251),x13252))
% 1.20/1.56 [1376]~P1(x13761)+P3(a75,f63(x13761,x13762),f63(x13761,f10(a75,x13762,f3(a75))))
% 1.20/1.56 [1377]~P2(a74,f20(a75,x13772),x13771)+E(f15(f8(a74,x13771,f20(a75,x13772))),f8(a75,f15(x13771),x13772))
% 1.20/1.56 [1378]~P2(a74,f20(a75,x13782),x13781)+E(f19(f8(a74,x13781,f20(a75,x13782))),f8(a75,f19(x13781),x13782))
% 1.20/1.56 [1615]~P3(a75,f2(a75),x16151)+P3(a75,f8(a75,x16151,f10(a75,x16152,f3(a75))),x16151)
% 1.20/1.56 [1651]E(x16511,x16512)+~E(f10(a1,f10(a1,f3(a1),x16511),x16511),f10(a1,f10(a1,f3(a1),x16512),x16512))
% 1.20/1.56 [1679]~P2(a1,x16791,x16792)+P2(a1,f10(a1,x16791,x16791),f10(a1,f10(a1,f3(a1),x16792),x16792))
% 1.20/1.56 [1681]~P2(a1,x16811,x16812)+P3(a1,f10(a1,x16811,x16811),f10(a1,f10(a1,f3(a1),x16812),x16812))
% 1.20/1.56 [1683]~P3(a1,x16831,x16832)+P2(a1,f10(a1,f10(a1,f3(a1),x16831),x16831),f10(a1,x16832,x16832))
% 1.20/1.56 [1685]~P3(a1,x16851,x16852)+P3(a1,f10(a1,f10(a1,f3(a1),x16851),x16851),f10(a1,x16852,x16852))
% 1.20/1.56 [1740]~P2(a1,x17401,x17402)+P2(a1,f10(a1,f10(a1,f3(a1),x17401),x17401),f10(a1,f10(a1,f3(a1),x17402),x17402))
% 1.20/1.56 [1742]~P3(a1,x17421,x17422)+P3(a1,f10(a1,f10(a1,f3(a1),x17421),x17421),f10(a1,f10(a1,f3(a1),x17422),x17422))
% 1.20/1.56 [1744]P2(a1,x17441,x17442)+~P2(a1,f10(a1,x17441,x17441),f10(a1,f10(a1,f3(a1),x17442),x17442))
% 1.20/1.56 [1746]P2(a1,x17461,x17462)+~P3(a1,f10(a1,x17461,x17461),f10(a1,f10(a1,f3(a1),x17462),x17462))
% 1.20/1.56 [1748]P3(a1,x17481,x17482)+~P2(a1,f10(a1,f10(a1,f3(a1),x17481),x17481),f10(a1,x17482,x17482))
% 1.20/1.56 [1750]P3(a1,x17501,x17502)+~P3(a1,f10(a1,f10(a1,f3(a1),x17501),x17501),f10(a1,x17502,x17502))
% 1.20/1.56 [1757]~P37(x17571)+E(f8(x17571,f3(x17571),f16(x17571,x17572)),f16(x17571,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f9(a1,x17572))))
% 1.20/1.56 [1767]P2(a1,x17671,x17672)+~P2(a1,f10(a1,f10(a1,f3(a1),x17671),x17671),f10(a1,f10(a1,f3(a1),x17672),x17672))
% 1.20/1.56 [1769]P3(a1,x17691,x17692)+~P3(a1,f10(a1,f10(a1,f3(a1),x17691),x17691),f10(a1,f10(a1,f3(a1),x17692),x17692))
% 1.20/1.56 [1770]~P2(a1,f2(a1),f16(a1,x17702))+E(f5(a1,f16(a1,f10(a1,f10(a1,f3(a1),x17701),x17701)),f16(a1,f10(a1,x17702,x17702))),f5(a1,f16(a1,x17701),f16(a1,x17702)))
% 1.20/1.56 [1772]P2(a1,f2(a1),f16(a1,x17722))+E(f5(a1,f16(a1,f10(a1,f10(a1,f3(a1),x17721),x17721)),f16(a1,f10(a1,x17722,x17722))),f5(a1,f10(a1,f16(a1,x17721),f3(a1)),f16(a1,x17722)))
% 1.20/1.56 [819]~P47(x8191)+E(f63(f17(x8191,f2(f76(x8191))),x8192),f2(x8191))
% 1.20/1.56 [820]~P51(x8201)+E(f63(f17(x8201,f3(f76(x8201))),x8202),f3(x8201))
% 1.20/1.56 [1701]~P37(x17011)+E(f10(x17011,f10(x17011,f3(x17011),f16(x17011,x17012)),f16(x17011,x17012)),f16(x17011,f10(a1,f10(a1,f3(a1),x17012),x17012)))
% 1.20/1.56 [1752]~P37(x17521)+E(f10(x17521,f3(x17521),f16(x17521,x17522)),f16(x17521,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),x17522)))
% 1.20/1.56 [1753]~P37(x17531)+E(f10(x17531,f16(x17531,x17532),f3(x17531)),f16(x17531,f10(a1,x17532,f10(a1,f10(a1,f3(a1),a13),a13))))
% 1.20/1.56 [1782]~P37(x17821)+E(f8(x17821,f16(x17821,x17822),f3(x17821)),f16(x17821,f10(a1,x17822,f9(a1,f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.56 [1783]~P3(a75,f16(a75,a13),x17832)+E(f8(a75,x17831,f8(a75,x17832,f16(a75,f10(a1,f10(a1,f3(a1),a13),a13)))),f8(a75,f10(a75,x17831,f3(a75)),x17832))
% 1.20/1.56 [1796]~P3(a74,x17961,x17962)+P3(a74,x17961,f23(a74,f10(a74,x17961,x17962),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.56 [1797]~P3(a74,x17971,x17972)+P3(a74,f23(a74,f10(a74,x17971,x17972),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))),x17972)
% 1.20/1.56 [899]~P51(x8991)+E(f10(x8991,x8992,x8993),f10(x8991,x8993,x8992))
% 1.20/1.56 [941]P2(a75,x9411,x9412)+~E(x9412,f10(a75,x9411,x9413))
% 1.20/1.56 [1012]E(x10121,x10122)+~E(f10(a75,x10123,x10121),f10(a75,x10123,x10122))
% 1.20/1.56 [1013]E(x10131,x10132)+~E(f10(a75,x10131,x10133),f10(a75,x10132,x10133))
% 1.20/1.56 [1225]~P2(a75,x12251,x12253)+P2(a75,x12251,f10(a75,x12252,x12253))
% 1.20/1.56 [1227]~P2(a75,x12271,x12272)+P2(a75,x12271,f10(a75,x12272,x12273))
% 1.20/1.56 [1229]~P3(a75,x12291,x12293)+P3(a75,x12291,f10(a75,x12292,x12293))
% 1.20/1.56 [1231]~P3(a75,x12311,x12312)+P3(a75,x12311,f10(a75,x12312,x12313))
% 1.20/1.56 [1232]~P3(a75,x12321,x12323)+P3(a75,f8(a75,x12321,x12322),x12323)
% 1.20/1.56 [1267]~P3(a74,f2(a74),x12673)+P3(a74,f2(a74),f62(x12671,x12672,x12673))
% 1.20/1.56 [1318]P2(a75,x13181,x13182)+~P2(a75,f10(a75,x13183,x13181),x13182)
% 1.20/1.56 [1319]P2(a75,x13191,x13192)+~P2(a75,f10(a75,x13191,x13193),x13192)
% 1.20/1.56 [1320]P3(a75,x13201,x13202)+~P3(a75,f10(a75,x13201,x13203),x13202)
% 1.20/1.56 [1411]~P2(a74,x14112,x14113)+P2(a74,f10(a74,x14111,x14112),f10(a74,x14111,x14113))
% 1.20/1.56 [1412]~P2(a75,x14122,x14123)+P2(a75,f10(a75,x14121,x14122),f10(a75,x14121,x14123))
% 1.20/1.56 [1413]~P2(a75,x14131,x14133)+P2(a75,f10(a75,x14131,x14132),f10(a75,x14133,x14132))
% 1.20/1.56 [1414]~P2(a75,x14143,x14142)+P2(a75,f8(a75,x14141,x14142),f8(a75,x14141,x14143))
% 1.20/1.56 [1415]~P2(a75,x14151,x14153)+P2(a75,f8(a75,x14151,x14152),f8(a75,x14153,x14152))
% 1.20/1.56 [1416]~P2(a75,x14161,x14163)+P2(a75,f5(a75,x14161,x14162),f5(a75,x14163,x14162))
% 1.20/1.56 [1417]~P2(a1,x14172,x14173)+P2(a1,f10(a1,x14171,x14172),f10(a1,x14171,x14173))
% 1.20/1.56 [1420]~P3(a75,x14202,x14203)+P3(a75,f10(a75,x14201,x14202),f10(a75,x14201,x14203))
% 1.20/1.56 [1421]~P3(a75,x14211,x14213)+P3(a75,f10(a75,x14211,x14212),f10(a75,x14213,x14212))
% 1.20/1.56 [1422]~P3(a1,x14221,x14223)+P3(a1,f10(a1,x14221,x14222),f10(a1,x14223,x14222))
% 1.20/1.56 [1537]~P2(a75,f8(a75,x15371,x15373),x15372)+P2(a75,x15371,f10(a75,x15372,x15373))
% 1.20/1.56 [1538]~P3(a75,f10(a75,x15381,x15383),x15382)+P3(a75,x15381,f8(a75,x15382,x15383))
% 1.20/1.56 [1539]~P2(a75,x15391,f10(a75,x15393,x15392))+P2(a75,f8(a75,x15391,x15392),x15393)
% 1.20/1.56 [1540]~P3(a75,x15401,f8(a75,x15403,x15402))+P3(a75,f10(a75,x15401,x15402),x15403)
% 1.20/1.56 [1609]P2(a75,x16091,x16092)+~P2(a75,f10(a75,x16093,x16091),f10(a75,x16093,x16092))
% 1.20/1.56 [1612]P3(a75,x16121,x16122)+~P3(a75,f10(a75,x16123,x16121),f10(a75,x16123,x16122))
% 1.20/1.56 [957]~P10(x9571)+E(f10(x9571,x9572,f9(x9571,x9573)),f8(x9571,x9572,x9573))
% 1.20/1.56 [958]~P19(x9581)+E(f10(x9581,x9582,f9(x9581,x9583)),f8(x9581,x9582,x9583))
% 1.20/1.56 [959]~P48(x9591)+E(f10(x9591,x9592,f9(x9591,x9593)),f8(x9591,x9592,x9593))
% 1.20/1.56 [960]~P19(x9601)+E(f8(x9601,x9602,f9(x9601,x9603)),f10(x9601,x9602,x9603))
% 1.20/1.56 [1007]~P60(x10071)+E(f11(x10071,f9(x10071,x10072),x10073),f11(x10071,x10072,f9(x10071,x10073)))
% 1.20/1.56 [1008]~P11(x10081)+E(f23(x10081,f9(x10081,x10082),f9(x10081,x10083)),f23(x10081,x10082,x10083))
% 1.20/1.56 [1009]~P60(x10091)+E(f11(x10091,f9(x10091,x10092),f9(x10091,x10093)),f11(x10091,x10092,x10093))
% 1.20/1.56 [1016]~P19(x10161)+E(f10(x10161,f8(x10161,x10162,x10163),x10163),x10162)
% 1.20/1.56 [1017]~P19(x10171)+E(f8(x10171,f10(x10171,x10172,x10173),x10173),x10172)
% 1.20/1.56 [1060]~P10(x10601)+E(f9(x10601,f8(x10601,x10602,x10603)),f8(x10601,x10603,x10602))
% 1.20/1.56 [1102]~P19(x11021)+E(f10(x11021,f9(x11021,x11022),f10(x11021,x11022,x11023)),x11023)
% 1.20/1.56 [1136]~P11(x11361)+E(f23(x11361,x11362,f9(x11361,x11363)),f9(x11361,f23(x11361,x11362,x11363)))
% 1.20/1.56 [1137]~P60(x11371)+E(f11(x11371,x11372,f9(x11371,x11373)),f9(x11371,f11(x11371,x11372,x11373)))
% 1.20/1.56 [1138]~P53(x11381)+E(f23(x11381,f9(x11381,x11382),x11383),f9(x11381,f23(x11381,x11382,x11383)))
% 1.20/1.56 [1139]~P60(x11391)+E(f11(x11391,f9(x11391,x11392),x11393),f9(x11391,f11(x11391,x11392,x11393)))
% 1.20/1.56 [1141]~P43(x11411)+E(f11(x11411,x11412,f9(x11411,x11413)),f9(x11411,f11(x11411,x11412,x11413)))
% 1.20/1.56 [1142]~P44(x11421)+E(f23(x11421,f9(x11421,x11422),x11423),f9(x11421,f23(x11421,x11422,x11423)))
% 1.20/1.56 [1144]~P43(x11441)+E(f11(x11441,f9(x11441,x11442),x11443),f9(x11441,f11(x11441,x11442,x11443)))
% 1.20/1.56 [1193]~P37(x11931)+E(f8(x11931,f16(x11931,x11932),f16(x11931,x11933)),f16(x11931,f8(a1,x11932,x11933)))
% 1.20/1.56 [1195]~P37(x11951)+E(f10(x11951,f16(x11951,x11952),f16(x11951,x11953)),f16(x11951,f10(a1,x11952,x11953)))
% 1.20/1.56 [1196]~P37(x11961)+E(f11(x11961,f16(x11961,x11962),f16(x11961,x11963)),f16(x11961,f11(a1,x11962,x11963)))
% 1.20/1.56 [1197]~P14(x11971)+E(f23(x11971,f4(x11971,x11972),f4(x11971,x11973)),f4(x11971,f23(x11971,x11972,x11973)))
% 1.20/1.56 [1198]~P19(x11981)+E(f10(x11981,f9(x11981,x11982),f9(x11981,x11983)),f9(x11981,f10(x11981,x11983,x11982)))
% 1.20/1.56 [1199]~P10(x11991)+E(f10(x11991,f9(x11991,x11992),f9(x11991,x11993)),f9(x11991,f10(x11991,x11992,x11993)))
% 1.20/1.56 [1200]~P54(x12001)+E(f11(x12001,f12(x12001,x12002),f12(x12001,x12003)),f12(x12001,f11(x12001,x12002,x12003)))
% 1.20/1.56 [1201]~P45(x12011)+E(f11(x12011,f12(x12011,x12012),f12(x12011,x12013)),f12(x12011,f11(x12011,x12012,x12013)))
% 1.20/1.56 [1202]~P10(x12021)+E(f8(x12021,f9(x12021,x12022),f9(x12021,x12023)),f9(x12021,f8(x12021,x12022,x12023)))
% 1.20/1.56 [1264]~P5(x12641)+E(f22(x12641,f8(x12641,x12642,x12643)),f22(x12641,f8(x12641,x12643,x12642)))
% 1.20/1.56 [1265]~P6(x12651)+E(f4(x12651,f8(x12651,x12652,x12653)),f4(x12651,f8(x12651,x12653,x12652)))
% 1.20/1.56 [1332]P3(a75,x13321,x13322)+~E(x13322,f10(a75,f10(a75,x13321,x13323),f3(a75)))
% 1.20/1.56 [1533]~P2(a75,x15332,x15333)+E(f8(a75,f10(a75,x15331,x15332),x15333),f8(a75,x15331,f8(a75,x15333,x15332)))
% 1.20/1.56 [1534]~P2(a75,x15343,x15342)+E(f8(a75,f10(a75,x15341,x15342),x15343),f10(a75,x15341,f8(a75,x15342,x15343)))
% 1.20/1.56 [1536]~P2(a75,x15363,x15361)+E(f8(a75,f10(a75,x15361,x15362),x15363),f10(a75,f8(a75,x15361,x15363),x15362))
% 1.20/1.56 [1579]~P2(a75,x15793,x15792)+P2(a75,x15791,f8(a75,f10(a75,x15792,x15791),x15793))
% 1.20/1.56 [1639]~P5(x16391)+P2(a74,f22(x16391,f10(x16391,x16392,x16393)),f10(a74,f22(x16391,x16392),f22(x16391,x16393)))
% 1.20/1.56 [1640]~P5(x16401)+P2(a74,f22(x16401,f8(x16401,x16402,x16403)),f10(a74,f22(x16401,x16402),f22(x16401,x16403)))
% 1.20/1.56 [1641]~P43(x16411)+P2(a74,f22(x16411,f11(x16411,x16412,x16413)),f11(a74,f22(x16411,x16412),f22(x16411,x16413)))
% 1.20/1.56 [1642]~P5(x16421)+P2(a74,f8(a74,f22(x16421,x16422),f22(x16421,x16423)),f22(x16421,f10(x16421,x16422,x16423)))
% 1.20/1.56 [1643]~P5(x16431)+P2(a74,f8(a74,f22(x16431,x16432),f22(x16431,x16433)),f22(x16431,f8(x16431,x16432,x16433)))
% 1.20/1.56 [1645]~P6(x16451)+P2(x16451,f4(x16451,f10(x16451,x16452,x16453)),f10(x16451,f4(x16451,x16452),f4(x16451,x16453)))
% 1.20/1.56 [1646]~P6(x16461)+P2(x16461,f4(x16461,f8(x16461,x16462,x16463)),f10(x16461,f4(x16461,x16462),f4(x16461,x16463)))
% 1.20/1.56 [1647]~P6(x16471)+P2(x16471,f8(x16471,f4(x16471,x16472),f4(x16471,x16473)),f4(x16471,f8(x16471,x16473,x16472)))
% 1.20/1.56 [1648]~P6(x16481)+P2(x16481,f8(x16481,f4(x16481,x16482),f4(x16481,x16483)),f4(x16481,f8(x16481,x16482,x16483)))
% 1.20/1.56 [1179]~P19(x11791)+E(f10(x11791,x11792,f10(x11791,f9(x11791,x11792),x11793)),x11793)
% 1.20/1.56 [1243]~P13(x12431)+E(f5(f76(x12431),x12432,f9(f76(x12431),x12433)),f9(f76(x12431),f5(f76(x12431),x12432,x12433)))
% 1.20/1.56 [1244]~P13(x12441)+E(f5(f76(x12441),f9(f76(x12441),x12442),x12443),f9(f76(x12441),f5(f76(x12441),x12442,x12443)))
% 1.20/1.56 [1292]~P37(x12921)+E(f8(x12921,f16(x12921,x12922),f16(x12921,x12923)),f16(x12921,f10(a1,x12922,f9(a1,x12923))))
% 1.20/1.56 [1399]~P6(x13991)+E(f4(x13991,f10(x13991,f4(x13991,x13992),f4(x13991,x13993))),f10(x13991,f4(x13991,x13992),f4(x13991,x13993)))
% 1.20/1.56 [1407]~P51(x14071)+E(f10(x14071,x14072,f11(x14071,x14073,x14072)),f11(x14071,f10(x14071,x14073,f3(x14071)),x14072))
% 1.20/1.56 [1408]~P51(x14081)+E(f10(x14081,f11(x14081,x14082,x14083),x14083),f11(x14081,f10(x14081,x14082,f3(x14081)),x14083))
% 1.20/1.56 [1731]~P2(a75,x17312,x17313)+E(f8(a75,f10(a75,x17311,x17312),f10(a75,x17313,f3(a75))),f8(a75,x17311,f10(a75,f8(a75,x17313,x17312),f3(a75))))
% 1.20/1.56 [1732]~P2(a75,x17322,x17321)+E(f8(a75,f10(a75,f8(a75,x17321,x17322),f3(a75)),x17323),f8(a75,f10(a75,x17321,f3(a75)),f10(a75,x17322,x17323)))
% 1.20/1.56 [1737]~P5(x17371)+P2(a74,f4(a74,f8(a74,f22(x17371,x17372),f22(x17371,x17373))),f22(x17371,f8(x17371,x17372,x17373)))
% 1.20/1.56 [1738]~P6(x17381)+P2(x17381,f4(x17381,f8(x17381,f4(x17381,x17382),f4(x17381,x17383))),f4(x17381,f8(x17381,x17382,x17383)))
% 1.20/1.56 [1170]~P46(x11701)+E(f63(f17(x11701,f9(f76(x11701),x11702)),x11703),f9(x11701,f63(f17(x11701,x11702),x11703)))
% 1.20/1.56 [1365]~P51(x13651)+E(f10(x13651,x13652,f10(x13651,x13653,x13654)),f10(x13651,x13653,f10(x13651,x13652,x13654)))
% 1.20/1.56 [1367]~P9(x13671)+E(f10(x13671,f10(x13671,x13672,x13673),x13674),f10(x13671,x13672,f10(x13671,x13673,x13674)))
% 1.20/1.56 [1368]~P51(x13681)+E(f10(x13681,f10(x13681,x13682,x13683),x13684),f10(x13681,x13682,f10(x13681,x13683,x13684)))
% 1.20/1.56 [1369]~P51(x13691)+E(f10(x13691,f10(x13691,x13692,x13693),x13694),f10(x13691,f10(x13691,x13692,x13694),x13693))
% 1.20/1.56 [1557]~P51(x15571)+E(f10(x15571,f11(x15571,x15572,x15573),f11(x15571,x15572,x15574)),f11(x15571,x15572,f10(x15571,x15573,x15574)))
% 1.20/1.56 [1559]~P43(x15591)+E(f10(x15591,f11(x15591,x15592,x15593),f11(x15591,x15592,x15594)),f11(x15591,x15592,f10(x15591,x15593,x15594)))
% 1.20/1.56 [1561]~P43(x15611)+E(f8(x15611,f11(x15611,x15612,x15613),f11(x15611,x15612,x15614)),f11(x15611,x15612,f8(x15611,x15613,x15614)))
% 1.20/1.56 [1562]~P44(x15621)+E(f10(x15621,f23(x15621,x15622,x15623),f23(x15621,x15624,x15623)),f23(x15621,f10(x15621,x15622,x15624),x15623))
% 1.20/1.56 [1563]~P53(x15631)+E(f10(x15631,f23(x15631,x15632,x15633),f23(x15631,x15634,x15633)),f23(x15631,f10(x15631,x15632,x15634),x15633))
% 1.20/1.56 [1564]~P44(x15641)+E(f8(x15641,f23(x15641,x15642,x15643),f23(x15641,x15644,x15643)),f23(x15641,f8(x15641,x15642,x15644),x15643))
% 1.20/1.56 [1565]~P53(x15651)+E(f8(x15651,f23(x15651,x15652,x15653),f23(x15651,x15654,x15653)),f23(x15651,f8(x15651,x15652,x15654),x15653))
% 1.20/1.56 [1568]~P43(x15681)+E(f10(x15681,f11(x15681,x15682,x15683),f11(x15681,x15684,x15683)),f11(x15681,f10(x15681,x15682,x15684),x15683))
% 1.20/1.56 [1569]~P49(x15691)+E(f10(x15691,f11(x15691,x15692,x15693),f11(x15691,x15694,x15693)),f11(x15691,f10(x15691,x15692,x15694),x15693))
% 1.20/1.56 [1571]~P43(x15711)+E(f8(x15711,f11(x15711,x15712,x15713),f11(x15711,x15714,x15713)),f11(x15711,f8(x15711,x15712,x15714),x15713))
% 1.20/1.56 [1572]~P51(x15721)+E(f10(x15721,f11(x15721,x15722,x15723),f11(x15721,x15724,x15723)),f11(x15721,f10(x15721,x15722,x15724),x15723))
% 1.20/1.56 [942]~P33(x9422)+E(f63(f9(f79(x9421,x9422),x9423),x9424),f9(x9422,f63(x9423,x9424)))
% 1.20/1.56 [1661]~P37(x16611)+E(f10(x16611,f16(x16611,x16612),f10(x16611,f16(x16611,x16613),x16614)),f10(x16611,f16(x16611,f10(a1,x16612,x16613)),x16614))
% 1.20/1.56 [1662]~P37(x16621)+E(f10(x16621,f16(x16621,x16622),f8(x16621,f16(x16621,x16623),x16624)),f8(x16621,f16(x16621,f10(a1,x16622,x16623)),x16624))
% 1.20/1.56 [1663]~P37(x16631)+E(f11(x16631,f16(x16631,x16632),f11(x16631,f16(x16631,x16633),x16634)),f11(x16631,f16(x16631,f11(a1,x16632,x16633)),x16634))
% 1.20/1.56 [1773]~P2(a74,f4(a74,f8(a74,x17733,x17731)),x17734)+P2(a74,f4(a74,f8(a74,x17731,x17732)),f10(a74,f4(a74,f8(a74,x17733,x17732)),x17734))
% 1.20/1.56 [1637]~P47(x16371)+E(f10(x16371,f63(f17(x16371,x16372),x16373),f63(f17(x16371,x16374),x16373)),f63(f17(x16371,f10(f76(x16371),x16372,x16374)),x16373))
% 1.20/1.56 [1638]~P46(x16381)+E(f8(x16381,f63(f17(x16381,x16382),x16383),f63(f17(x16381,x16384),x16383)),f63(f17(x16381,f8(f76(x16381),x16382,x16384)),x16383))
% 1.20/1.56 [1703]~P37(x17031)+E(f10(x17031,f16(x17031,x17032),f8(x17031,x17033,f16(x17031,x17034))),f10(x17031,f16(x17031,f10(a1,x17032,f9(a1,x17034))),x17033))
% 1.20/1.56 [1666]~P51(x16661)+E(f10(x16661,f10(x16661,x16662,x16663),f10(x16661,x16664,x16665)),f10(x16661,f10(x16661,x16662,x16664),f10(x16661,x16663,x16665)))
% 1.20/1.56 [1667]~P10(x16671)+E(f8(x16671,f10(x16671,x16672,x16673),f10(x16671,x16674,x16675)),f10(x16671,f8(x16671,x16672,x16674),f8(x16671,x16673,x16675)))
% 1.20/1.56 [1298]~P24(x12982)+E(f63(f8(f79(x12981,x12982),x12983,x12984),x12985),f8(x12982,f63(x12983,x12985),f63(x12984,x12985)))
% 1.20/1.56 [1756]~P68(x17561)+E(f10(x17561,f11(x17561,x17562,x17563),f10(x17561,f11(x17561,x17564,x17563),x17565)),f10(x17561,f11(x17561,f10(x17561,x17562,x17564),x17563),x17565))
% 1.20/1.56 [1763]~P60(x17631)+E(f10(x17631,f11(x17631,x17632,f8(x17631,x17633,x17634)),f11(x17631,f8(x17631,x17632,x17635),x17634)),f8(x17631,f11(x17631,x17632,x17633),f11(x17631,x17635,x17634)))
% 1.20/1.56 [1786]~P5(x17861)+P2(a74,f22(x17861,f8(x17861,f10(x17861,x17862,x17863),f10(x17861,x17864,x17865))),f10(a74,f22(x17861,f8(x17861,x17862,x17864)),f22(x17861,f8(x17861,x17863,x17865))))
% 1.20/1.56 [1787]~P6(x17871)+P2(x17871,f4(x17871,f8(x17871,f10(x17871,x17872,x17873),f10(x17871,x17874,x17875))),f10(x17871,f4(x17871,f8(x17871,x17872,x17874)),f4(x17871,f8(x17871,x17873,x17875))))
% 1.20/1.56 [1788]~P43(x17881)+E(f10(x17881,f10(x17881,f11(x17881,f8(x17881,x17882,x17883),f8(x17881,x17884,x17885)),f11(x17881,f8(x17881,x17882,x17883),x17885)),f11(x17881,x17883,f8(x17881,x17884,x17885))),f8(x17881,f11(x17881,x17882,x17884),f11(x17881,x17883,x17885)))
% 1.20/1.56 [1805]~P3(a74,f23(a74,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85)))),f20(a75,f10(a75,f10(a75,a78,a80),f3(a75))))+~P3(a74,f2(a74),f23(a74,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85)))))+P3(a74,f21(a74,f20(a75,f10(a75,f10(a75,a78,a80),f3(a75)))),f21(a74,f23(a74,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85))))))
% 1.20/1.56 [877]E(x8771,f2(a1))+~P3(a1,f2(a1),x8771)+E(f12(a1,x8771),f3(a1))
% 1.20/1.56 [822]E(x8221,f2(a74))+P3(a74,f2(a74),x8221)+E(f12(a74,x8221),f9(a74,f3(a74)))
% 1.20/1.56 [823]E(x8231,f2(a1))+P3(a1,f2(a1),x8231)+E(f12(a1,x8231),f9(a1,f3(a1)))
% 1.20/1.56 [1730]E(x17301,f2(a75))+E(x17301,f10(a75,f2(a75),f3(a75)))+~P3(a75,x17301,f10(a75,f10(a75,f2(a75),f3(a75)),f3(a75)))
% 1.20/1.56 [1790]E(x17901,f2(a75))+E(x17901,f10(a75,f2(a75),f3(a75)))+~P3(a75,x17901,f16(a75,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))))
% 1.20/1.56 [1792]~P14(x17921)+~P37(x17921)+P3(x17921,f2(x17921),f23(x17921,f3(x17921),f16(x17921,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.56 [1803]~P3(a74,f2(a74),f22(a14,f8(a14,x18031,a86)))+~P3(a74,f22(a14,f8(a14,x18031,a86)),a24)+P3(a74,f22(a14,f8(a14,f63(f17(a14,a82),x18031),f63(f17(a14,a82),a86))),f23(a74,f4(a74,f8(a74,f22(a14,f63(f17(a14,a82),a86)),f9(a74,a85))),f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.56 [884]E(x8841,x8842)+P3(a75,x8842,x8841)+P3(a75,x8841,x8842)
% 1.20/1.56 [885]E(x8851,x8852)+P3(a1,x8852,x8851)+P3(a1,x8851,x8852)
% 1.20/1.56 [947]E(x9471,x9472)+P3(a74,x9471,x9472)+~P2(a74,x9471,x9472)
% 1.20/1.56 [950]E(x9501,x9502)+P3(a75,x9501,x9502)+~P2(a75,x9501,x9502)
% 1.20/1.56 [951]E(x9511,x9512)+P3(a1,x9511,x9512)+~P2(a1,x9511,x9512)
% 1.20/1.56 [1018]E(x10181,x10182)+~P2(a74,x10182,x10181)+~P2(a74,x10181,x10182)
% 1.20/1.56 [1019]E(x10191,x10192)+~P2(a75,x10192,x10191)+~P2(a75,x10191,x10192)
% 1.20/1.56 [1020]E(x10201,x10202)+~P2(a1,x10202,x10201)+~P2(a1,x10201,x10202)
% 1.20/1.56 [659]~P22(x6591)+~E(x6592,f2(x6591))+E(f9(x6591,x6592),x6592)
% 1.20/1.56 [669]~P5(x6691)+~E(x6692,f2(x6691))+E(f22(x6691,x6692),f2(a74))
% 1.20/1.56 [670]~P19(x6701)+~E(f2(x6701),x6702)+E(f9(x6701,x6702),f2(x6701))
% 1.20/1.56 [671]~P6(x6711)+~E(x6712,f2(x6711))+E(f4(x6711,x6712),f2(x6711))
% 1.20/1.56 [672]~P19(x6721)+~E(x6722,f2(x6721))+E(f9(x6721,x6722),f2(x6721))
% 1.20/1.56 [673]~P5(x6731)+~E(x6732,f2(x6731))+E(f12(x6731,x6732),f2(x6731))
% 1.20/1.56 [674]~P54(x6741)+~E(x6742,f2(x6741))+E(f12(x6741,x6742),f2(x6741))
% 1.20/1.56 [675]~P34(x6751)+~E(x6752,f2(x6751))+E(f12(x6751,x6752),f2(x6751))
% 1.20/1.56 [676]~P52(x6761)+~E(x6762,f2(x6761))+E(f21(x6761,x6762),f2(x6761))
% 1.20/1.56 [677]~P11(x6771)+~E(x6772,f3(x6771))+E(f21(x6771,x6772),f3(x6771))
% 1.20/1.56 [679]~P22(x6792)+~E(f9(x6792,x6791),x6791)+E(x6791,f2(x6792))
% 1.20/1.56 [686]~P5(x6862)+E(x6861,f2(x6862))+~E(f22(x6862,x6861),f2(a74))
% 1.20/1.56 [687]~P6(x6872)+~E(f4(x6872,x6871),f2(x6872))+E(x6871,f2(x6872))
% 1.20/1.56 [688]~P19(x6882)+~E(f9(x6882,x6881),f2(x6882))+E(x6881,f2(x6882))
% 1.20/1.56 [689]~P5(x6892)+~E(f12(x6892,x6891),f2(x6892))+E(x6891,f2(x6892))
% 1.20/1.56 [690]~P54(x6902)+~E(f12(x6902,x6901),f2(x6902))+E(x6901,f2(x6902))
% 1.20/1.56 [691]~P52(x6912)+~E(f21(x6912,x6911),f2(x6912))+E(x6911,f2(x6912))
% 1.20/1.56 [693]~P53(x6932)+~E(f21(x6932,x6931),f2(x6932))+E(x6931,f2(x6932))
% 1.20/1.56 [694]~P11(x6942)+~E(f21(x6942,x6941),f3(x6942))+E(x6941,f3(x6942))
% 1.20/1.56 [695]~P19(x6951)+~E(f9(x6951,x6952),f2(x6951))+E(f2(x6951),x6952)
% 1.20/1.56 [738]~E(x7382,f2(a75))+~E(x7381,f2(a75))+E(f10(a75,x7381,x7382),f2(a75))
% 1.20/1.56 [761]~P53(x7612)+E(f23(x7612,x7611,x7611),f3(x7612))+E(x7611,f2(x7612))
% 1.20/1.56 [762]~P12(x7622)+E(f5(x7622,x7621,x7621),f3(x7622))+E(x7621,f2(x7622))
% 1.20/1.56 [763]~P52(x7632)+E(f23(x7632,x7631,x7631),f3(x7632))+E(x7631,f2(x7632))
% 1.20/1.56 [781]~P22(x7811)+~E(x7812,f2(x7811))+E(f10(x7811,x7812,x7812),f2(x7811))
% 1.20/1.56 [782]~P52(x7821)+~E(x7822,f2(x7821))+E(f23(x7821,x7822,x7822),f2(x7821))
% 1.20/1.56 [796]~P16(x7961)+P3(x7961,x7962,f2(x7961))+E(f4(x7961,x7962),x7962)
% 1.20/1.56 [842]~P5(x8422)+E(x8421,f2(x8422))+P3(a74,f2(a74),f22(x8422,x8421))
% 1.20/1.56 [848]~P54(x8481)+P3(x8481,f2(x8481),x8482)+~E(f12(x8481,x8482),f3(x8481))
% 1.20/1.56 [859]~P5(x8591)+~E(x8592,f2(x8591))+P2(a74,f22(x8591,x8592),f2(a74))
% 1.20/1.56 [861]~P6(x8612)+P3(x8612,f2(x8612),f4(x8612,x8611))+E(x8611,f2(x8612))
% 1.20/1.56 [866]~P6(x8661)+P2(x8661,f4(x8661,x8662),f2(x8661))+~E(x8662,f2(x8661))
% 1.20/1.56 [869]~P22(x8692)+~E(f10(x8692,x8691,x8691),f2(x8692))+E(x8691,f2(x8692))
% 1.20/1.56 [907]~P6(x9071)+~P2(x9071,f2(x9071),x9072)+E(f4(x9071,x9072),x9072)
% 1.20/1.56 [908]~P6(x9081)+~P3(x9081,f2(x9081),x9082)+E(f4(x9081,x9082),x9082)
% 1.20/1.56 [918]~P54(x9181)+~P3(x9181,f2(x9181),x9182)+E(f12(x9181,x9182),f3(x9181))
% 1.20/1.56 [922]~P40(x9221)+P4(x9221,x9222)+P2(a75,f57(x9222,x9221),f61(x9222,x9221))
% 1.20/1.56 [926]~P6(x9261)+~P2(x9261,x9262,f2(x9261))+E(f4(x9261,x9262),f9(x9261,x9262))
% 1.20/1.56 [927]~P6(x9271)+~P3(x9271,x9272,f2(x9271))+E(f4(x9271,x9272),f9(x9271,x9272))
% 1.20/1.56 [928]~P16(x9281)+~P3(x9281,x9282,f2(x9281))+E(f4(x9281,x9282),f9(x9281,x9282))
% 1.20/1.56 [956]~P5(x9562)+E(x9561,f2(x9562))+~P2(a74,f22(x9562,x9561),f2(a74))
% 1.20/1.56 [962]~P5(x9622)+~E(x9621,f2(x9622))+~P3(a74,f2(a74),f22(x9622,x9621))
% 1.20/1.56 [971]~P6(x9712)+~P2(x9712,f4(x9712,x9711),f2(x9712))+E(x9711,f2(x9712))
% 1.20/1.56 [986]~P6(x9862)+~P3(x9862,f2(x9862),f4(x9862,x9861))+~E(x9861,f2(x9862))
% 1.20/1.56 [1032]E(x10321,x10322)+~E(f8(a75,x10322,x10321),f2(a75))+~E(f8(a75,x10321,x10322),f2(a75))
% 1.20/1.56 [1073]~P22(x10731)+~P2(x10731,x10732,f2(x10731))+P2(x10731,x10732,f9(x10731,x10732))
% 1.20/1.56 [1074]~P54(x10741)+~P3(x10741,x10742,f2(x10741))+P3(x10741,x10742,f9(x10741,x10742))
% 1.20/1.56 [1075]~P22(x10751)+~P2(x10751,f2(x10751),x10752)+P2(x10751,f9(x10751,x10752),x10752)
% 1.20/1.56 [1076]~P22(x10761)+~P3(x10761,f2(x10761),x10762)+P3(x10761,f9(x10761,x10762),x10762)
% 1.20/1.56 [1082]~P18(x10821)+~P2(x10821,x10822,f2(x10821))+P2(x10821,f2(x10821),f9(x10821,x10822))
% 1.20/1.56 [1083]~P18(x10831)+~P3(x10831,x10832,f2(x10831))+P3(x10831,f2(x10831),f9(x10831,x10832))
% 1.20/1.56 [1084]~P14(x10841)+~P2(x10841,f2(x10841),x10842)+P2(x10841,f2(x10841),f21(x10841,x10842))
% 1.20/1.56 [1085]~P54(x10851)+~P3(x10851,f2(x10851),x10852)+P3(x10851,f2(x10851),f12(x10851,x10852))
% 1.20/1.56 [1086]~P14(x10861)+~P3(x10861,f2(x10861),x10862)+P3(x10861,f2(x10861),f21(x10861,x10862))
% 1.20/1.56 [1087]~P15(x10871)+~P3(x10871,f2(x10871),x10872)+P3(x10871,f2(x10871),f21(x10871,x10872))
% 1.20/1.56 [1088]~P14(x10881)+~P2(x10881,x10882,f2(x10881))+P2(x10881,f21(x10881,x10882),f2(x10881))
% 1.20/1.56 [1089]~P54(x10891)+~P3(x10891,x10892,f2(x10891))+P3(x10891,f12(x10891,x10892),f2(x10891))
% 1.20/1.56 [1090]~P14(x10901)+~P3(x10901,x10902,f2(x10901))+P3(x10901,f21(x10901,x10902),f2(x10901))
% 1.20/1.56 [1091]~P15(x10911)+~P3(x10911,x10912,f2(x10911))+P3(x10911,f21(x10911,x10912),f2(x10911))
% 1.20/1.56 [1092]~P18(x10921)+~P2(x10921,f2(x10921),x10922)+P2(x10921,f9(x10921,x10922),f2(x10921))
% 1.20/1.56 [1093]~P18(x10931)+~P3(x10931,f2(x10931),x10932)+P3(x10931,f9(x10931,x10932),f2(x10931))
% 1.20/1.56 [1098]~P22(x10981)+~P2(x10981,x10982,f9(x10981,x10982))+P2(x10981,x10982,f2(x10981))
% 1.20/1.56 [1099]~P54(x10991)+~P3(x10991,x10992,f9(x10991,x10992))+P3(x10991,x10992,f2(x10991))
% 1.20/1.56 [1100]~P22(x11001)+~P2(x11001,f9(x11001,x11002),x11002)+P2(x11001,f2(x11001),x11002)
% 1.20/1.56 [1101]~P22(x11011)+~P3(x11011,f9(x11011,x11012),x11012)+P3(x11011,f2(x11011),x11012)
% 1.20/1.56 [1123]~P18(x11231)+~P2(x11231,f2(x11231),f9(x11231,x11232))+P2(x11231,x11232,f2(x11231))
% 1.20/1.56 [1124]~P18(x11241)+~P3(x11241,f2(x11241),f9(x11241,x11242))+P3(x11241,x11242,f2(x11241))
% 1.20/1.56 [1125]~P14(x11251)+~P2(x11251,f21(x11251,x11252),f2(x11251))+P2(x11251,x11252,f2(x11251))
% 1.20/1.56 [1126]~P54(x11261)+~P3(x11261,f12(x11261,x11262),f2(x11261))+P3(x11261,x11262,f2(x11261))
% 1.20/1.56 [1127]~P14(x11271)+~P3(x11271,f21(x11271,x11272),f2(x11271))+P3(x11271,x11272,f2(x11271))
% 1.20/1.56 [1128]~P14(x11281)+~P2(x11281,f2(x11281),f21(x11281,x11282))+P2(x11281,f2(x11281),x11282)
% 1.20/1.56 [1129]~P54(x11291)+~P3(x11291,f2(x11291),f12(x11291,x11292))+P3(x11291,f2(x11291),x11292)
% 1.20/1.56 [1130]~P14(x11301)+~P3(x11301,f2(x11301),f21(x11301,x11302))+P3(x11301,f2(x11301),x11302)
% 1.20/1.56 [1131]~P18(x11311)+~P2(x11311,f9(x11311,x11312),f2(x11311))+P2(x11311,f2(x11311),x11312)
% 1.20/1.56 [1132]~P18(x11321)+~P3(x11321,f9(x11321,x11322),f2(x11321))+P3(x11321,f2(x11321),x11322)
% 1.20/1.56 [1184]~P3(a1,x11842,x11841)+~P2(a1,x11841,f2(a1))+E(f5(a1,x11841,x11842),f2(a1))
% 1.20/1.56 [1187]~P3(a1,x11871,x11872)+~P2(a1,f2(a1),x11871)+E(f5(a1,x11871,x11872),f2(a1))
% 1.20/1.56 [1272]~P2(a75,f15(x12721),x12722)+P2(a74,x12721,f20(a75,x12722))+~P2(a74,f2(a74),x12721)
% 1.20/1.56 [1273]~P2(a75,x12731,f19(x12732))+P2(a74,f20(a75,x12731),x12732)+~P2(a74,f2(a74),x12732)
% 1.20/1.56 [1274]P2(a1,x12741,x12742)+P2(a1,x12741,a13)+~P2(a75,f16(a75,x12741),f16(a75,x12742))
% 1.20/1.56 [1278]~P3(a1,x12781,x12782)+~P3(a1,a13,x12782)+P3(a75,f16(a75,x12781),f16(a75,x12782))
% 1.20/1.56 [1283]P3(a75,f19(x12831),x12832)+~P3(a74,x12831,f20(a75,x12832))+~P2(a74,f2(a74),x12831)
% 1.20/1.56 [1285]~P22(x12851)+~P2(x12851,f2(x12851),x12852)+P2(x12851,f2(x12851),f10(x12851,x12852,x12852))
% 1.20/1.56 [1286]~P22(x12861)+~P3(x12861,f2(x12861),x12862)+P3(x12861,f2(x12861),f10(x12861,x12862,x12862))
% 1.20/1.56 [1287]~P22(x12871)+~P2(x12871,x12872,f2(x12871))+P2(x12871,f10(x12871,x12872,x12872),f2(x12871))
% 1.20/1.56 [1288]~P22(x12881)+~P3(x12881,x12882,f2(x12881))+P3(x12881,f10(x12881,x12882,x12882),f2(x12881))
% 1.20/1.56 [1289]~P54(x12891)+~P3(x12891,x12892,f2(x12891))+P3(x12891,f10(x12891,x12892,x12892),f2(x12891))
% 1.20/1.56 [1297]~P2(a74,x12971,x12972)+~P2(a74,f9(a74,x12972),x12971)+P2(a74,f4(a74,x12971),x12972)
% 1.20/1.56 [1299]~P3(a1,x12992,x12991)+P3(a1,a13,x12991)+~P3(a75,f16(a75,x12992),f16(a75,x12991))
% 1.20/1.56 [1371]~P22(x13711)+~P2(x13711,f10(x13711,x13712,x13712),f2(x13711))+P2(x13711,x13712,f2(x13711))
% 1.20/1.56 [1372]~P22(x13721)+~P3(x13721,f10(x13721,x13722,x13722),f2(x13721))+P3(x13721,x13722,f2(x13721))
% 1.20/1.56 [1373]~P54(x13731)+~P3(x13731,f10(x13731,x13732,x13732),f2(x13731))+P3(x13731,x13732,f2(x13731))
% 1.20/1.56 [1374]~P22(x13741)+~P2(x13741,f2(x13741),f10(x13741,x13742,x13742))+P2(x13741,f2(x13741),x13742)
% 1.20/1.56 [1375]~P22(x13751)+~P3(x13751,f2(x13751),f10(x13751,x13752,x13752))+P3(x13751,f2(x13751),x13752)
% 1.20/1.56 [1379]~P2(a1,x13792,x13791)+~P3(a1,f2(a1),x13792)+P3(a1,f2(a1),f5(a1,x13791,x13792))
% 1.20/1.56 [1380]P3(a75,f8(a75,x13801,x13802),x13801)+~P3(a75,f2(a75),x13801)+~P3(a75,f2(a75),x13802)
% 1.20/1.56 [1381]P3(a75,f5(a75,x13811,x13812),x13811)+~P3(a75,f2(a75),x13811)+~P3(a75,f3(a75),x13812)
% 1.20/1.56 [1382]P3(a1,f5(a1,x13821,x13822),x13821)+~P3(a1,f2(a1),x13821)+~P3(a1,f3(a1),x13822)
% 1.20/1.56 [1387]~P2(a74,x13871,f2(a74))+~P2(a74,x13872,f2(a74))+P2(a74,f2(a74),f23(a74,x13871,x13872))
% 1.20/1.56 [1388]~P2(a1,x13881,f2(a1))+~P3(a1,x13882,f2(a1))+P2(a1,f2(a1),f5(a1,x13881,x13882))
% 1.20/1.56 [1389]~P2(a74,x13892,f2(a74))+~P2(a74,f2(a74),x13892)+P2(a74,f2(a74),f23(a74,x13891,x13892))
% 1.20/1.56 [1390]~P2(a74,x13901,f2(a74))+~P2(a74,f2(a74),x13901)+P2(a74,f2(a74),f23(a74,x13901,x13902))
% 1.20/1.56 [1391]~P2(a74,f2(a74),x13912)+~P2(a74,f2(a74),x13911)+P2(a74,f2(a74),f23(a74,x13911,x13912))
% 1.20/1.56 [1392]~P2(a1,f2(a1),x13922)+~P2(a1,f2(a1),x13921)+P2(a1,f2(a1),f5(a1,x13921,x13922))
% 1.20/1.56 [1393]~P2(a1,f2(a1),x13931)+~P3(a1,f2(a1),x13932)+P2(a1,f2(a1),f5(a1,x13931,x13932))
% 1.20/1.56 [1394]~P2(a1,x13941,f2(a1))+~P3(a1,f2(a1),x13942)+P2(a1,f5(a1,x13941,x13942),f2(a1))
% 1.20/1.56 [1395]~P3(a1,x13952,f2(a1))+~P2(a1,f2(a1),x13951)+P2(a1,f5(a1,x13951,x13952),f2(a1))
% 1.20/1.56 [1396]~P3(a1,x13962,f2(a1))+~P3(a1,f2(a1),x13961)+P3(a1,f5(a1,x13961,x13962),f2(a1))
% 1.20/1.56 [1398]~P3(a1,x13981,f2(a1))+~P3(a1,f2(a1),x13982)+P3(a1,f5(a1,x13981,x13982),f2(a1))
% 1.20/1.56 [1447]P2(a74,x14471,f2(a74))+P2(a74,f2(a74),x14472)+~P2(a74,f2(a74),f23(a74,x14472,x14471))
% 1.20/1.56 [1448]P2(a74,x14481,f2(a74))+P2(a74,f2(a74),x14482)+~P2(a74,f2(a74),f23(a74,x14481,x14482))
% 1.20/1.56 [1449]P3(a75,f2(a75),x14491)+P3(a75,f2(a75),x14492)+~P3(a75,f2(a75),f10(a75,x14492,x14491))
% 1.20/1.56 [1523]P2(a1,x15231,x15232)+~P3(a1,f2(a1),x15231)+~P3(a1,f2(a1),f5(a1,x15232,x15231))
% 1.20/1.56 [1524]P2(a1,x15241,x15242)+~P2(a1,f2(a1),x15242)+~P3(a1,f2(a1),f5(a1,x15242,x15241))
% 1.20/1.56 [1527]P2(a1,x15271,f2(a1))+~P3(a1,x15272,f2(a1))+~P2(a1,f2(a1),f5(a1,x15271,x15272))
% 1.20/1.56 [1528]P3(a1,x15281,f2(a1))+~P3(a1,f2(a1),x15282)+~P3(a1,f5(a1,x15281,x15282),f2(a1))
% 1.20/1.56 [1529]P3(a1,f2(a1),x15291)+~P3(a1,x15292,f2(a1))+~P3(a1,f5(a1,x15291,x15292),f2(a1))
% 1.20/1.56 [1530]P2(a1,f2(a1),x15301)+~P3(a1,f2(a1),x15302)+~P2(a1,f2(a1),f5(a1,x15301,x15302))
% 1.20/1.56 [1531]P3(a1,f2(a1),x15311)+~P2(a1,f2(a1),x15312)+~P3(a1,f2(a1),f5(a1,x15312,x15311))
% 1.20/1.56 [697]~P30(x6971)+E(f7(x6971,x6972),f2(a75))+~E(x6972,f2(f76(x6971)))
% 1.20/1.56 [698]~P30(x6982)+~E(f7(x6982,x6981),f2(a75))+E(x6981,f2(f76(x6982)))
% 1.20/1.56 [705]~P53(x7052)+E(x7051,f2(x7052))+E(f21(x7052,f21(x7052,x7051)),x7051)
% 1.20/1.56 [708]~P5(x7082)+E(x7081,f2(x7082))+E(f22(x7082,f12(x7082,x7081)),f3(a74))
% 1.20/1.56 [709]~P54(x7091)+~E(x7092,f2(f76(x7091)))+E(f12(f76(x7091),x7092),f2(f76(x7091)))
% 1.20/1.56 [717]~P5(x7171)+~E(x7172,f2(x7171))+E(f22(x7171,f12(x7171,x7172)),f2(a74))
% 1.20/1.56 [828]~P42(x8281)+~P37(x8281)+E(f22(x8281,f16(x8281,x8282)),f4(a74,f16(a74,x8282)))
% 1.20/1.56 [830]~P45(x8302)+E(x8301,f2(x8302))+E(f22(x8302,f21(x8302,x8301)),f21(a74,f22(x8302,x8301)))
% 1.20/1.56 [837]~P15(x8372)+E(x8371,f2(x8372))+E(f21(x8372,f4(x8372,x8371)),f4(x8372,f21(x8372,x8371)))
% 1.20/1.56 [838]~P53(x8382)+E(x8381,f2(x8382))+E(f21(x8382,f9(x8382,x8381)),f9(x8382,f21(x8382,x8381)))
% 1.20/1.56 [845]~P11(x8451)+~P37(x8451)+E(f23(x8451,x8452,f16(x8451,a13)),f2(x8451))
% 1.20/1.56 [856]~P53(x8562)+E(x8561,f2(x8562))+E(f11(x8562,x8561,f21(x8562,x8561)),f3(x8562))
% 1.20/1.56 [857]~P53(x8572)+E(x8571,f2(x8572))+E(f11(x8572,f21(x8572,x8571),x8571),f3(x8572))
% 1.20/1.56 [858]~P13(x8582)+E(x8581,f2(x8582))+E(f11(x8582,f21(x8582,x8581),x8581),f3(x8582))
% 1.20/1.56 [878]~P54(x8781)+P3(f76(x8781),x8782,f2(f76(x8781)))+E(f4(f76(x8781),x8782),x8782)
% 1.20/1.56 [919]~P54(x9191)+P3(x9191,x9192,f2(x9191))+~E(f12(x9191,x9192),f9(x9191,f3(x9191)))
% 1.20/1.56 [939]~P54(x9391)+~P3(x9391,x9392,f2(x9391))+E(f12(x9391,x9392),f9(x9391,f3(x9391)))
% 1.20/1.56 [1021]~P54(x10211)+~P3(f76(x10211),x10212,f2(f76(x10211)))+E(f4(f76(x10211),x10212),f9(f76(x10211),x10212))
% 1.20/1.56 [1071]E(x10711,f2(a75))+E(x10712,f2(a75))+~E(f10(a75,x10712,x10711),f10(a75,f2(a75),f3(a75)))
% 1.20/1.56 [1072]E(x10721,f2(a75))+E(x10722,f2(a75))+~E(f10(a75,f2(a75),f3(a75)),f10(a75,x10722,x10721))
% 1.20/1.56 [1153]~E(x11532,f2(a75))+~E(x11531,f10(a75,f2(a75),f3(a75)))+E(f10(a75,x11531,x11532),f10(a75,f2(a75),f3(a75)))
% 1.20/1.56 [1154]~E(x11541,f2(a75))+~E(x11542,f10(a75,f2(a75),f3(a75)))+E(f10(a75,x11541,x11542),f10(a75,f2(a75),f3(a75)))
% 1.20/1.56 [1155]~E(x11552,f2(a75))+~E(x11551,f10(a75,f2(a75),f3(a75)))+E(f10(a75,f2(a75),f3(a75)),f10(a75,x11551,x11552))
% 1.20/1.56 [1156]~E(x11561,f2(a75))+~E(x11562,f10(a75,f2(a75),f3(a75)))+E(f10(a75,f2(a75),f3(a75)),f10(a75,x11561,x11562))
% 1.20/1.56 [1220]E(x12201,f2(a75))+E(x12201,f10(a75,f2(a75),f3(a75)))+~E(f10(a75,x12202,x12201),f10(a75,f2(a75),f3(a75)))
% 1.20/1.56 [1221]E(x12211,f2(a75))+E(x12211,f10(a75,f2(a75),f3(a75)))+~E(f10(a75,x12211,x12212),f10(a75,f2(a75),f3(a75)))
% 1.20/1.56 [1222]E(x12221,f2(a75))+E(x12221,f10(a75,f2(a75),f3(a75)))+~E(f10(a75,f2(a75),f3(a75)),f10(a75,x12222,x12221))
% 1.20/1.56 [1223]E(x12231,f2(a75))+E(x12231,f10(a75,f2(a75),f3(a75)))+~E(f10(a75,f2(a75),f3(a75)),f10(a75,x12231,x12232))
% 1.20/1.56 [1242]P3(a1,x12421,a13)+~P3(a1,x12422,a13)+E(f10(a75,f16(a75,x12421),f16(a75,x12422)),f16(a75,x12421))
% 1.20/1.56 [1311]E(x13111,f10(a75,f2(a75),f3(a75)))+E(x13112,f10(a75,f2(a75),f3(a75)))+~E(f10(a75,x13111,x13112),f10(a75,f2(a75),f3(a75)))
% 1.20/1.56 [1312]E(x13121,f10(a75,f2(a75),f3(a75)))+E(x13122,f10(a75,f2(a75),f3(a75)))+~E(f10(a75,f2(a75),f3(a75)),f10(a75,x13121,x13122))
% 1.20/1.56 [1327]~P3(a75,x13271,x13272)+P3(a75,f10(a75,x13271,f3(a75)),x13272)+E(f10(a75,x13271,f3(a75)),x13272)
% 1.20/1.56 [1347]E(x13471,x13472)+P3(a75,x13471,x13472)+~P3(a75,x13471,f10(a75,x13472,f3(a75)))
% 1.20/1.56 [1348]E(x13481,x13482)+P3(a1,x13481,x13482)+~P3(a1,x13481,f10(a1,x13482,f3(a1)))
% 1.20/1.56 [1352]P3(a1,x13521,a13)+P3(a1,x13522,a13)+E(f10(a75,f16(a75,x13521),f16(a75,x13522)),f16(a75,f10(a1,x13521,x13522)))
% 1.20/1.56 [1400]P3(a75,f42(x14002,x14001),x14002)+E(x14001,f2(a75))+~P3(a75,x14001,f10(a75,x14002,f3(a75)))
% 1.20/1.56 [1409]E(x14091,x14092)+~P2(a75,x14092,x14091)+~P3(a75,x14091,f10(a75,x14092,f3(a75)))
% 1.20/1.56 [1410]E(x14101,f2(a75))+~P3(a75,x14101,f10(a75,x14102,f3(a75)))+E(f10(a75,f42(x14102,x14101),f3(a75)),x14101)
% 1.20/1.56 [1435]~P40(x14351)+P4(x14351,x14352)+~P2(x14351,f63(x14352,f61(x14352,x14351)),f63(x14352,f57(x14352,x14351)))
% 1.20/1.56 [1494]P2(a75,x14941,x14942)+~P2(a75,x14941,f10(a75,x14942,f3(a75)))+E(x14941,f10(a75,x14942,f3(a75)))
% 1.20/1.56 [1582]E(f19(x15821),x15822)+~P2(a74,f20(a75,x15822),x15821)+~P3(a74,x15821,f10(a74,f20(a75,x15822),f3(a74)))
% 1.20/1.56 [1644]~P3(a74,f20(a75,x16442),x16441)+~P2(a74,x16441,f10(a74,f20(a75,x16442),f3(a74)))+E(f15(x16441),f10(a75,x16442,f3(a75)))
% 1.20/1.56 [1677]P3(a75,x16771,x16772)+~P3(a75,f2(a75),x16772)+E(f10(a75,f5(a75,f8(a75,x16771,x16772),x16772),f3(a75)),f5(a75,x16771,x16772))
% 1.20/1.56 [1700]~P2(a75,x17002,x17001)+~P3(a75,f2(a75),x17002)+E(f10(a75,f5(a75,f8(a75,x17001,x17002),x17002),f3(a75)),f5(a75,x17001,x17002))
% 1.20/1.56 [1343]P3(a74,x13431,a29)+~P2(a74,f22(a14,x13432),a81)+~E(f22(a14,f63(f17(a14,a82),x13432)),f9(a74,x13431))
% 1.20/1.56 [1351]P3(a74,x13511,f3(a74))+~P2(a74,f22(a14,x13512),a81)+~E(f22(a14,f63(f17(a14,a82),x13512)),f9(a74,x13511))
% 1.20/1.56 [1498]~P2(a74,f3(a74),x14981)+~P3(a75,f2(a75),x14982)+E(f19(f23(a74,x14981,f20(a75,x14982))),f5(a75,f19(x14981),x14982))
% 1.20/1.56 [1652]P3(a74,f9(a74,a85),x16521)+~P2(a74,f22(a14,x16522),a81)+~P3(a74,f22(a14,f63(f17(a14,a82),x16522)),x16521)
% 1.20/1.56 [1721]~P2(a75,f67(x17212),x17211)+~P3(a74,f2(a74),x17212)+P3(a74,f22(a14,f8(a14,f83(f63(a73,x17211)),a86)),x17212)
% 1.20/1.56 [1734]~P13(x17341)+~P37(x17341)+E(f23(x17341,x17342,f16(x17341,f10(a1,f10(a1,f3(a1),a13),a13))),x17342)
% 1.20/1.56 [1776]P3(a74,f9(a74,a85),x17761)+~P2(a74,f22(a14,x17762),a81)+~P3(a74,f9(a74,f9(a74,f22(a14,f63(f17(a14,a82),x17762)))),x17761)
% 1.20/1.56 [734]~E(x7342,x7343)+~P29(x7341)+P2(x7341,x7342,x7343)
% 1.20/1.56 [736]~E(x7362,x7363)+~P40(x7361)+P2(x7361,x7362,x7363)
% 1.20/1.56 [854]~P3(x8543,x8541,x8542)+~E(x8541,x8542)+~P35(x8543)
% 1.20/1.56 [855]~P3(x8553,x8551,x8552)+~E(x8551,x8552)+~P40(x8553)
% 1.20/1.56 [901]P2(x9011,x9013,x9012)+~P35(x9011)+P2(x9011,x9012,x9013)
% 1.20/1.56 [906]P3(x9061,x9063,x9062)+~P35(x9061)+P2(x9061,x9062,x9063)
% 1.20/1.56 [968]~P29(x9681)+~P3(x9681,x9682,x9683)+P2(x9681,x9682,x9683)
% 1.20/1.56 [970]~P40(x9701)+~P3(x9701,x9702,x9703)+P2(x9701,x9702,x9703)
% 1.20/1.56 [1038]~P3(x10381,x10383,x10382)+~P29(x10381)+~P2(x10381,x10382,x10383)
% 1.20/1.56 [1042]~P3(x10421,x10423,x10422)+~P29(x10421)+~P3(x10421,x10422,x10423)
% 1.20/1.56 [1045]~P3(x10451,x10453,x10452)+~P35(x10451)+~P2(x10451,x10452,x10453)
% 1.20/1.56 [1046]~P3(x10461,x10463,x10462)+~P35(x10461)+~P3(x10461,x10462,x10463)
% 1.20/1.56 [1047]~P3(x10471,x10473,x10472)+~P40(x10471)+~P3(x10471,x10472,x10473)
% 1.20/1.56 [1176]~P2(a74,x11761,x11763)+P2(a74,x11761,x11762)+~P2(a74,x11763,x11762)
% 1.20/1.56 [1177]~P2(a75,x11771,x11773)+P2(a75,x11771,x11772)+~P2(a75,x11773,x11772)
% 1.20/1.56 [1178]~P2(a1,x11781,x11783)+P2(a1,x11781,x11782)+~P2(a1,x11783,x11782)
% 1.20/1.56 [700]~P19(x7002)+~E(x7003,f9(x7002,x7001))+E(x7001,f9(x7002,x7003))
% 1.20/1.56 [702]~P19(x7021)+~E(f9(x7021,x7023),x7022)+E(f9(x7021,x7022),x7023)
% 1.20/1.56 [706]~P19(x7063)+E(x7061,x7062)+~E(f9(x7063,x7061),f9(x7063,x7062))
% 1.20/1.56 [707]~P39(x7073)+E(x7071,x7072)+~E(f9(x7073,x7071),f9(x7073,x7072))
% 1.20/1.56 [755]~E(x7552,x7553)+~P10(x7551)+E(f8(x7551,x7552,x7553),f2(x7551))
% 1.20/1.56 [756]~E(x7562,x7563)+~P19(x7561)+E(f8(x7561,x7562,x7563),f2(x7561))
% 1.20/1.56 [764]~P70(x7641)+~E(x7643,f2(x7641))+E(f10(x7641,x7642,x7643),x7642)
% 1.20/1.56 [783]~P69(x7831)+~E(x7833,f2(x7831))+E(f11(x7831,x7832,x7833),f2(x7831))
% 1.20/1.56 [784]~P69(x7841)+~E(x7842,f2(x7841))+E(f11(x7841,x7842,x7843),f2(x7841))
% 1.20/1.56 [826]~P19(x8261)+~E(x8263,f9(x8261,x8262))+E(f10(x8261,x8262,x8263),f2(x8261))
% 1.20/1.56 [827]~P19(x8271)+~E(x8272,f9(x8271,x8273))+E(f10(x8271,x8272,x8273),f2(x8271))
% 1.20/1.56 [862]~P70(x8622)+~E(f10(x8622,x8623,x8621),x8623)+E(x8621,f2(x8622))
% 1.20/1.56 [864]~P10(x8643)+E(x8641,x8642)+~E(f8(x8643,x8641,x8642),f2(x8643))
% 1.20/1.56 [865]~P19(x8653)+E(x8651,x8652)+~E(f8(x8653,x8651,x8652),f2(x8653))
% 1.20/1.56 [895]~P19(x8952)+~E(f10(x8952,x8953,x8951),f2(x8952))+E(x8951,f9(x8952,x8953))
% 1.20/1.56 [896]~P19(x8962)+~E(f10(x8962,x8961,x8963),f2(x8962))+E(x8961,f9(x8962,x8963))
% 1.20/1.56 [897]~P19(x8971)+~E(f10(x8971,x8972,x8973),f2(x8971))+E(f9(x8971,x8972),x8973)
% 1.20/1.56 [898]~P53(x8981)+~E(f11(x8981,x8982,x8983),f3(x8981))+E(f21(x8981,x8982),x8983)
% 1.20/1.56 [952]~P50(x9521)+~E(x9522,f9(x9521,x9523))+E(f11(x9521,x9522,x9522),f11(x9521,x9523,x9523))
% 1.20/1.56 [1022]E(x10221,x10222)+~E(f11(a74,x10223,x10221),f11(a74,x10223,x10222))+E(x10223,f2(a74))
% 1.20/1.56 [1023]E(x10231,x10232)+~E(f11(a74,x10231,x10233),f11(a74,x10232,x10233))+E(x10233,f2(a74))
% 1.20/1.56 [1080]~P6(x10801)+P2(x10801,x10802,x10803)+~P2(x10801,f4(x10801,x10802),x10803)
% 1.20/1.56 [1081]~P54(x10811)+P3(x10811,x10812,x10813)+~P3(x10811,f4(x10811,x10812),x10813)
% 1.20/1.56 [1105]~P1(x11051)+~P3(a75,x11052,x11053)+P3(a75,f63(x11051,x11052),f63(x11051,x11053))
% 1.20/1.56 [1109]~P18(x11091)+~P2(x11091,x11093,x11092)+P2(x11091,f9(x11091,x11092),f9(x11091,x11093))
% 1.20/1.56 [1111]~P39(x11111)+~P2(x11111,x11113,x11112)+P2(x11111,f9(x11111,x11112),f9(x11111,x11113))
% 1.20/1.56 [1112]~P18(x11121)+~P3(x11121,x11123,x11122)+P3(x11121,f9(x11121,x11122),f9(x11121,x11123))
% 1.20/1.56 [1159]~P18(x11591)+~P2(x11591,x11593,f9(x11591,x11592))+P2(x11591,x11592,f9(x11591,x11593))
% 1.20/1.56 [1161]~P18(x11611)+~P3(x11611,x11613,f9(x11611,x11612))+P3(x11611,x11612,f9(x11611,x11613))
% 1.20/1.56 [1163]~P18(x11631)+~P2(x11631,f9(x11631,x11633),x11632)+P2(x11631,f9(x11631,x11632),x11633)
% 1.20/1.56 [1165]~P6(x11651)+~P2(x11651,f4(x11651,x11652),x11653)+P2(x11651,f9(x11651,x11652),x11653)
% 1.20/1.56 [1167]~P18(x11671)+~P3(x11671,f9(x11671,x11673),x11672)+P3(x11671,f9(x11671,x11672),x11673)
% 1.20/1.56 [1168]~P54(x11681)+~P3(x11681,f4(x11681,x11682),x11683)+P3(x11681,f9(x11681,x11682),x11683)
% 1.20/1.56 [1180]~P2(a75,x11803,x11801)+~E(f8(a75,x11801,x11803),x11802)+E(x11801,f10(a75,x11802,x11803))
% 1.20/1.56 [1181]~P2(a75,x11812,x11811)+~E(x11811,f10(a75,x11813,x11812))+E(f8(a75,x11811,x11812),x11813)
% 1.20/1.56 [1188]~P18(x11881)+P2(x11881,x11882,x11883)+~P2(x11881,f9(x11881,x11883),f9(x11881,x11882))
% 1.20/1.56 [1189]~P39(x11891)+P2(x11891,x11892,x11893)+~P2(x11891,f9(x11891,x11893),f9(x11891,x11892))
% 1.20/1.56 [1190]~P18(x11901)+P3(x11901,x11902,x11903)+~P3(x11901,f9(x11901,x11903),f9(x11901,x11902))
% 1.20/1.56 [1275]~P18(x12751)+~P2(x12751,x12752,x12753)+P2(x12751,f8(x12751,x12752,x12753),f2(x12751))
% 1.20/1.56 [1276]~P18(x12761)+~P3(x12761,x12762,x12763)+P3(x12761,f8(x12761,x12762,x12763),f2(x12761))
% 1.20/1.56 [1357]~P18(x13571)+P2(x13571,x13572,x13573)+~P2(x13571,f8(x13571,x13572,x13573),f2(x13571))
% 1.20/1.56 [1358]~P18(x13581)+P3(x13581,x13582,x13583)+~P3(x13581,f8(x13581,x13582,x13583),f2(x13581))
% 1.20/1.56 [1550]~P3(a75,x15503,x15501)+~P3(a75,x15503,x15502)+P3(a75,f8(a75,x15501,x15502),f8(a75,x15501,x15503))
% 1.20/1.56 [1551]~P2(a75,x15512,x15511)+~P3(a75,x15511,x15513)+P3(a75,f8(a75,x15511,x15512),f8(a75,x15513,x15512))
% 1.20/1.56 [1553]~P2(a1,x15533,x15531)+P2(a1,f5(a1,x15531,x15532),f5(a1,x15533,x15532))+~P3(a1,x15532,f2(a1))
% 1.20/1.56 [1554]~P2(a75,x15543,x15542)+P2(a75,f5(a75,x15541,x15542),f5(a75,x15541,x15543))+~P3(a75,f2(a75),x15543)
% 1.20/1.56 [1555]~P2(a1,x15551,x15553)+P2(a1,f5(a1,x15551,x15552),f5(a1,x15553,x15552))+~P3(a1,f2(a1),x15552)
% 1.20/1.56 [1631]~P2(a75,x16313,x16312)+~P2(a75,f10(a75,x16311,x16313),x16312)+P2(a75,x16311,f8(a75,x16312,x16313))
% 1.20/1.56 [1632]~P2(a75,x16322,x16323)+~P2(a75,x16321,f8(a75,x16323,x16322))+P2(a75,f10(a75,x16321,x16322),x16323)
% 1.20/1.56 [754]~P50(x7541)+~E(x7542,f2(f76(x7541)))+E(f63(f17(x7541,x7542),x7543),f2(x7541))
% 1.20/1.56 [882]~P50(x8821)+E(f18(x8821,x8822,x8823),f2(a75))+E(f63(f17(x8821,x8823),x8822),f2(x8821))
% 1.20/1.56 [1025]~P53(x10252)+E(x10251,f2(x10252))+E(f23(x10252,f9(x10252,x10253),f9(x10252,x10251)),f23(x10252,x10253,x10251))
% 1.20/1.56 [1157]~P53(x11572)+E(x11571,f2(x11572))+E(f23(x11572,x11573,f9(x11572,x11571)),f9(x11572,f23(x11572,x11573,x11571)))
% 1.20/1.56 [1217]~P44(x12172)+E(x12171,f2(x12172))+E(f23(a74,f22(x12172,x12173),f22(x12172,x12171)),f22(x12172,f23(x12172,x12173,x12171)))
% 1.20/1.56 [1218]~P15(x12182)+E(x12181,f2(x12182))+E(f23(x12182,f4(x12182,x12183),f4(x12182,x12181)),f4(x12182,f23(x12182,x12183,x12181)))
% 1.20/1.56 [1219]~P11(x12191)+~P44(x12191)+E(f23(a74,f22(x12191,x12192),f22(x12191,x12193)),f22(x12191,f23(x12191,x12192,x12193)))
% 1.20/1.56 [1328]~P14(x13281)+~P3(x13281,f2(x13281),x13283)+E(f23(x13281,f4(x13281,x13282),x13283),f4(x13281,f23(x13281,x13282,x13283)))
% 1.20/1.56 [1370]~P3(a75,x13701,x13703)+~P3(a75,x13703,x13702)+P3(a75,f10(a75,x13701,f3(a75)),x13702)
% 1.20/1.56 [1386]~P3(a75,x13863,x13862)+P3(a75,x13861,f10(a75,x13862,f3(a75)))+~E(x13861,f10(a75,x13863,f3(a75)))
% 1.20/1.56 [1405]~P12(x14052)+E(x14051,f2(x14052))+E(f5(x14052,f10(x14052,x14053,x14051),x14051),f10(x14052,f5(x14052,x14053,x14051),f3(x14052)))
% 1.20/1.56 [1406]~P12(x14062)+E(x14061,f2(x14062))+E(f5(x14062,f10(x14062,x14061,x14063),x14061),f10(x14062,f5(x14062,x14063,x14061),f3(x14062)))
% 1.20/1.56 [1573]~P59(x15732)+E(x15731,f2(x15732))+~E(f10(x15732,f11(x15732,x15733,x15733),f11(x15732,x15731,x15731)),f2(x15732))
% 1.20/1.56 [1574]~P59(x15742)+E(x15741,f2(x15742))+~E(f10(x15742,f11(x15742,x15741,x15741),f11(x15742,x15743,x15743)),f2(x15742))
% 1.20/1.56 [1580]P3(a75,x15802,x15801)+E(f10(a75,x15801,f30(x15801,x15802,x15803)),x15802)+P71(f63(x15803,f8(a75,x15802,x15801)))
% 1.20/1.56 [1581]P3(a75,x15812,x15811)+E(f10(a75,x15811,f33(x15811,x15812,x15813)),x15812)+P71(f63(x15813,f8(a75,x15812,x15811)))
% 1.20/1.56 [1583]E(f10(a75,x15831,f30(x15831,x15832,x15833)),x15832)+P71(f63(x15833,f8(a75,x15832,x15831)))+~P71(f63(x15833,f2(a75)))
% 1.20/1.56 [1584]E(f10(a75,x15841,f33(x15841,x15842,x15843)),x15842)+P71(f63(x15843,f8(a75,x15842,x15841)))+~P71(f63(x15843,f2(a75)))
% 1.20/1.56 [1618]~P2(a75,x16182,x16183)+~P2(a75,x16182,x16181)+E(f8(a75,f8(a75,x16181,x16182),f8(a75,x16183,x16182)),f8(a75,x16181,x16183))
% 1.20/1.56 [1636]~P3(a75,x16362,x16363)+~P71(f63(x16361,f8(a75,x16362,x16363)))+P71(f63(x16361,f2(a75)))
% 1.20/1.56 [1702]~P2(a74,x17022,x17021)+~P3(a74,x17021,f10(a74,x17022,x17023))+P3(a74,f4(a74,f8(a74,x17021,x17022)),x17023)
% 1.20/1.56 [1722]P3(a75,x17221,x17222)+~P71(f63(x17223,f30(x17222,x17221,x17223)))+P71(f63(x17223,f8(a75,x17221,x17222)))
% 1.20/1.56 [1723]P3(a75,x17231,x17232)+~P71(f63(x17233,f33(x17232,x17231,x17233)))+P71(f63(x17233,f8(a75,x17231,x17232)))
% 1.20/1.56 [1724]~P71(f63(x17241,f30(x17243,x17242,x17241)))+P71(f63(x17241,f8(a75,x17242,x17243)))+~P71(f63(x17241,f2(a75)))
% 1.20/1.56 [1725]~P71(f63(x17251,f33(x17253,x17252,x17251)))+P71(f63(x17251,f8(a75,x17252,x17253)))+~P71(f63(x17251,f2(a75)))
% 1.20/1.56 [1735]~P15(x17351)+~P3(x17351,x17352,x17353)+P3(x17351,x17352,f23(x17351,f10(x17351,x17352,x17353),f10(x17351,f3(x17351),f3(x17351))))
% 1.20/1.56 [1736]~P15(x17361)+~P3(x17361,x17362,x17363)+P3(x17361,f23(x17361,f10(x17361,x17362,x17363),f10(x17361,f3(x17361),f3(x17361))),x17363)
% 1.20/1.56 [1774]~P5(x17742)+P3(a74,f2(a74),f48(x17741,x17742))+~P3(a74,f22(x17742,f63(x17741,f49(x17741,x17742,x17743))),f20(a75,f10(a75,x17743,f3(a75))))
% 1.20/1.56 [1775]~P5(x17752)+P3(a74,f2(a74),f50(x17751,x17752))+~P2(a74,f22(x17752,f63(x17751,f51(x17751,x17752,x17753))),f20(a75,f10(a75,x17753,f3(a75))))
% 1.20/1.56 [1050]~P7(x10503)+E(x10501,x10502)+~E(f10(x10503,x10504,x10501),f10(x10503,x10504,x10502))
% 1.20/1.56 [1051]~P8(x10513)+E(x10511,x10512)+~E(f10(x10513,x10514,x10511),f10(x10513,x10514,x10512))
% 1.20/1.56 [1053]~P7(x10533)+E(x10531,x10532)+~E(f10(x10533,x10531,x10534),f10(x10533,x10532,x10534))
% 1.20/1.56 [1169]~P41(x11692)+~P3(f79(x11691,x11692),x11693,x11694)+P2(f79(x11691,x11692),x11693,x11694)
% 1.20/1.56 [1277]~P41(x12771)+~P3(f79(x12772,x12771),x12774,x12773)+~P2(f79(x12772,x12771),x12773,x12774)
% 1.20/1.56 [1326]~P3(a75,x13263,x13264)+P3(a75,x13261,x13262)+~E(f10(a75,x13263,x13262),f10(a75,x13261,x13264))
% 1.20/1.56 [1439]~P27(x14391)+~P2(x14391,x14393,x14394)+P2(x14391,f10(x14391,x14392,x14393),f10(x14391,x14392,x14394))
% 1.20/1.56 [1440]~P28(x14401)+~P2(x14401,x14403,x14404)+P2(x14401,f10(x14401,x14402,x14403),f10(x14401,x14402,x14404))
% 1.20/1.56 [1441]~P27(x14411)+~P2(x14411,x14412,x14414)+P2(x14411,f10(x14411,x14412,x14413),f10(x14411,x14414,x14413))
% 1.20/1.56 [1442]~P28(x14421)+~P2(x14421,x14422,x14424)+P2(x14421,f10(x14421,x14422,x14423),f10(x14421,x14424,x14423))
% 1.20/1.56 [1443]~P27(x14431)+~P3(x14431,x14433,x14434)+P3(x14431,f10(x14431,x14432,x14433),f10(x14431,x14432,x14434))
% 1.20/1.56 [1444]~P32(x14441)+~P3(x14441,x14443,x14444)+P3(x14441,f10(x14441,x14442,x14443),f10(x14441,x14442,x14444))
% 1.20/1.56 [1445]~P27(x14451)+~P3(x14451,x14452,x14454)+P3(x14451,f10(x14451,x14452,x14453),f10(x14451,x14454,x14453))
% 1.20/1.56 [1446]~P32(x14461)+~P3(x14461,x14462,x14464)+P3(x14461,f10(x14461,x14462,x14463),f10(x14461,x14464,x14463))
% 1.20/1.56 [1548]~P2(a75,x15482,x15484)+~P2(a75,x15481,x15483)+P2(a75,f10(a75,x15481,x15482),f10(a75,x15483,x15484))
% 1.20/1.56 [1549]~P3(a75,x15492,x15494)+~P3(a75,x15491,x15493)+P3(a75,f10(a75,x15491,x15492),f10(a75,x15493,x15494))
% 1.20/1.56 [1552]~P2(a1,x15522,x15524)+~P3(a1,x15521,x15523)+P3(a1,f10(a1,x15521,x15522),f10(a1,x15523,x15524))
% 1.20/1.56 [1624]~P27(x16241)+P2(x16241,x16242,x16243)+~P2(x16241,f10(x16241,x16244,x16242),f10(x16241,x16244,x16243))
% 1.20/1.56 [1626]~P27(x16261)+P2(x16261,x16262,x16263)+~P2(x16261,f10(x16261,x16262,x16264),f10(x16261,x16263,x16264))
% 1.20/1.56 [1628]~P27(x16281)+P3(x16281,x16282,x16283)+~P3(x16281,f10(x16281,x16284,x16282),f10(x16281,x16284,x16283))
% 1.20/1.56 [1630]~P27(x16301)+P3(x16301,x16302,x16303)+~P3(x16301,f10(x16301,x16302,x16304),f10(x16301,x16303,x16304))
% 1.20/1.56 [1383]~P11(x13832)+E(x13831,f2(x13832))+E(f23(x13832,f11(x13832,x13833,x13831),f11(x13832,x13834,x13831)),f23(x13832,x13833,x13834))
% 1.20/1.56 [1384]~P11(x13842)+E(x13841,f2(x13842))+E(f23(x13842,f11(x13842,x13841,x13843),f11(x13842,x13841,x13844)),f23(x13842,x13843,x13844))
% 1.20/1.56 [1634]~E(x16343,f10(a75,x16344,x16342))+P71(f63(x16341,x16342))+~P71(f63(x16341,f8(a75,x16343,x16344)))
% 1.20/1.56 [1706]~P54(x17061)+P3(x17061,x17062,f10(x17061,x17063,x17064))+~P3(x17061,f4(x17061,f8(x17061,x17062,x17063)),x17064)
% 1.20/1.56 [1707]~P54(x17071)+P3(x17071,f8(x17071,x17072,x17073),x17074)+~P3(x17071,f4(x17071,f8(x17071,x17074,x17072)),x17073)
% 1.20/1.56 [1789]~P41(x17892)+P2(f79(x17891,x17892),x17893,x17894)+~P2(x17892,f63(x17893,f68(x17894,x17893,x17891,x17892)),f63(x17894,f68(x17894,x17893,x17891,x17892)))
% 1.20/1.56 [1691]~P38(x16911)+~P68(x16911)+E(f10(x16911,f11(x16911,f16(x16911,x16912),x16913),f11(x16911,f16(x16911,x16912),x16914)),f11(x16911,f16(x16911,x16912),f10(x16911,x16913,x16914)))
% 1.20/1.56 [1692]~P38(x16921)+~P60(x16921)+E(f8(x16921,f11(x16921,f16(x16921,x16922),x16923),f11(x16921,f16(x16921,x16922),x16924)),f11(x16921,f16(x16921,x16922),f8(x16921,x16923,x16924)))
% 1.20/1.56 [1693]~P38(x16931)+~P68(x16931)+E(f10(x16931,f11(x16931,x16932,f16(x16931,x16933)),f11(x16931,x16934,f16(x16931,x16933))),f11(x16931,f10(x16931,x16932,x16934),f16(x16931,x16933)))
% 1.20/1.56 [1694]~P38(x16941)+~P60(x16941)+E(f8(x16941,f11(x16941,x16942,f16(x16941,x16943)),f11(x16941,x16944,f16(x16941,x16943))),f11(x16941,f8(x16941,x16942,x16944),f16(x16941,x16943)))
% 1.20/1.56 [1777]~P5(x17771)+P2(a74,f22(x17771,f63(x17772,x17773)),f48(x17772,x17771))+~P3(a74,f22(x17771,f63(x17772,f49(x17772,x17771,x17774))),f20(a75,f10(a75,x17774,f3(a75))))
% 1.20/1.56 [1778]~P5(x17781)+P2(a74,f22(x17781,f63(x17782,x17783)),f50(x17782,x17781))+~P2(a74,f22(x17781,f63(x17782,f51(x17782,x17781,x17784))),f20(a75,f10(a75,x17784,f3(a75))))
% 1.20/1.56 [1804]~P3(a74,x18041,x18042)+~P3(a74,f4(a74,f8(a74,x18043,x18044)),x18042)+~P2(a74,f11(a74,f16(a74,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))),x18042),f10(a74,f4(a74,f8(a74,x18043,x18044)),x18041))
% 1.20/1.56 [1235]~P41(x12351)+P2(x12351,f63(x12352,x12353),f63(x12354,x12353))+~P2(f79(x12355,x12351),x12352,x12354)
% 1.20/1.56 [1673]~E(x16732,x16734)+~P70(x16731)+E(f10(x16731,f11(x16731,x16732,x16733),f11(x16731,x16734,x16735)),f10(x16731,f11(x16731,x16732,x16735),f11(x16731,x16734,x16733)))
% 1.20/1.56 [1758]~P60(x17582)+~E(f10(x17582,f11(x17582,x17584,x17585),x17581),f10(x17582,f11(x17582,x17583,x17585),x17586))+E(x17581,f10(x17582,f11(x17582,f8(x17582,x17583,x17584),x17585),x17586))
% 1.20/1.56 [1759]~P60(x17591)+~E(f10(x17591,f11(x17591,x17592,x17594),x17595),f10(x17591,f11(x17591,x17593,x17594),x17596))+E(f10(x17591,f11(x17591,f8(x17591,x17592,x17593),x17594),x17595),x17596)
% 1.20/1.56 [1760]~P60(x17601)+E(f10(x17601,f11(x17601,x17602,x17603),x17604),f10(x17601,f11(x17601,x17605,x17603),x17606))+~E(x17606,f10(x17601,f11(x17601,f8(x17601,x17602,x17605),x17603),x17604))
% 1.20/1.56 [1761]~P60(x17611)+E(f10(x17611,f11(x17611,x17612,x17613),x17614),f10(x17611,f11(x17611,x17615,x17613),x17616))+~E(f10(x17611,f11(x17611,f8(x17611,x17612,x17615),x17613),x17614),x17616)
% 1.20/1.56 [1791]E(x17911,f3(a1))+E(x17911,f2(a1))+~P2(a1,f2(a1),x17911)+~P3(a1,x17911,f16(a1,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13))))
% 1.20/1.56 [921]~P34(x9212)+~P3(x9212,f2(x9212),x9211)+E(f12(x9212,x9211),f3(x9212))+E(x9211,f2(x9212))
% 1.20/1.56 [1061]~P54(x10611)+~P37(x10611)+P2(x10611,f2(x10611),f16(x10611,x10612))+~P2(a1,a13,x10612)
% 1.20/1.56 [1062]~P54(x10621)+~P37(x10621)+P3(x10621,f2(x10621),f16(x10621,x10622))+~P3(a1,a13,x10622)
% 1.20/1.56 [1063]~P54(x10631)+~P37(x10631)+P2(x10631,f16(x10631,x10632),f2(x10631))+~P2(a1,x10632,a13)
% 1.20/1.56 [1064]~P54(x10641)+~P37(x10641)+P3(x10641,f16(x10641,x10642),f2(x10641))+~P3(a1,x10642,a13)
% 1.20/1.56 [1106]P3(a1,x11061,x11062)+P3(a1,x11062,x11061)+E(x11061,f2(a1))+~E(f5(a1,x11062,x11061),f2(a1))
% 1.20/1.56 [1113]P3(a1,x11132,x11131)+E(x11131,f2(a1))+P2(a1,x11132,f2(a1))+~E(f5(a1,x11132,x11131),f2(a1))
% 1.20/1.56 [1114]P3(a1,x11141,x11142)+E(x11141,f2(a1))+P2(a1,f2(a1),x11142)+~E(f5(a1,x11142,x11141),f2(a1))
% 1.20/1.56 [1117]~P37(x11172)+~P54(x11172)+~P2(x11172,f16(x11172,x11171),f2(x11172))+P2(a1,x11171,a13)
% 1.20/1.56 [1118]~P37(x11182)+~P54(x11182)+~P3(x11182,f16(x11182,x11181),f2(x11182))+P3(a1,x11181,a13)
% 1.20/1.56 [1119]~P37(x11192)+~P54(x11192)+~P2(x11192,f2(x11192),f16(x11192,x11191))+P2(a1,a13,x11191)
% 1.20/1.56 [1120]~P37(x11202)+~P54(x11202)+~P3(x11202,f2(x11202),f16(x11202,x11201))+P3(a1,a13,x11201)
% 1.20/1.56 [1150]~P15(x11502)+~P3(x11502,f21(x11502,x11501),f2(x11502))+P3(x11502,x11501,f2(x11502))+E(x11501,f2(x11502))
% 1.20/1.56 [1151]~P15(x11512)+~P3(x11512,f2(x11512),f21(x11512,x11511))+P3(x11512,f2(x11512),x11511)+E(x11511,f2(x11512))
% 1.20/1.56 [879]~P34(x8792)+P3(x8792,f2(x8792),x8791)+E(x8791,f2(x8792))+E(f12(x8792,x8791),f9(x8792,f3(x8792)))
% 1.20/1.56 [989]~P54(x9891)+~P37(x9891)+P3(x9891,f16(x9891,x9892),f2(x9891))+E(f4(x9891,f16(x9891,x9892)),f16(x9891,x9892))
% 1.20/1.56 [1026]~P54(x10262)+~P3(f76(x10262),f2(f76(x10262)),x10261)+E(f12(f76(x10262),x10261),f3(f76(x10262)))+E(x10261,f2(f76(x10262)))
% 1.20/1.56 [1191]~P54(x11911)+~P37(x11911)+~P3(x11911,f16(x11911,x11912),f2(x11911))+E(f4(x11911,f16(x11911,x11912)),f9(x11911,f16(x11911,x11912)))
% 1.20/1.56 [998]~P54(x9982)+P3(f76(x9982),f2(f76(x9982)),x9981)+E(x9981,f2(f76(x9982)))+E(f12(f76(x9982),x9981),f9(f76(x9982),f3(f76(x9982))))
% 1.20/1.56 [1653]~P37(x16532)+~P54(x16532)+~P2(x16532,f16(x16532,x16531),f3(x16532))+P2(a1,x16531,f10(a1,f10(a1,f3(a1),a13),a13))
% 1.20/1.56 [1654]~P37(x16542)+~P54(x16542)+~P3(x16542,f16(x16542,x16541),f3(x16542))+P3(a1,x16541,f10(a1,f10(a1,f3(a1),a13),a13))
% 1.20/1.56 [1655]~P37(x16552)+~P54(x16552)+~P2(x16552,f3(x16552),f16(x16552,x16551))+P2(a1,f10(a1,f10(a1,f3(a1),a13),a13),x16551)
% 1.20/1.56 [1656]~P37(x16562)+~P54(x16562)+~P3(x16562,f3(x16562),f16(x16562,x16561))+P3(a1,f10(a1,f10(a1,f3(a1),a13),a13),x16561)
% 1.20/1.56 [1726]~P54(x17261)+~P37(x17261)+P2(x17261,f3(x17261),f16(x17261,x17262))+~P2(a1,f10(a1,f10(a1,f3(a1),a13),a13),x17262)
% 1.20/1.56 [1727]~P54(x17271)+~P37(x17271)+P3(x17271,f3(x17271),f16(x17271,x17272))+~P3(a1,f10(a1,f10(a1,f3(a1),a13),a13),x17272)
% 1.20/1.56 [1728]~P54(x17281)+~P37(x17281)+P2(x17281,f16(x17281,x17282),f3(x17281))+~P2(a1,x17282,f10(a1,f10(a1,f3(a1),a13),a13))
% 1.20/1.56 [1729]~P54(x17291)+~P37(x17291)+P3(x17291,f16(x17291,x17292),f3(x17291))+~P3(a1,x17292,f10(a1,f10(a1,f3(a1),a13),a13))
% 1.20/1.56 [1795]~P14(x17951)+~P37(x17951)+~P3(x17951,f2(x17951),x17952)+P3(x17951,f2(x17951),f23(x17951,x17952,f16(x17951,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.56 [1801]~P14(x18011)+~P37(x18011)+P3(x18011,f2(x18011),x18012)+~P3(x18011,f2(x18011),f23(x18011,x18012,f16(x18011,f10(a1,f10(a1,f10(a1,f3(a1),a13),a13),f10(a1,f10(a1,f3(a1),a13),a13)))))
% 1.20/1.56 [914]P3(x9143,x9141,x9142)+~P54(x9143)+E(x9141,x9142)+P3(x9143,x9142,x9141)
% 1.20/1.56 [915]P3(x9153,x9151,x9152)+~P35(x9153)+E(x9151,x9152)+P3(x9153,x9152,x9151)
% 1.20/1.56 [916]P3(x9161,x9162,x9163)+~E(x9162,x9163)+~P35(x9161)+P2(x9161,x9162,x9163)
% 1.20/1.56 [974]~P40(x9743)+~P2(x9743,x9742,x9741)+E(x9741,x9742)+P3(x9743,x9742,x9741)
% 1.20/1.56 [976]~P35(x9763)+~P2(x9763,x9761,x9762)+E(x9761,x9762)+P3(x9763,x9761,x9762)
% 1.20/1.56 [982]~P40(x9823)+~P2(x9823,x9821,x9822)+E(x9821,x9822)+P3(x9823,x9821,x9822)
% 1.20/1.56 [1059]~P2(x10593,x10592,x10591)+~P2(x10593,x10591,x10592)+E(x10591,x10592)+~P40(x10593)
% 1.20/1.56 [1121]P3(x11211,x11213,x11212)+~P29(x11211)+~P2(x11211,x11213,x11212)+P2(x11211,x11212,x11213)
% 1.20/1.56 [723]~P36(x7233)+~P50(x7233)+E(x7231,x7232)+~E(f17(x7233,x7231),f17(x7233,x7232))
% 1.20/1.56 [724]~P36(x7243)+~P37(x7243)+E(x7241,x7242)+~E(f16(x7243,x7241),f16(x7243,x7242))
% 1.20/1.56 [785]~E(x7853,x7851)+~P53(x7852)+E(f23(x7852,x7853,x7851),f3(x7852))+E(x7851,f2(x7852))
% 1.20/1.56 [874]~P53(x8743)+E(x8741,x8742)+~E(f23(x8743,x8741,x8742),f3(x8743))+E(x8742,f2(x8743))
% 1.20/1.56 [886]~P69(x8862)+~E(f11(x8862,x8863,x8861),f2(x8862))+E(x8861,f2(x8862))+E(x8863,f2(x8862))
% 1.20/1.56 [888]~P63(x8882)+~E(f11(x8882,x8883,x8881),f2(x8882))+E(x8881,f2(x8882))+E(x8883,f2(x8882))
% 1.20/1.56 [1104]~P50(x11043)+E(x11041,x11042)+~E(f11(x11043,x11041,x11041),f11(x11043,x11042,x11042))+E(x11041,f9(x11043,x11042))
% 1.20/1.56 [1133]~P54(x11331)+~P37(x11331)+~P2(a1,x11332,x11333)+P2(x11331,f16(x11331,x11332),f16(x11331,x11333))
% 1.20/1.56 [1134]~P54(x11341)+~P37(x11341)+~P3(a1,x11342,x11343)+P3(x11341,f16(x11341,x11342),f16(x11341,x11343))
% 1.20/1.56 [1211]~P37(x12113)+~P54(x12113)+~P2(x12113,f16(x12113,x12111),f16(x12113,x12112))+P2(a1,x12111,x12112)
% 1.20/1.56 [1212]~P37(x12123)+~P54(x12123)+~P3(x12123,f16(x12123,x12121),f16(x12123,x12122))+P3(a1,x12121,x12122)
% 1.20/1.56 [1301]~P15(x13011)+~P3(x13011,x13013,x13012)+~P3(x13011,x13012,f2(x13011))+P3(x13011,f21(x13011,x13012),f21(x13011,x13013))
% 1.20/1.56 [1302]~P15(x13021)+~P3(x13021,x13023,x13022)+~P3(x13021,f2(x13021),x13023)+P3(x13021,f21(x13021,x13022),f21(x13021,x13023))
% 1.20/1.56 [1322]~P6(x13221)+~P2(x13221,x13222,x13223)+~P2(x13221,f9(x13221,x13222),x13223)+P2(x13221,f4(x13221,x13222),x13223)
% 1.20/1.56 [1323]~P54(x13231)+~P3(x13231,x13232,x13233)+~P3(x13231,f9(x13231,x13232),x13233)+P3(x13231,f4(x13231,x13232),x13233)
% 1.20/1.56 [1359]~P15(x13591)+P3(x13591,x13592,x13593)+~P3(x13591,x13592,f2(x13591))+~P3(x13591,f21(x13591,x13593),f21(x13591,x13592))
% 1.20/1.56 [1360]~P15(x13601)+P3(x13601,x13602,x13603)+~P3(x13601,f2(x13601),x13603)+~P3(x13601,f21(x13601,x13603),f21(x13601,x13602))
% 1.20/1.56 [1385]E(x13851,x13852)+~P2(a75,x13853,x13852)+~P2(a75,x13853,x13851)+~E(f8(a75,x13851,x13853),f8(a75,x13852,x13853))
% 1.20/1.56 [1450]~P14(x14501)+~P2(x14501,x14503,f2(x14501))+~P2(x14501,x14502,f2(x14501))+P2(x14501,f2(x14501),f23(x14501,x14502,x14503))
% 1.20/1.56 [1451]~P15(x14511)+~P2(x14511,x14512,f2(x14511))+~P3(x14511,x14513,f2(x14511))+P2(x14511,f2(x14511),f23(x14511,x14512,x14513))
% 1.20/1.56 [1452]~P59(x14521)+~P2(x14521,x14523,f2(x14521))+~P2(x14521,x14522,f2(x14521))+P2(x14521,f2(x14521),f11(x14521,x14522,x14523))
% 1.20/1.56 [1454]~P65(x14541)+~P2(x14541,x14543,f2(x14541))+~P2(x14541,x14542,f2(x14541))+P2(x14541,f2(x14541),f11(x14541,x14542,x14543))
% 1.20/1.56 [1455]~P14(x14551)+~P3(x14551,x14553,f2(x14551))+~P3(x14551,x14552,f2(x14551))+P3(x14551,f2(x14551),f23(x14551,x14552,x14553))
% 1.20/1.56 [1456]~P15(x14561)+~P3(x14561,x14563,f2(x14561))+~P3(x14561,x14562,f2(x14561))+P3(x14561,f2(x14561),f23(x14561,x14562,x14563))
% 1.20/1.56 [1457]~P59(x14571)+~P3(x14571,x14573,f2(x14571))+~P3(x14571,x14572,f2(x14571))+P3(x14571,f2(x14571),f11(x14571,x14572,x14573))
% 1.20/1.56 [1459]~P14(x14591)+~P2(x14591,f2(x14591),x14593)+~P2(x14591,f2(x14591),x14592)+P2(x14591,f2(x14591),f23(x14591,x14592,x14593))
% 1.20/1.56 [1460]~P15(x14601)+~P2(x14601,f2(x14601),x14602)+~P3(x14601,f2(x14601),x14603)+P2(x14601,f2(x14601),f23(x14601,x14602,x14603))
% 1.20/1.56 [1461]~P59(x14611)+~P2(x14611,f2(x14611),x14613)+~P2(x14611,f2(x14611),x14612)+P2(x14611,f2(x14611),f11(x14611,x14612,x14613))
% 1.20/1.56 [1462]~P64(x14621)+~P2(x14621,f2(x14621),x14623)+~P2(x14621,f2(x14621),x14622)+P2(x14621,f2(x14621),f11(x14621,x14622,x14623))
% 1.20/1.56 [1463]~P65(x14631)+~P2(x14631,f2(x14631),x14633)+~P2(x14631,f2(x14631),x14632)+P2(x14631,f2(x14631),f11(x14631,x14632,x14633))
% 1.20/1.56 [1466]~P31(x14661)+~P3(x14661,f2(x14661),x14663)+~P3(x14661,f2(x14661),x14662)+P3(x14661,f2(x14661),f10(x14661,x14662,x14663))
% 1.20/1.56 [1467]~P14(x14671)+~P3(x14671,f2(x14671),x14673)+~P3(x14671,f2(x14671),x14672)+P3(x14671,f2(x14671),f23(x14671,x14672,x14673))
% 1.20/1.56 [1468]~P15(x14681)+~P3(x14681,f2(x14681),x14683)+~P3(x14681,f2(x14681),x14682)+P3(x14681,f2(x14681),f23(x14681,x14682,x14683))
% 1.20/1.56 [1469]~P62(x14691)+~P3(x14691,f2(x14691),x14693)+~P3(x14691,f2(x14691),x14692)+P3(x14691,f2(x14691),f11(x14691,x14692,x14693))
% 1.20/1.56 [1470]~P57(x14701)+~P3(x14701,f3(x14701),x14703)+~P3(x14701,f3(x14701),x14702)+P3(x14701,f3(x14701),f11(x14701,x14702,x14703))
% 1.20/1.56 [1471]~P31(x14711)+~P2(x14711,x14713,f2(x14711))+~P2(x14711,x14712,f2(x14711))+P2(x14711,f10(x14711,x14712,x14713),f2(x14711))
% 1.20/1.56 [1472]~P31(x14721)+~P2(x14721,x14723,f2(x14721))+~P3(x14721,x14722,f2(x14721))+P3(x14721,f10(x14721,x14722,x14723),f2(x14721))
% 1.20/1.56 [1473]~P31(x14731)+~P2(x14731,x14732,f2(x14731))+~P3(x14731,x14733,f2(x14731))+P3(x14731,f10(x14731,x14732,x14733),f2(x14731))
% 1.20/1.56 [1474]~P31(x14741)+~P3(x14741,x14743,f2(x14741))+~P3(x14741,x14742,f2(x14741))+P3(x14741,f10(x14741,x14742,x14743),f2(x14741))
% 1.20/1.56 [1475]~P14(x14751)+~P2(x14751,x14753,f2(x14751))+~P2(x14751,f2(x14751),x14752)+P2(x14751,f23(x14751,x14752,x14753),f2(x14751))
% 1.20/1.56 [1476]~P14(x14761)+~P2(x14761,x14762,f2(x14761))+~P2(x14761,f2(x14761),x14763)+P2(x14761,f23(x14761,x14762,x14763),f2(x14761))
% 1.20/1.56 [1477]~P15(x14771)+~P2(x14771,x14772,f2(x14771))+~P3(x14771,f2(x14771),x14773)+P2(x14771,f23(x14771,x14772,x14773),f2(x14771))
% 1.20/1.56 [1478]~P15(x14781)+~P3(x14781,x14783,f2(x14781))+~P2(x14781,f2(x14781),x14782)+P2(x14781,f23(x14781,x14782,x14783),f2(x14781))
% 1.20/1.56 [1480]~P59(x14801)+~P2(x14801,x14803,f2(x14801))+~P2(x14801,f2(x14801),x14802)+P2(x14801,f11(x14801,x14802,x14803),f2(x14801))
% 1.20/1.56 [1481]~P59(x14811)+~P2(x14811,x14812,f2(x14811))+~P2(x14811,f2(x14811),x14813)+P2(x14811,f11(x14811,x14812,x14813),f2(x14811))
% 1.20/1.56 [1483]~P64(x14831)+~P2(x14831,x14833,f2(x14831))+~P2(x14831,f2(x14831),x14832)+P2(x14831,f11(x14831,x14832,x14833),f2(x14831))
% 1.20/1.56 [1485]~P64(x14851)+~P2(x14851,x14852,f2(x14851))+~P2(x14851,f2(x14851),x14853)+P2(x14851,f11(x14851,x14852,x14853),f2(x14851))
% 1.20/1.56 [1486]~P14(x14861)+~P3(x14861,x14863,f2(x14861))+~P3(x14861,f2(x14861),x14862)+P3(x14861,f23(x14861,x14862,x14863),f2(x14861))
% 1.20/1.56 [1487]~P14(x14871)+~P3(x14871,x14872,f2(x14871))+~P3(x14871,f2(x14871),x14873)+P3(x14871,f23(x14871,x14872,x14873),f2(x14871))
% 1.20/1.56 [1488]~P15(x14881)+~P3(x14881,x14883,f2(x14881))+~P3(x14881,f2(x14881),x14882)+P3(x14881,f23(x14881,x14882,x14883),f2(x14881))
% 1.20/1.56 [1489]~P15(x14891)+~P3(x14891,x14892,f2(x14891))+~P3(x14891,f2(x14891),x14893)+P3(x14891,f23(x14891,x14892,x14893),f2(x14891))
% 1.20/1.56 [1491]~P62(x14911)+~P3(x14911,x14913,f2(x14911))+~P3(x14911,f2(x14911),x14912)+P3(x14911,f11(x14911,x14912,x14913),f2(x14911))
% 1.20/1.56 [1492]~P62(x14921)+~P3(x14921,x14922,f2(x14921))+~P3(x14921,f2(x14921),x14923)+P3(x14921,f11(x14921,x14922,x14923),f2(x14921))
% 1.20/1.56 [1499]~P14(x14991)+~P2(x14991,f23(x14991,x14993,x14992),f2(x14991))+P2(x14991,x14992,f2(x14991))+P2(x14991,x14993,f2(x14991))
% 1.20/1.56 [1500]~P59(x15001)+~P2(x15001,f11(x15001,x15003,x15002),f2(x15001))+P2(x15001,x15002,f2(x15001))+P2(x15001,x15003,f2(x15001))
% 1.20/1.56 [1501]~P14(x15011)+~P3(x15011,f23(x15011,x15013,x15012),f2(x15011))+P3(x15011,x15012,f2(x15011))+P3(x15011,x15013,f2(x15011))
% 1.20/1.56 [1502]~P14(x15021)+~P2(x15021,f2(x15021),f23(x15021,x15023,x15022))+P2(x15021,x15022,f2(x15021))+P2(x15021,f2(x15021),x15023)
% 1.20/1.56 [1503]~P14(x15031)+~P2(x15031,f2(x15031),f23(x15031,x15032,x15033))+P2(x15031,x15032,f2(x15031))+P2(x15031,f2(x15031),x15033)
% 1.20/1.56 [1504]~P59(x15041)+~P2(x15041,f2(x15041),f11(x15041,x15043,x15042))+P2(x15041,x15042,f2(x15041))+P2(x15041,f2(x15041),x15043)
% 1.20/1.56 [1505]~P59(x15051)+~P2(x15051,f2(x15051),f11(x15051,x15052,x15053))+P2(x15051,x15052,f2(x15051))+P2(x15051,f2(x15051),x15053)
% 1.20/1.56 [1506]~P14(x15061)+P2(x15061,f2(x15061),x15062)+~P2(x15061,f2(x15061),f23(x15061,x15063,x15062))+P2(x15061,x15062,f2(x15061))
% 1.20/1.56 [1507]~P14(x15071)+P2(x15071,f2(x15071),x15072)+~P2(x15071,f2(x15071),f23(x15071,x15072,x15073))+P2(x15071,x15072,f2(x15071))
% 1.20/1.56 [1508]~P59(x15081)+P2(x15081,f2(x15081),x15082)+~P2(x15081,f2(x15081),f11(x15081,x15083,x15082))+P2(x15081,x15082,f2(x15081))
% 1.20/1.56 [1509]~P59(x15091)+P2(x15091,f2(x15091),x15092)+~P2(x15091,f2(x15091),f11(x15091,x15092,x15093))+P2(x15091,x15092,f2(x15091))
% 1.20/1.56 [1510]~P14(x15101)+~P3(x15101,f2(x15101),f23(x15101,x15103,x15102))+P3(x15101,x15102,f2(x15101))+P3(x15101,f2(x15101),x15103)
% 1.20/1.56 [1511]~P14(x15111)+~P3(x15111,f2(x15111),f23(x15111,x15112,x15113))+P3(x15111,x15112,f2(x15111))+P3(x15111,f2(x15111),x15113)
% 1.20/1.56 [1512]~P14(x15121)+P3(x15121,f2(x15121),x15122)+~P3(x15121,f2(x15121),f23(x15121,x15123,x15122))+P3(x15121,x15122,f2(x15121))
% 1.20/1.56 [1513]~P14(x15131)+P3(x15131,f2(x15131),x15132)+~P3(x15131,f2(x15131),f23(x15131,x15132,x15133))+P3(x15131,x15132,f2(x15131))
% 1.20/1.56 [1514]~P14(x15141)+P2(x15141,f2(x15141),x15142)+~P2(x15141,f23(x15141,x15143,x15142),f2(x15141))+P2(x15141,x15142,f2(x15141))
% 1.20/1.56 [1515]~P14(x15151)+P2(x15151,f2(x15151),x15152)+~P2(x15151,f23(x15151,x15152,x15153),f2(x15151))+P2(x15151,x15152,f2(x15151))
% 1.20/1.56 [1516]~P59(x15161)+P2(x15161,f2(x15161),x15162)+~P2(x15161,f11(x15161,x15163,x15162),f2(x15161))+P2(x15161,x15162,f2(x15161))
% 1.20/1.56 [1517]~P59(x15171)+P2(x15171,f2(x15171),x15172)+~P2(x15171,f11(x15171,x15172,x15173),f2(x15171))+P2(x15171,x15172,f2(x15171))
% 1.20/1.56 [1518]~P14(x15181)+P3(x15181,f2(x15181),x15182)+~P3(x15181,f23(x15181,x15183,x15182),f2(x15181))+P3(x15181,x15182,f2(x15181))
% 1.20/1.56 [1519]~P14(x15191)+P3(x15191,f2(x15191),x15192)+~P3(x15191,f23(x15191,x15192,x15193),f2(x15191))+P3(x15191,x15192,f2(x15191))
% 1.20/1.56 [1520]~P14(x15201)+~P2(x15201,f23(x15201,x15202,x15203),f2(x15201))+P2(x15201,f2(x15201),x15202)+P2(x15201,f2(x15201),x15203)
% 1.20/1.56 [1521]~P59(x15211)+~P2(x15211,f11(x15211,x15212,x15213),f2(x15211))+P2(x15211,f2(x15211),x15212)+P2(x15211,f2(x15211),x15213)
% 1.20/1.56 [1522]~P14(x15221)+~P3(x15221,f23(x15221,x15222,x15223),f2(x15221))+P3(x15221,f2(x15221),x15222)+P3(x15221,f2(x15221),x15223)
% 1.20/1.56 [1546]~P62(x15461)+~P3(x15461,f2(x15461),f11(x15461,x15463,x15462))+P3(x15461,f2(x15461),x15462)+~P3(x15461,f2(x15461),x15463)
% 1.20/1.56 [1547]~P62(x15471)+~P3(x15471,f2(x15471),f11(x15471,x15472,x15473))+P3(x15471,f2(x15471),x15472)+~P3(x15471,f2(x15471),x15473)
% 1.20/1.56 [1657]~P2(a1,x16572,x16573)+P2(a1,f5(a1,x16571,x16572),f5(a1,x16571,x16573))+~P3(a1,x16571,f2(a1))+~P3(a1,f2(a1),x16572)
% 1.20/1.56 [1658]~P2(a1,x16583,x16582)+P2(a1,f5(a1,x16581,x16582),f5(a1,x16581,x16583))+~P2(a1,f2(a1),x16581)+~P3(a1,f2(a1),x16583)
% 1.20/1.56 [1704]~P2(a75,x17043,x17041)+P2(a75,x17041,x17042)+~P2(a75,x17043,x17042)+~P2(a75,f8(a75,x17041,x17043),f8(a75,x17042,x17043))
% 1.20/1.56 [1705]~P2(a75,x17053,x17051)+P3(a75,x17051,x17052)+~P2(a75,x17053,x17052)+~P3(a75,f8(a75,x17051,x17053),f8(a75,x17052,x17053))
% 1.20/1.56 [1033]~P50(x10332)+~E(f18(x10332,x10333,x10331),f2(a75))+~E(f63(f17(x10332,x10331),x10333),f2(x10332))+E(x10331,f2(f76(x10332)))
% 1.20/1.56 [1245]~P53(x12452)+E(x12451,f2(x12452))+E(x12453,f2(x12452))+E(f11(x12452,f21(x12452,x12451),f21(x12452,x12453)),f21(x12452,f11(x12452,x12453,x12451)))
% 1.20/1.56 [1303]~P59(x13031)+~E(x13033,f2(x13031))+~E(x13032,f2(x13031))+E(f10(x13031,f11(x13031,x13032,x13032),f11(x13031,x13033,x13033)),f2(x13031))
% 1.20/1.56 [1496]~P45(x14961)+~P2(a74,x14963,f22(x14961,x14962))+~P3(a74,f2(a74),x14963)+P2(a74,f22(x14961,f21(x14961,x14962)),f21(a74,x14963))
% 1.20/1.56 [1695]~P53(x16952)+E(x16951,f2(x16952))+E(x16953,f2(x16952))+E(f11(x16952,f11(x16952,f21(x16952,x16953),f10(x16952,x16953,x16951)),f21(x16952,x16951)),f10(x16952,f21(x16952,x16953),f21(x16952,x16951)))
% 1.20/1.56 [1696]~P53(x16962)+E(x16961,f2(x16962))+E(x16963,f2(x16962))+E(f11(x16962,f11(x16962,f21(x16962,x16963),f8(x16962,x16961,x16963)),f21(x16962,x16961)),f8(x16962,f21(x16962,x16963),f21(x16962,x16961)))
% 1.20/1.56 [1697]~P13(x16972)+E(x16971,f2(x16972))+E(x16973,f2(x16972))+E(f11(x16972,f11(x16972,f10(x16972,x16973,x16971),f21(x16972,x16973)),f21(x16972,x16971)),f10(x16972,f21(x16972,x16973),f21(x16972,x16971)))
% 1.20/1.56 [1525]~P3(a74,x15251,x15253)+P3(a74,x15251,a85)+~P2(a74,f22(a14,x15252),a81)+~E(f22(a14,f63(f17(a14,a82),x15252)),f9(a74,x15253))
% 1.20/1.56 [1526]~P3(a74,x15261,x15263)+P3(a74,x15261,a37)+~P2(a74,f22(a14,x15262),a81)+~E(f22(a14,f63(f17(a14,a82),x15262)),f9(a74,x15263))
% 1.20/1.56 [1764]~P53(x17642)+E(x17641,f2(x17642))+E(x17643,f2(x17642))+E(f9(x17642,f11(x17642,f11(x17642,f21(x17642,x17643),f8(x17642,x17643,x17641)),f21(x17642,x17641))),f8(x17642,f21(x17642,x17643),f21(x17642,x17641)))
% 1.20/1.56 [1203]~P40(x12031)+~P2(x12031,x12034,x12033)+P2(x12031,x12032,x12033)+~P2(x12031,x12032,x12034)
% 1.20/1.56 [1204]~P29(x12041)+~P2(x12041,x12042,x12044)+P2(x12041,x12042,x12043)+~P2(x12041,x12044,x12043)
% 1.20/1.56 [1205]~P40(x12051)+~P3(x12051,x12054,x12053)+P3(x12051,x12052,x12053)+~P2(x12051,x12052,x12054)
% 1.20/1.56 [1206]~P40(x12061)+~P3(x12061,x12062,x12064)+P3(x12061,x12062,x12063)+~P2(x12061,x12064,x12063)
% 1.20/1.56 [1207]~P40(x12071)+~P3(x12071,x12074,x12073)+P3(x12071,x12072,x12073)+~P3(x12071,x12072,x12074)
% 1.20/1.56 [1208]~P29(x12081)+~P3(x12081,x12082,x12084)+P3(x12081,x12082,x12083)+~P2(x12081,x12084,x12083)
% 1.20/1.56 [1209]~P29(x12091)+~P3(x12091,x12094,x12093)+P3(x12091,x12092,x12093)+~P2(x12091,x12092,x12094)
% 1.20/1.56 [1210]~P29(x12101)+~P3(x12101,x12102,x12104)+P3(x12101,x12102,x12103)+~P3(x12101,x12104,x12103)
% 1.20/1.56 [789]~P11(x7892)+~E(x7894,f2(x7892))+~E(x7891,f2(x7892))+E(x7891,f23(x7892,x7893,x7894))
% 1.20/1.56 [790]~P11(x7901)+~E(x7903,f2(x7901))+~E(x7904,f2(x7901))+E(f23(x7901,x7902,x7903),x7904)
% 1.20/1.56 [880]~P11(x8802)+E(x8801,f2(x8802))+~E(x8801,f23(x8802,x8804,x8803))+~E(x8803,f2(x8802))
% 1.20/1.56 [881]~P11(x8812)+E(x8811,f2(x8812))+~E(f23(x8812,x8814,x8813),x8811)+~E(x8813,f2(x8812))
% 1.20/1.56 [990]~P53(x9902)+~E(f23(x9902,x9903,x9901),x9904)+E(x9901,f2(x9902))+E(x9903,f11(x9902,x9904,x9901))
% 1.20/1.56 [991]~P53(x9912)+~E(f11(x9912,x9913,x9911),x9914)+E(x9911,f2(x9912))+E(x9913,f23(x9912,x9914,x9911))
% 1.20/1.56 [992]~P11(x9922)+~E(f11(x9922,x9923,x9921),x9924)+E(x9921,f2(x9922))+E(x9923,f23(x9922,x9924,x9921))
% 1.20/1.56 [993]~P11(x9932)+~E(f23(x9932,x9933,x9931),x9934)+E(x9931,f2(x9932))+E(x9933,f11(x9932,x9934,x9931))
% 1.20/1.56 [995]~P53(x9952)+~E(x9953,f11(x9952,x9954,x9951))+E(x9951,f2(x9952))+E(f23(x9952,x9953,x9951),x9954)
% 1.20/1.56 [996]~P11(x9962)+~E(x9963,f11(x9962,x9964,x9961))+E(x9961,f2(x9962))+E(f23(x9962,x9963,x9961),x9964)
% 1.20/1.56 [997]~P11(x9972)+~E(x9973,f23(x9972,x9974,x9971))+E(x9971,f2(x9972))+E(f11(x9972,x9973,x9971),x9974)
% 1.20/1.56 [999]~P11(x9992)+~E(x9991,f2(x9992))+~E(f11(x9992,x9991,x9994),x9993)+E(x9991,f23(x9992,x9993,x9994))
% 1.20/1.56 [1000]~P11(x10001)+~E(x10004,f2(x10001))+~E(x10002,f11(x10001,x10004,x10003))+E(f23(x10001,x10002,x10003),x10004)
% 1.20/1.56 [1175]~P40(x11751)+~P4(x11751,x11752)+~P2(a75,x11754,x11753)+P2(x11751,f63(x11752,x11753),f63(x11752,x11754))
% 1.20/1.56 [1300]~P41(x13002)+P3(f79(x13001,x13002),x13004,x13003)+~P2(f79(x13001,x13002),x13004,x13003)+P2(f79(x13001,x13002),x13003,x13004)
% 1.20/1.56 [1429]~P31(x14291)+~P2(x14291,x14292,x14293)+~P2(x14291,f2(x14291),x14294)+P2(x14291,x14292,f10(x14291,x14293,x14294))
% 1.20/1.56 [1430]~P31(x14301)+~P2(x14301,x14302,x14304)+~P2(x14301,f2(x14301),x14303)+P2(x14301,x14302,f10(x14301,x14303,x14304))
% 1.20/1.56 [1431]~P31(x14311)+~P2(x14311,x14312,x14314)+~P3(x14311,f2(x14311),x14313)+P3(x14311,x14312,f10(x14311,x14313,x14314))
% 1.20/1.56 [1432]~P31(x14321)+~P3(x14321,x14322,x14324)+~P2(x14321,f2(x14321),x14323)+P3(x14321,x14322,f10(x14321,x14323,x14324))
% 1.20/1.56 [1433]~P57(x14331)+~P3(x14331,x14332,x14334)+~P3(x14331,f2(x14331),x14333)+P3(x14331,x14332,f10(x14331,x14333,x14334))
% 1.20/1.56 [1589]~P14(x15891)+~P2(x15891,x15894,x15892)+~P2(x15891,x15893,f2(x15891))+P2(x15891,f23(x15891,x15892,x15893),f23(x15891,x15894,x15893))
% 1.20/1.56 [1590]~P65(x15901)+~P2(x15901,x15904,x15903)+~P2(x15901,x15902,f2(x15901))+P2(x15901,f11(x15901,x15902,x15903),f11(x15901,x15902,x15904))
% 1.20/1.56 [1591]~P65(x15911)+~P2(x15911,x15914,x15912)+~P2(x15911,x15913,f2(x15911))+P2(x15911,f11(x15911,x15912,x15913),f11(x15911,x15914,x15913))
% 1.20/1.56 [1592]~P15(x15921)+~P3(x15921,x15924,x15922)+~P3(x15921,x15923,f2(x15921))+P3(x15921,f23(x15921,x15922,x15923),f23(x15921,x15924,x15923))
% 1.20/1.56 [1596]~P59(x15961)+~P3(x15961,x15964,x15962)+~P3(x15961,x15963,f2(x15961))+P3(x15961,f11(x15961,x15962,x15963),f11(x15961,x15964,x15963))
% 1.20/1.56 [1597]~P59(x15971)+~P3(x15971,x15974,x15973)+~P3(x15971,x15972,f2(x15971))+P3(x15971,f11(x15971,x15972,x15973),f11(x15971,x15972,x15974))
% 1.20/1.56 [1598]~P14(x15981)+~P2(x15981,x15982,x15984)+~P2(x15981,f2(x15981),x15983)+P2(x15981,f23(x15981,x15982,x15983),f23(x15981,x15984,x15983))
% 1.20/1.56 [1599]~P67(x15991)+~P2(x15991,x15993,x15994)+~P2(x15991,f2(x15991),x15992)+P2(x15991,f11(x15991,x15992,x15993),f11(x15991,x15992,x15994))
% 1.20/1.56 [1600]~P66(x16001)+~P2(x16001,x16003,x16004)+~P2(x16001,f2(x16001),x16002)+P2(x16001,f11(x16001,x16002,x16003),f11(x16001,x16002,x16004))
% 1.20/1.56 [1601]~P67(x16011)+~P2(x16011,x16012,x16014)+~P2(x16011,f2(x16011),x16013)+P2(x16011,f11(x16011,x16012,x16013),f11(x16011,x16014,x16013))
% 1.20/1.56 [1602]~P15(x16021)+~P3(x16021,x16022,x16024)+~P3(x16021,f2(x16021),x16023)+P3(x16021,f23(x16021,x16022,x16023),f23(x16021,x16024,x16023))
% 1.20/1.56 [1604]~P55(x16041)+~P3(x16041,x16043,x16044)+~P3(x16041,f2(x16041),x16042)+P3(x16041,f11(x16041,x16042,x16043),f11(x16041,x16042,x16044))
% 1.20/1.56 [1605]~P62(x16051)+~P3(x16051,x16053,x16054)+~P3(x16051,f2(x16051),x16052)+P3(x16051,f11(x16051,x16052,x16053),f11(x16051,x16052,x16054))
% 1.20/1.56 [1606]~P59(x16061)+~P3(x16061,x16062,x16064)+~P3(x16061,f2(x16061),x16063)+P3(x16061,f11(x16061,x16062,x16063),f11(x16061,x16064,x16063))
% 1.20/1.56 [1607]~P62(x16071)+~P3(x16071,x16072,x16074)+~P3(x16071,f2(x16071),x16073)+P3(x16071,f11(x16071,x16072,x16073),f11(x16071,x16074,x16073))
% 1.20/1.56 [1608]~P59(x16081)+~P3(x16081,x16083,x16084)+~P3(x16081,f2(x16081),x16082)+P3(x16081,f11(x16081,x16082,x16083),f11(x16081,x16082,x16084))
% 1.20/1.56 [1664]P3(x16641,x16643,x16642)+~P59(x16641)+P3(x16641,x16642,x16643)+~P3(x16641,f11(x16641,x16644,x16642),f11(x16641,x16644,x16643))
% 1.20/1.56 [1665]P3(x16651,x16653,x16652)+~P59(x16651)+P3(x16651,x16652,x16653)+~P3(x16651,f11(x16651,x16652,x16654),f11(x16651,x16653,x16654))
% 1.20/1.56 [1668]~P59(x16681)+P3(x16681,x16682,x16683)+~P3(x16681,f11(x16681,x16682,x16684),f11(x16681,x16683,x16684))+P3(x16681,x16684,f2(x16681))
% 1.20/1.56 [1669]~P59(x16691)+P3(x16691,x16692,x16693)+~P3(x16691,f11(x16691,x16694,x16692),f11(x16691,x16694,x16693))+P3(x16691,x16694,f2(x16691))
% 1.20/1.56 [1670]~P59(x16701)+P3(x16701,x16702,x16703)+~P3(x16701,f11(x16701,x16704,x16703),f11(x16701,x16704,x16702))+P3(x16701,f2(x16701),x16704)
% 1.20/1.56 [1671]~P59(x16711)+P3(x16711,x16712,x16713)+~P3(x16711,f11(x16711,x16713,x16714),f11(x16711,x16712,x16714))+P3(x16711,f2(x16711),x16714)
% 1.20/1.56 [1674]~P59(x16741)+P3(x16741,f2(x16741),x16742)+~P3(x16741,f11(x16741,x16743,x16742),f11(x16741,x16744,x16742))+P3(x16741,x16742,f2(x16741))
% 1.20/1.56 [1675]~P59(x16751)+P3(x16751,f2(x16751),x16752)+~P3(x16751,f11(x16751,x16752,x16753),f11(x16751,x16752,x16754))+P3(x16751,x16752,f2(x16751))
% 1.20/1.56 [1698]~P59(x16981)+P3(x16981,x16982,x16983)+~P3(x16981,f11(x16981,x16984,x16983),f11(x16981,x16984,x16982))+~P3(x16981,x16984,f2(x16981))
% 1.20/1.56 [1699]~P59(x16991)+P3(x16991,x16992,x16993)+~P3(x16991,f11(x16991,x16994,x16992),f11(x16991,x16994,x16993))+~P3(x16991,f2(x16991),x16994)
% 1.20/1.56 [1751]~P54(x17511)+~P3(x17511,x17512,f10(x17511,x17513,x17514))+~P3(x17511,f8(x17511,x17513,x17514),x17512)+P3(x17511,f4(x17511,f8(x17511,x17512,x17513)),x17514)
% 1.20/1.56 [1780]~P5(x17801)+~P3(a74,f2(a74),x17804)+~P2(a74,f22(x17801,f63(x17802,f53(x17802,x17801,x17804))),x17804)+P2(a74,f22(x17801,f63(x17802,x17803)),f20(a75,f10(a75,f52(x17802,x17801),f3(a75))))
% 1.20/1.56 [1781]~P5(x17811)+~P3(a74,f2(a74),x17814)+~P2(a74,f22(x17811,f63(x17812,f47(x17812,x17811,x17814))),x17814)+P3(a74,f22(x17811,f63(x17812,x17813)),f20(a75,f10(a75,f46(x17812,x17811),f3(a75))))
% 1.20/1.56 [1785]~P44(x17852)+E(x17851,f2(x17852))+E(x17853,f2(x17852))+E(f9(x17852,f11(x17852,f11(x17852,f21(x17852,x17853),f23(x17852,f8(x17852,x17853,x17851),x17854)),f21(x17852,x17851))),f23(x17852,f8(x17852,f21(x17852,x17853),f21(x17852,x17851)),x17854))
% 1.20/1.56 [1784]~P3(a74,f2(a74),x17844)+~P3(a74,f22(a14,f8(a14,x17842,x17843)),f62(x17841,x17843,x17844))+~P3(a74,f2(a74),f22(a14,f8(a14,x17842,x17843)))+P3(a74,f22(a14,f8(a14,f63(f17(a14,x17841),x17842),f63(f17(a14,x17841),x17843))),x17844)
% 1.20/1.56 [1078]~P10(x10785)+E(x10781,x10782)+~E(x10783,x10784)+~E(f8(x10785,x10783,x10784),f8(x10785,x10781,x10782))
% 1.20/1.56 [1354]~P18(x13541)+~P2(x13541,x13544,x13545)+P2(x13541,x13542,x13543)+~E(f8(x13541,x13544,x13545),f8(x13541,x13542,x13543))
% 1.20/1.56 [1356]~P18(x13561)+~P3(x13561,x13564,x13565)+P3(x13561,x13562,x13563)+~E(f8(x13561,x13564,x13565),f8(x13561,x13562,x13563))
% 1.20/1.56 [1575]~P28(x15751)+~P2(x15751,x15753,x15755)+~P2(x15751,x15752,x15754)+P2(x15751,f10(x15751,x15752,x15753),f10(x15751,x15754,x15755))
% 1.20/1.56 [1576]~P32(x15761)+~P2(x15761,x15763,x15765)+~P3(x15761,x15762,x15764)+P3(x15761,f10(x15761,x15762,x15763),f10(x15761,x15764,x15765))
% 1.20/1.56 [1577]~P32(x15771)+~P2(x15771,x15772,x15774)+~P3(x15771,x15773,x15775)+P3(x15771,f10(x15771,x15772,x15773),f10(x15771,x15774,x15775))
% 1.20/1.56 [1578]~P32(x15781)+~P3(x15781,x15783,x15785)+~P3(x15781,x15782,x15784)+P3(x15781,f10(x15781,x15782,x15783),f10(x15781,x15784,x15785))
% 1.20/1.56 [1717]~P5(x17171)+~P3(a74,f22(x17171,x17173),x17175)+~P3(a74,f22(x17171,x17172),x17174)+P3(a74,f22(x17171,f10(x17171,x17172,x17173)),f10(a74,x17174,x17175))
% 1.20/1.56 [1718]~P43(x17181)+~P3(a74,f22(x17181,x17183),x17185)+~P3(a74,f22(x17181,x17182),x17184)+P3(a74,f22(x17181,f11(x17181,x17182,x17183)),f11(a74,x17184,x17185))
% 1.20/1.56 [1755]~P70(x17555)+E(x17551,x17552)+E(x17553,x17554)+~E(f10(x17555,f11(x17555,x17553,x17551),f11(x17555,x17554,x17552)),f10(x17555,f11(x17555,x17553,x17552),f11(x17555,x17554,x17551)))
% 1.20/1.56 [1771]~E(f22(a14,x17711),f3(a74))+P3(a74,f22(a14,f8(a14,x17711,a6)),f3(a74))+P3(a74,f22(a14,f10(a14,x17711,a6)),f3(a74))+P3(a74,f22(a14,f10(a14,x17711,f3(a14))),f3(a74))+P3(a74,f22(a14,f8(a14,x17711,f3(a14))),f3(a74))
% 1.20/1.56 [732]~P53(x7323)+E(x7321,x7322)+~E(f21(x7323,x7321),f21(x7323,x7322))+E(x7322,f2(x7323))+E(x7321,f2(x7323))
% 1.20/1.56 [1308]~P31(x13082)+~P2(x13082,f2(x13082),x13083)+~P2(x13082,f2(x13082),x13081)+~E(f10(x13082,x13083,x13081),f2(x13082))+E(x13081,f2(x13082))
% 1.20/1.56 [1309]~P31(x13092)+~P2(x13092,f2(x13092),x13093)+~P2(x13092,f2(x13092),x13091)+~E(f10(x13092,x13091,x13093),f2(x13092))+E(x13091,f2(x13092))
% 1.20/1.56 [1313]~P13(x13132)+~E(f11(x13132,x13134,x13133),f11(x13132,x13135,x13131))+E(f23(x13132,x13134,x13131),f23(x13132,x13135,x13133))+E(x13131,f2(x13132))+E(x13133,f2(x13132))
% 1.20/1.56 [1314]~P13(x13142)+~E(f23(x13142,x13144,x13143),f23(x13142,x13145,x13141))+E(f11(x13142,x13144,x13141),f11(x13142,x13145,x13143))+E(x13141,f2(x13142))+E(x13143,f2(x13142))
% 1.20/1.56 [1765]~P5(x17654)+~P41(x17651)+~P2(x17651,x17652,x17655)+P2(x17651,x17652,f43(x17653,x17652,x17651,x17654))+P3(a74,f22(x17654,f63(x17653,x17655)),f10(a74,f3(a74),f22(x17654,f63(x17653,x17652))))
% 1.20/1.56 [1799]~P5(x17991)+~P2(x17995,x17994,x17993)+~P41(x17995)+P3(a74,f22(x17991,f63(x17992,x17993)),f10(a74,f3(a74),f22(x17991,f63(x17992,x17994))))+~P3(a74,f22(x17991,f8(x17991,f63(x17992,x17994),f63(x17992,f43(x17992,x17994,x17995,x17991)))),f3(a74))
% 1.20/1.56 [1659]~P70(x16594)+E(x16591,x16592)+~E(x16595,x16596)+E(x16593,f2(x16594))+~E(f10(x16594,x16595,f11(x16594,x16593,x16591)),f10(x16594,x16596,f11(x16594,x16593,x16592)))
% 1.20/1.56 [1291]~P31(x12911)+~P2(x12911,f2(x12911),x12913)+~P2(x12911,f2(x12911),x12912)+~E(x12913,f2(x12911))+~E(x12912,f2(x12911))+E(f10(x12911,x12912,x12913),f2(x12911))
% 1.20/1.56 [1708]~P15(x17081)+~P2(x17081,x17085,x17083)+~P2(x17081,x17082,x17084)+~P2(x17081,f2(x17081),x17082)+~P3(x17081,f2(x17081),x17085)+P2(x17081,f23(x17081,x17082,x17083),f23(x17081,x17084,x17085))
% 1.20/1.56 [1709]~P67(x17091)+~P2(x17091,x17093,x17095)+~P2(x17091,x17092,x17094)+~P2(x17091,f2(x17091),x17093)+~P2(x17091,f2(x17091),x17094)+P2(x17091,f11(x17091,x17092,x17093),f11(x17091,x17094,x17095))
% 1.20/1.56 [1710]~P67(x17101)+~P2(x17101,x17103,x17105)+~P2(x17101,x17102,x17104)+~P2(x17101,f2(x17101),x17103)+~P2(x17101,f2(x17101),x17102)+P2(x17101,f11(x17101,x17102,x17103),f11(x17101,x17104,x17105))
% 1.20/1.56 [1711]~P15(x17111)+~P2(x17111,x17115,x17113)+~P3(x17111,x17112,x17114)+~P2(x17111,f2(x17111),x17112)+~P3(x17111,f2(x17111),x17115)+P3(x17111,f23(x17111,x17112,x17113),f23(x17111,x17114,x17115))
% 1.20/1.56 [1712]~P15(x17121)+~P2(x17121,x17122,x17124)+~P3(x17121,x17125,x17123)+~P3(x17121,f2(x17121),x17125)+~P3(x17121,f2(x17121),x17122)+P3(x17121,f23(x17121,x17122,x17123),f23(x17121,x17124,x17125))
% 1.20/1.56 %EqnAxiom
% 1.20/1.56 [1]E(x11,x11)
% 1.20/1.56 [2]E(x22,x21)+~E(x21,x22)
% 1.20/1.56 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.20/1.56 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 1.20/1.56 [5]~E(x51,x52)+E(f20(x51,x53),f20(x52,x53))
% 1.20/1.56 [6]~E(x61,x62)+E(f20(x63,x61),f20(x63,x62))
% 1.20/1.56 [7]~E(x71,x72)+E(f15(x71),f15(x72))
% 1.20/1.56 [8]~E(x81,x82)+E(f10(x81,x83,x84),f10(x82,x83,x84))
% 1.20/1.56 [9]~E(x91,x92)+E(f10(x93,x91,x94),f10(x93,x92,x94))
% 1.20/1.56 [10]~E(x101,x102)+E(f10(x103,x104,x101),f10(x103,x104,x102))
% 1.20/1.56 [11]~E(x111,x112)+E(f3(x111),f3(x112))
% 1.20/1.56 [12]~E(x121,x122)+E(f8(x121,x123,x124),f8(x122,x123,x124))
% 1.20/1.56 [13]~E(x131,x132)+E(f8(x133,x131,x134),f8(x133,x132,x134))
% 1.20/1.56 [14]~E(x141,x142)+E(f8(x143,x144,x141),f8(x143,x144,x142))
% 1.20/1.56 [15]~E(x151,x152)+E(f44(x151,x153),f44(x152,x153))
% 1.20/1.56 [16]~E(x161,x162)+E(f44(x163,x161),f44(x163,x162))
% 1.20/1.56 [17]~E(x171,x172)+E(f21(x171,x173),f21(x172,x173))
% 1.20/1.56 [18]~E(x181,x182)+E(f21(x183,x181),f21(x183,x182))
% 1.20/1.56 [19]~E(x191,x192)+E(f19(x191),f19(x192))
% 1.20/1.56 [20]~E(x201,x202)+E(f4(x201,x203),f4(x202,x203))
% 1.20/1.56 [21]~E(x211,x212)+E(f4(x213,x211),f4(x213,x212))
% 1.20/1.56 [22]~E(x221,x222)+E(f63(x221,x223),f63(x222,x223))
% 1.20/1.56 [23]~E(x231,x232)+E(f63(x233,x231),f63(x233,x232))
% 1.20/1.56 [24]~E(x241,x242)+E(f22(x241,x243),f22(x242,x243))
% 1.20/1.56 [25]~E(x251,x252)+E(f22(x253,x251),f22(x253,x252))
% 1.20/1.56 [26]~E(x261,x262)+E(f11(x261,x263,x264),f11(x262,x263,x264))
% 1.20/1.56 [27]~E(x271,x272)+E(f11(x273,x271,x274),f11(x273,x272,x274))
% 1.20/1.56 [28]~E(x281,x282)+E(f11(x283,x284,x281),f11(x283,x284,x282))
% 1.20/1.56 [29]~E(x291,x292)+E(f9(x291,x293),f9(x292,x293))
% 1.20/1.56 [30]~E(x301,x302)+E(f9(x303,x301),f9(x303,x302))
% 1.20/1.56 [31]~E(x311,x312)+E(f16(x311,x313),f16(x312,x313))
% 1.20/1.56 [32]~E(x321,x322)+E(f16(x323,x321),f16(x323,x322))
% 1.20/1.56 [33]~E(x331,x332)+E(f23(x331,x333,x334),f23(x332,x333,x334))
% 1.20/1.56 [34]~E(x341,x342)+E(f23(x343,x341,x344),f23(x343,x342,x344))
% 1.20/1.56 [35]~E(x351,x352)+E(f23(x353,x354,x351),f23(x353,x354,x352))
% 1.20/1.56 [36]~E(x361,x362)+E(f5(x361,x363,x364),f5(x362,x363,x364))
% 1.20/1.56 [37]~E(x371,x372)+E(f5(x373,x371,x374),f5(x373,x372,x374))
% 1.20/1.56 [38]~E(x381,x382)+E(f5(x383,x384,x381),f5(x383,x384,x382))
% 1.20/1.56 [39]~E(x391,x392)+E(f59(x391),f59(x392))
% 1.20/1.56 [40]~E(x401,x402)+E(f76(x401),f76(x402))
% 1.20/1.56 [41]~E(x411,x412)+E(f61(x411,x413),f61(x412,x413))
% 1.20/1.56 [42]~E(x421,x422)+E(f61(x423,x421),f61(x423,x422))
% 1.20/1.56 [43]~E(x431,x432)+E(f60(x431),f60(x432))
% 1.20/1.56 [44]~E(x441,x442)+E(f17(x441,x443),f17(x442,x443))
% 1.20/1.56 [45]~E(x451,x452)+E(f17(x453,x451),f17(x453,x452))
% 1.20/1.56 [46]~E(x461,x462)+E(f18(x461,x463,x464),f18(x462,x463,x464))
% 1.20/1.56 [47]~E(x471,x472)+E(f18(x473,x471,x474),f18(x473,x472,x474))
% 1.20/1.56 [48]~E(x481,x482)+E(f18(x483,x484,x481),f18(x483,x484,x482))
% 1.20/1.56 [49]~E(x491,x492)+E(f79(x491,x493),f79(x492,x493))
% 1.20/1.56 [50]~E(x501,x502)+E(f79(x503,x501),f79(x503,x502))
% 1.20/1.56 [51]~E(x511,x512)+E(f12(x511,x513),f12(x512,x513))
% 1.20/1.56 [52]~E(x521,x522)+E(f12(x523,x521),f12(x523,x522))
% 1.20/1.56 [53]~E(x531,x532)+E(f7(x531,x533),f7(x532,x533))
% 1.20/1.56 [54]~E(x541,x542)+E(f7(x543,x541),f7(x543,x542))
% 1.20/1.56 [55]~E(x551,x552)+E(f39(x551),f39(x552))
% 1.20/1.56 [56]~E(x561,x562)+E(f42(x561,x563),f42(x562,x563))
% 1.20/1.56 [57]~E(x571,x572)+E(f42(x573,x571),f42(x573,x572))
% 1.20/1.56 [58]~E(x581,x582)+E(f69(x581),f69(x582))
% 1.20/1.56 [59]~E(x591,x592)+E(f83(x591),f83(x592))
% 1.20/1.56 [60]~E(x601,x602)+E(f35(x601,x603),f35(x602,x603))
% 1.20/1.56 [61]~E(x611,x612)+E(f35(x613,x611),f35(x613,x612))
% 1.20/1.56 [62]~E(x621,x622)+E(f47(x621,x623,x624),f47(x622,x623,x624))
% 1.20/1.56 [63]~E(x631,x632)+E(f47(x633,x631,x634),f47(x633,x632,x634))
% 1.20/1.56 [64]~E(x641,x642)+E(f47(x643,x644,x641),f47(x643,x644,x642))
% 1.20/1.56 [65]~E(x651,x652)+E(f27(x651),f27(x652))
% 1.20/1.56 [66]~E(x661,x662)+E(f33(x661,x663,x664),f33(x662,x663,x664))
% 1.20/1.56 [67]~E(x671,x672)+E(f33(x673,x671,x674),f33(x673,x672,x674))
% 1.20/1.56 [68]~E(x681,x682)+E(f33(x683,x684,x681),f33(x683,x684,x682))
% 1.20/1.56 [69]~E(x691,x692)+E(f48(x691,x693),f48(x692,x693))
% 1.20/1.56 [70]~E(x701,x702)+E(f48(x703,x701),f48(x703,x702))
% 1.20/1.56 [71]~E(x711,x712)+E(f57(x711,x713),f57(x712,x713))
% 1.20/1.56 [72]~E(x721,x722)+E(f57(x723,x721),f57(x723,x722))
% 1.20/1.56 [73]~E(x731,x732)+E(f43(x731,x733,x734,x735),f43(x732,x733,x734,x735))
% 1.20/1.56 [74]~E(x741,x742)+E(f43(x743,x741,x744,x745),f43(x743,x742,x744,x745))
% 1.20/1.56 [75]~E(x751,x752)+E(f43(x753,x754,x751,x755),f43(x753,x754,x752,x755))
% 1.20/1.56 [76]~E(x761,x762)+E(f43(x763,x764,x765,x761),f43(x763,x764,x765,x762))
% 1.20/1.56 [77]~E(x771,x772)+E(f30(x771,x773,x774),f30(x772,x773,x774))
% 1.20/1.56 [78]~E(x781,x782)+E(f30(x783,x781,x784),f30(x783,x782,x784))
% 1.20/1.56 [79]~E(x791,x792)+E(f30(x793,x794,x791),f30(x793,x794,x792))
% 1.20/1.56 [80]~E(x801,x802)+E(f58(x801,x803),f58(x802,x803))
% 1.20/1.56 [81]~E(x811,x812)+E(f58(x813,x811),f58(x813,x812))
% 1.20/1.56 [82]~E(x821,x822)+E(f49(x821,x823,x824),f49(x822,x823,x824))
% 1.20/1.56 [83]~E(x831,x832)+E(f49(x833,x831,x834),f49(x833,x832,x834))
% 1.20/1.56 [84]~E(x841,x842)+E(f49(x843,x844,x841),f49(x843,x844,x842))
% 1.20/1.56 [85]~E(x851,x852)+E(f71(x851),f71(x852))
% 1.20/1.56 [86]~E(x861,x862)+E(f36(x861),f36(x862))
% 1.20/1.56 [87]~E(x871,x872)+E(f45(x871),f45(x872))
% 1.20/1.56 [88]~E(x881,x882)+E(f54(x881),f54(x882))
% 1.20/1.56 [89]~E(x891,x892)+E(f62(x891,x893,x894),f62(x892,x893,x894))
% 1.20/1.56 [90]~E(x901,x902)+E(f62(x903,x901,x904),f62(x903,x902,x904))
% 1.20/1.56 [91]~E(x911,x912)+E(f62(x913,x914,x911),f62(x913,x914,x912))
% 1.20/1.56 [92]~E(x921,x922)+E(f52(x921,x923),f52(x922,x923))
% 1.20/1.56 [93]~E(x931,x932)+E(f52(x933,x931),f52(x933,x932))
% 1.20/1.56 [94]~E(x941,x942)+E(f67(x941),f67(x942))
% 1.20/1.56 [95]~E(x951,x952)+E(f50(x951,x953),f50(x952,x953))
% 1.20/1.56 [96]~E(x961,x962)+E(f50(x963,x961),f50(x963,x962))
% 1.20/1.56 [97]~E(x971,x972)+E(f66(x971,x973),f66(x972,x973))
% 1.20/1.56 [98]~E(x981,x982)+E(f66(x983,x981),f66(x983,x982))
% 1.20/1.56 [99]~E(x991,x992)+E(f41(x991),f41(x992))
% 1.20/1.56 [100]~E(x1001,x1002)+E(f68(x1001,x1003,x1004,x1005),f68(x1002,x1003,x1004,x1005))
% 1.20/1.56 [101]~E(x1011,x1012)+E(f68(x1013,x1011,x1014,x1015),f68(x1013,x1012,x1014,x1015))
% 1.20/1.56 [102]~E(x1021,x1022)+E(f68(x1023,x1024,x1021,x1025),f68(x1023,x1024,x1022,x1025))
% 1.20/1.56 [103]~E(x1031,x1032)+E(f68(x1033,x1034,x1035,x1031),f68(x1033,x1034,x1035,x1032))
% 1.20/1.56 [104]~E(x1041,x1042)+E(f53(x1041,x1043,x1044),f53(x1042,x1043,x1044))
% 1.20/1.56 [105]~E(x1051,x1052)+E(f53(x1053,x1051,x1054),f53(x1053,x1052,x1054))
% 1.20/1.56 [106]~E(x1061,x1062)+E(f53(x1063,x1064,x1061),f53(x1063,x1064,x1062))
% 1.20/1.56 [107]~E(x1071,x1072)+E(f34(x1071),f34(x1072))
% 1.20/1.56 [108]~E(x1081,x1082)+E(f38(x1081),f38(x1082))
% 1.20/1.56 [109]~E(x1091,x1092)+E(f51(x1091,x1093,x1094),f51(x1092,x1093,x1094))
% 1.20/1.56 [110]~E(x1101,x1102)+E(f51(x1103,x1101,x1104),f51(x1103,x1102,x1104))
% 1.20/1.56 [111]~E(x1111,x1112)+E(f51(x1113,x1114,x1111),f51(x1113,x1114,x1112))
% 1.20/1.56 [112]~E(x1121,x1122)+E(f40(x1121),f40(x1122))
% 1.20/1.56 [113]~E(x1131,x1132)+E(f46(x1131,x1133),f46(x1132,x1133))
% 1.20/1.56 [114]~E(x1141,x1142)+E(f46(x1143,x1141),f46(x1143,x1142))
% 1.20/1.56 [115]~P1(x1151)+P1(x1152)+~E(x1151,x1152)
% 1.20/1.56 [116]~P5(x1161)+P5(x1162)+~E(x1161,x1162)
% 1.20/1.56 [117]P3(x1172,x1173,x1174)+~E(x1171,x1172)+~P3(x1171,x1173,x1174)
% 1.20/1.56 [118]P3(x1183,x1182,x1184)+~E(x1181,x1182)+~P3(x1183,x1181,x1184)
% 1.20/1.56 [119]P3(x1193,x1194,x1192)+~E(x1191,x1192)+~P3(x1193,x1194,x1191)
% 1.20/1.56 [120]~P6(x1201)+P6(x1202)+~E(x1201,x1202)
% 1.20/1.56 [121]P2(x1212,x1213,x1214)+~E(x1211,x1212)+~P2(x1211,x1213,x1214)
% 1.20/1.56 [122]P2(x1223,x1222,x1224)+~E(x1221,x1222)+~P2(x1223,x1221,x1224)
% 1.20/1.56 [123]P2(x1233,x1234,x1232)+~E(x1231,x1232)+~P2(x1233,x1234,x1231)
% 1.20/1.56 [124]~P7(x1241)+P7(x1242)+~E(x1241,x1242)
% 1.20/1.56 [125]~P22(x1251)+P22(x1252)+~E(x1251,x1252)
% 1.20/1.56 [126]~P71(x1261)+P71(x1262)+~E(x1261,x1262)
% 1.20/1.56 [127]~P47(x1271)+P47(x1272)+~E(x1271,x1272)
% 1.20/1.56 [128]~P8(x1281)+P8(x1282)+~E(x1281,x1282)
% 1.20/1.56 [129]~P35(x1291)+P35(x1292)+~E(x1291,x1292)
% 1.20/1.56 [130]~P27(x1301)+P27(x1302)+~E(x1301,x1302)
% 1.20/1.56 [131]~P54(x1311)+P54(x1312)+~E(x1311,x1312)
% 1.20/1.56 [132]~P9(x1321)+P9(x1322)+~E(x1321,x1322)
% 1.20/1.56 [133]~P18(x1331)+P18(x1332)+~E(x1331,x1332)
% 1.20/1.56 [134]~P59(x1341)+P59(x1342)+~E(x1341,x1342)
% 1.20/1.56 [135]~P29(x1351)+P29(x1352)+~E(x1351,x1352)
% 1.20/1.56 [136]~P10(x1361)+P10(x1362)+~E(x1361,x1362)
% 1.20/1.56 [137]~P15(x1371)+P15(x1372)+~E(x1371,x1372)
% 1.20/1.56 [138]~P43(x1381)+P43(x1382)+~E(x1381,x1382)
% 1.20/1.56 [139]~P37(x1391)+P37(x1392)+~E(x1391,x1392)
% 1.20/1.56 [140]~P53(x1401)+P53(x1402)+~E(x1401,x1402)
% 1.20/1.56 [141]~P55(x1411)+P55(x1412)+~E(x1411,x1412)
% 1.20/1.56 [142]~P28(x1421)+P28(x1422)+~E(x1421,x1422)
% 1.20/1.56 [143]~P40(x1431)+P40(x1432)+~E(x1431,x1432)
% 1.20/1.56 [144]~P44(x1441)+P44(x1442)+~E(x1441,x1442)
% 1.20/1.56 [145]~P14(x1451)+P14(x1452)+~E(x1451,x1452)
% 1.20/1.56 [146]~P65(x1461)+P65(x1462)+~E(x1461,x1462)
% 1.20/1.56 [147]~P19(x1471)+P19(x1472)+~E(x1471,x1472)
% 1.20/1.56 [148]~P36(x1481)+P36(x1482)+~E(x1481,x1482)
% 1.20/1.56 [149]~P62(x1491)+P62(x1492)+~E(x1491,x1492)
% 1.20/1.56 [150]~P20(x1501)+P20(x1502)+~E(x1501,x1502)
% 1.20/1.56 [151]~P52(x1511)+P52(x1512)+~E(x1511,x1512)
% 1.20/1.56 [152]~P70(x1521)+P70(x1522)+~E(x1521,x1522)
% 1.20/1.56 [153]~P13(x1531)+P13(x1532)+~E(x1531,x1532)
% 1.20/1.56 [154]~P46(x1541)+P46(x1542)+~E(x1541,x1542)
% 1.20/1.56 [155]~P51(x1551)+P51(x1552)+~E(x1551,x1552)
% 1.20/1.56 [156]~P21(x1561)+P21(x1562)+~E(x1561,x1562)
% 1.20/1.56 [157]~P32(x1571)+P32(x1572)+~E(x1571,x1572)
% 1.20/1.56 [158]~P12(x1581)+P12(x1582)+~E(x1581,x1582)
% 1.20/1.56 [159]~P31(x1591)+P31(x1592)+~E(x1591,x1592)
% 1.20/1.56 [160]~P11(x1601)+P11(x1602)+~E(x1601,x1602)
% 1.20/1.56 [161]~P16(x1611)+P16(x1612)+~E(x1611,x1612)
% 1.20/1.56 [162]~P60(x1621)+P60(x1622)+~E(x1621,x1622)
% 1.20/1.56 [163]~P30(x1631)+P30(x1632)+~E(x1631,x1632)
% 1.20/1.56 [164]~P64(x1641)+P64(x1642)+~E(x1641,x1642)
% 1.20/1.56 [165]~P42(x1651)+P42(x1652)+~E(x1651,x1652)
% 1.20/1.56 [166]~P38(x1661)+P38(x1662)+~E(x1661,x1662)
% 1.20/1.56 [167]~P23(x1671)+P23(x1672)+~E(x1671,x1672)
% 1.20/1.56 [168]~P67(x1681)+P67(x1682)+~E(x1681,x1682)
% 1.20/1.56 [169]~P69(x1691)+P69(x1692)+~E(x1691,x1692)
% 1.20/1.56 [170]~P39(x1701)+P39(x1702)+~E(x1701,x1702)
% 1.20/1.56 [171]~P50(x1711)+P50(x1712)+~E(x1711,x1712)
% 1.20/1.56 [172]~P45(x1721)+P45(x1722)+~E(x1721,x1722)
% 1.20/1.56 [173]~P58(x1731)+P58(x1732)+~E(x1731,x1732)
% 1.20/1.56 [174]~P66(x1741)+P66(x1742)+~E(x1741,x1742)
% 1.20/1.56 [175]~P57(x1751)+P57(x1752)+~E(x1751,x1752)
% 1.20/1.56 [176]~P41(x1761)+P41(x1762)+~E(x1761,x1762)
% 1.20/1.56 [177]~P63(x1771)+P63(x1772)+~E(x1771,x1772)
% 1.20/1.56 [178]~P17(x1781)+P17(x1782)+~E(x1781,x1782)
% 1.20/1.56 [179]~P68(x1791)+P68(x1792)+~E(x1791,x1792)
% 1.20/1.56 [180]~P34(x1801)+P34(x1802)+~E(x1801,x1802)
% 1.20/1.56 [181]~P48(x1811)+P48(x1812)+~E(x1811,x1812)
% 1.20/1.56 [182]~P33(x1821)+P33(x1822)+~E(x1821,x1822)
% 1.20/1.56 [183]~P26(x1831)+P26(x1832)+~E(x1831,x1832)
% 1.20/1.56 [184]~P24(x1841)+P24(x1842)+~E(x1841,x1842)
% 1.20/1.56 [185]P4(x1852,x1853)+~E(x1851,x1852)+~P4(x1851,x1853)
% 1.20/1.56 [186]P4(x1863,x1862)+~E(x1861,x1862)+~P4(x1863,x1861)
% 1.20/1.56 [187]~P49(x1871)+P49(x1872)+~E(x1871,x1872)
% 1.20/1.56 [188]~P61(x1881)+P61(x1882)+~E(x1881,x1882)
% 1.20/1.56 [189]~P56(x1891)+P56(x1892)+~E(x1891,x1892)
% 1.20/1.56 [190]~P25(x1901)+P25(x1902)+~E(x1901,x1902)
% 1.20/1.56
% 1.20/1.56 %-------------------------------------------
% 1.20/1.56 cnf(1827,plain,
% 1.20/1.56 (~P3(a75,f10(a75,x18271,x18272),x18272)),
% 1.20/1.56 inference(rename_variables,[],[583])).
% 1.20/1.56 cnf(1832,plain,
% 1.20/1.56 (P2(a75,x18321,f10(a75,x18322,x18321))),
% 1.20/1.56 inference(rename_variables,[],[465])).
% 1.20/1.56 cnf(1837,plain,
% 1.20/1.56 (P2(a1,x18371,x18371)),
% 1.20/1.56 inference(rename_variables,[],[418])).
% 1.20/1.56 cnf(1857,plain,
% 1.20/1.56 (~P3(a75,f10(a75,x18571,x18572),x18571)),
% 1.20/1.56 inference(rename_variables,[],[584])).
% 1.20/1.56 cnf(1862,plain,
% 1.20/1.56 (~P3(a75,f10(a75,x18621,x18622),x18622)),
% 1.20/1.56 inference(rename_variables,[],[583])).
% 1.20/1.56 cnf(1865,plain,
% 1.20/1.56 (~P3(a75,f10(a75,x18651,x18652),x18652)),
% 1.20/1.56 inference(rename_variables,[],[583])).
% 1.20/1.56 cnf(1868,plain,
% 1.20/1.56 (~P2(a75,f10(a75,x18681,f3(a75)),x18681)),
% 1.20/1.56 inference(rename_variables,[],[587])).
% 1.20/1.56 cnf(1877,plain,
% 1.20/1.56 (P2(a74,x18771,x18771)),
% 1.20/1.56 inference(rename_variables,[],[416])).
% 1.20/1.56 cnf(1892,plain,
% 1.20/1.56 (~P3(a74,f10(a74,f4(a74,x18921),f3(a74)),x18921)),
% 1.20/1.56 inference(rename_variables,[],[589])).
% 1.20/1.56 cnf(1899,plain,
% 1.20/1.56 (~E(f10(a1,x18991,x18991),f10(a1,f10(a1,f3(a1),x18992),x18992))),
% 1.20/1.56 inference(rename_variables,[],[591])).
% 1.20/1.56 cnf(1907,plain,
% 1.20/1.56 (P2(a74,x19071,f20(a75,f15(x19071)))),
% 1.20/1.56 inference(rename_variables,[],[449])).
% 1.20/1.56 cnf(1910,plain,
% 1.20/1.56 (P3(a74,x19101,f10(a74,f20(a75,f19(x19101)),f3(a74)))),
% 1.20/1.56 inference(rename_variables,[],[483])).
% 1.20/1.56 cnf(1920,plain,
% 1.20/1.56 (P2(a74,x19201,f20(a75,f15(x19201)))),
% 1.20/1.56 inference(rename_variables,[],[449])).
% 1.20/1.56 cnf(1929,plain,
% 1.20/1.56 (~E(f10(a75,x19291,f3(a75)),f2(a75))),
% 1.20/1.56 inference(rename_variables,[],[581])).
% 1.20/1.56 cnf(1943,plain,
% 1.20/1.56 (~E(f10(a75,x19431,f3(a75)),f2(a75))),
% 1.20/1.56 inference(rename_variables,[],[581])).
% 1.20/1.56 cnf(1954,plain,
% 1.20/1.56 ($false),
% 1.20/1.56 inference(scs_inference,[],[592,416,1877,417,418,1837,194,223,420,570,191,399,435,505,508,527,529,465,1832,468,583,1827,1862,1865,584,1857,449,1907,1920,472,587,1868,469,575,506,589,1892,486,581,1929,1943,483,1910,591,1899,543,559,2,931,871,839,817,816,811,713,829,836,1015,966,1404,1403,1342,1340,1336,1335,1332,1320,1319,1318,1250,1232,1231,1229,1227,1225,1171,1024,1004,941,1029,824,759,758,720,1267,10,9,1622,1612,1544,1543,1434,1420,1147,1145,1037,1036,1016,1013,953,1239,1296,1238,863,834,1364,1737]),
% 1.20/1.56 ['proof']).
% 1.20/1.56 % SZS output end Proof
% 1.20/1.56 % Total time :0.230000s
%------------------------------------------------------------------------------