TSTP Solution File: SWW225+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n025.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 00:13:13 EDT 2023
% Result : Theorem 2.75s 2.88s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 19:20:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 2.75/2.82 %-------------------------------------------
% 2.75/2.82 % File :CSE---1.6
% 2.75/2.82 % Problem :theBenchmark
% 2.75/2.82 % Transform :cnf
% 2.75/2.82 % Format :tptp:raw
% 2.75/2.82 % Command :java -jar mcs_scs.jar %d %s
% 2.75/2.82
% 2.75/2.82 % Result :Theorem 1.190000s
% 2.75/2.82 % Output :CNFRefutation 1.190000s
% 2.75/2.82 %-------------------------------------------
% 2.75/2.82 %------------------------------------------------------------------------------
% 2.75/2.82 % File : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% 2.75/2.82 % Domain : Software Verification
% 2.75/2.82 % Problem : Fundamental Theorem of Algebra 437364, 1000 axioms selected
% 2.75/2.82 % Version : Especial.
% 2.75/2.82 % English :
% 2.75/2.82
% 2.75/2.82 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 2.75/2.82 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 2.75/2.82 % Source : [Bla11]
% 2.75/2.82 % Names : fta_437364.1000.p [Bla11]
% 2.75/2.82
% 2.75/2.82 % Status : Theorem
% 2.75/2.82 % Rating : 0.39 v8.1.0, 0.33 v7.5.0, 0.38 v7.4.0, 0.30 v7.3.0, 0.38 v7.2.0, 0.34 v7.1.0, 0.39 v7.0.0, 0.37 v6.4.0, 0.38 v6.2.0, 0.44 v6.1.0, 0.50 v6.0.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.64 v5.3.0, 0.70 v5.2.0
% 2.75/2.82 % Syntax : Number of formulae : 1269 ( 409 unt; 0 def)
% 2.75/2.82 % Number of atoms : 2949 ( 715 equ)
% 2.75/2.82 % Maximal formula atoms : 13 ( 2 avg)
% 2.75/2.82 % Number of connectives : 1855 ( 175 ~; 56 |; 138 &)
% 2.75/2.82 % ( 238 <=>;1248 =>; 0 <=; 0 <~>)
% 2.75/2.82 % Maximal formula depth : 13 ( 4 avg)
% 2.75/2.82 % Maximal term depth : 7 ( 2 avg)
% 2.75/2.82 % Number of predicates : 76 ( 75 usr; 0 prp; 1-3 aty)
% 2.75/2.82 % Number of functors : 43 ( 43 usr; 14 con; 0-4 aty)
% 2.75/2.82 % Number of variables : 2639 (2601 !; 38 ?)
% 2.75/2.82 % SPC : FOF_THM_RFO_SEQ
% 2.75/2.82
% 2.75/2.82 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2.75/2.82 % 2011-03-01 11:39:21
% 2.75/2.82 %------------------------------------------------------------------------------
% 2.75/2.82 %----Relevant facts (995)
% 2.75/2.82 fof(fact_ext,axiom,
% 2.75/2.82 ! [V_ga_2,V_fa_2] :
% 2.75/2.82 ( ! [B_x] : hAPP(V_fa_2,B_x) = hAPP(V_ga_2,B_x)
% 2.75/2.82 => V_fa_2 = V_ga_2 ) ).
% 2.75/2.82
% 2.75/2.82 fof(fact_fz_I1_J,axiom,
% 2.75/2.82 c_SEQ_Osubseq(v_f____) ).
% 2.75/2.82
% 2.75/2.82 fof(fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096,axiom,
% 2.75/2.82 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____))) ).
% 2.75/2.82
% 2.75/2.82 fof(fact_order__refl,axiom,
% 2.75/2.82 ! [V_x,T_a] :
% 2.75/2.82 ( class_Orderings_Opreorder(T_a)
% 2.75/2.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 2.75/2.82
% 2.75/2.82 fof(fact_add__Suc__right,axiom,
% 2.75/2.82 ! [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)) ).
% 2.75/2.82
% 2.75/2.82 fof(fact_add__Suc,axiom,
% 2.75/2.82 ! [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)) ).
% 2.75/2.82
% 2.75/2.82 fof(fact_add__Suc__shift,axiom,
% 2.75/2.82 ! [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)) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__le__cancel__right,axiom,
% 2.75/2.83 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 2.75/2.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 2.75/2.83 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__le__cancel__left,axiom,
% 2.75/2.83 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.75/2.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 2.75/2.83 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__right__mono,axiom,
% 2.75/2.83 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.83 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__left__mono,axiom,
% 2.75/2.83 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.83 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__mono,axiom,
% 2.75/2.83 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.83 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__le__imp__le__right,axiom,
% 2.75/2.83 ! [V_b,V_c,V_a,T_a] :
% 2.75/2.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__le__imp__le__left,axiom,
% 2.75/2.83 ! [V_b,V_a,V_c,T_a] :
% 2.75/2.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__refl,axiom,
% 2.75/2.83 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_nat__le__linear,axiom,
% 2.75/2.83 ! [V_n,V_m] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.83 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_eq__imp__le,axiom,
% 2.75/2.83 ! [V_n,V_m] :
% 2.75/2.83 ( V_m = V_n
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__trans,axiom,
% 2.75/2.83 ! [V_k,V_j,V_i] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__antisym,axiom,
% 2.75/2.83 ! [V_n,V_m] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 2.75/2.83 => V_m = V_n ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_Suc__leD,axiom,
% 2.75/2.83 ! [V_n,V_m] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__SucE,axiom,
% 2.75/2.83 ! [V_n,V_m] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 2.75/2.83 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.83 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__SucI,axiom,
% 2.75/2.83 ! [V_n,V_m] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_Suc__le__mono,axiom,
% 2.75/2.83 ! [V_m_2,V_n_2] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
% 2.75/2.83 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__Suc__eq,axiom,
% 2.75/2.83 ! [V_n_2,V_m_2] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 2.75/2.83 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.83 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_not__less__eq__eq,axiom,
% 2.75/2.83 ! [V_n_2,V_m_2] :
% 2.75/2.83 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.83 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_Suc__n__not__le__n,axiom,
% 2.75/2.83 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__leE,axiom,
% 2.75/2.83 ! [V_n,V_k,V_m] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 2.75/2.83 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.83 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__leD1,axiom,
% 2.75/2.83 ! [V_n,V_k,V_m] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__leD2,axiom,
% 2.75/2.83 ! [V_n,V_k,V_m] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__le__mono,axiom,
% 2.75/2.83 ! [V_l,V_k,V_j,V_i] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__le__mono1,axiom,
% 2.75/2.83 ! [V_k,V_j,V_i] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_trans__le__add2,axiom,
% 2.75/2.83 ! [V_m,V_j,V_i] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_trans__le__add1,axiom,
% 2.75/2.83 ! [V_m,V_j,V_i] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_nat__add__left__cancel__le,axiom,
% 2.75/2.83 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 2.75/2.83 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__iff__add,axiom,
% 2.75/2.83 ! [V_n_2,V_m_2] :
% 2.75/2.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.83 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__add1,axiom,
% 2.75/2.83 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__add2,axiom,
% 2.75/2.83 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_linorder__le__cases,axiom,
% 2.75/2.83 ! [V_y,V_x,T_a] :
% 2.75/2.83 ( class_Orderings_Olinorder(T_a)
% 2.75/2.83 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__funE,axiom,
% 2.75/2.83 ! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
% 2.75/2.83 ( class_Orderings_Oord(T_b)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2)) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_xt1_I6_J,axiom,
% 2.75/2.83 ! [V_z,V_x,V_y,T_a] :
% 2.75/2.83 ( class_Orderings_Oorder(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_xt1_I5_J,axiom,
% 2.75/2.83 ! [V_x,V_y,T_a] :
% 2.75/2.83 ( class_Orderings_Oorder(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 2.75/2.83 => V_x = V_y ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_order__trans,axiom,
% 2.75/2.83 ! [V_z,V_y,V_x,T_a] :
% 2.75/2.83 ( class_Orderings_Opreorder(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_order__antisym,axiom,
% 2.75/2.83 ! [V_y,V_x,T_a] :
% 2.75/2.83 ( class_Orderings_Oorder(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 2.75/2.83 => V_x = V_y ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_xt1_I4_J,axiom,
% 2.75/2.83 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.83 ( class_Orderings_Oorder(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 2.75/2.83 => ( V_b = V_c
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_ord__le__eq__trans,axiom,
% 2.75/2.83 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.83 ( class_Orderings_Oord(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.83 => ( V_b = V_c
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_xt1_I3_J,axiom,
% 2.75/2.83 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.83 ( class_Orderings_Oorder(T_a)
% 2.75/2.83 => ( V_a = V_b
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_ord__eq__le__trans,axiom,
% 2.75/2.83 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.83 ( class_Orderings_Oord(T_a)
% 2.75/2.83 => ( V_a = V_b
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_order__antisym__conv,axiom,
% 2.75/2.83 ! [V_x_2,V_y_2,T_a] :
% 2.75/2.83 ( class_Orderings_Oorder(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 2.75/2.83 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__funD,axiom,
% 2.75/2.83 ! [V_x_2,V_ga_2,V_fa_2,T_a,T_b] :
% 2.75/2.83 ( class_Orderings_Oord(T_b)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2),hAPP(V_ga_2,V_x_2)) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_order__eq__refl,axiom,
% 2.75/2.83 ! [V_y,V_x,T_a] :
% 2.75/2.83 ( class_Orderings_Opreorder(T_a)
% 2.75/2.83 => ( V_x = V_y
% 2.75/2.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_order__eq__iff,axiom,
% 2.75/2.83 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.83 ( class_Orderings_Oorder(T_a)
% 2.75/2.83 => ( V_x_2 = V_y_2
% 2.75/2.83 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 2.75/2.83 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_linorder__linear,axiom,
% 2.75/2.83 ! [V_y,V_x,T_a] :
% 2.75/2.83 ( class_Orderings_Olinorder(T_a)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 2.75/2.83 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_le__fun__def,axiom,
% 2.75/2.83 ! [V_ga_2,V_fa_2,T_a,T_b] :
% 2.75/2.83 ( class_Orderings_Oord(T_b)
% 2.75/2.83 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 2.75/2.83 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x),hAPP(V_ga_2,B_x)) ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__right__imp__eq,axiom,
% 2.75/2.83 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.83 ( class_Groups_Ocancel__semigroup__add(T_a)
% 2.75/2.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 2.75/2.83 => V_b = V_c ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__imp__eq,axiom,
% 2.75/2.83 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.83 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 2.75/2.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 2.75/2.83 => V_b = V_c ) ) ).
% 2.75/2.83
% 2.75/2.83 fof(fact_add__left__imp__eq,axiom,
% 2.75/2.83 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.83 ( class_Groups_Ocancel__semigroup__add(T_a)
% 2.75/2.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 2.75/2.84 => V_b = V_c ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_add__right__cancel,axiom,
% 2.75/2.84 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 2.75/2.84 ( class_Groups_Ocancel__semigroup__add(T_a)
% 2.75/2.84 => ( 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)
% 2.75/2.84 <=> V_b_2 = V_c_2 ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_add__left__cancel,axiom,
% 2.75/2.84 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 2.75/2.84 ( class_Groups_Ocancel__semigroup__add(T_a)
% 2.75/2.84 => ( 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)
% 2.75/2.84 <=> V_b_2 = V_c_2 ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.75/2.84 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.84 ( class_Groups_Oab__semigroup__add(T_a)
% 2.75/2.84 => 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)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_Suc__inject,axiom,
% 2.75/2.84 ! [V_y,V_x] :
% 2.75/2.84 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 2.75/2.84 => V_x = V_y ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat_Oinject,axiom,
% 2.75/2.84 ! [V_nat_H_2,V_nat_2] :
% 2.75/2.84 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 2.75/2.84 <=> V_nat_2 = V_nat_H_2 ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_Suc__n__not__n,axiom,
% 2.75/2.84 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 2.75/2.84
% 2.75/2.84 fof(fact_n__not__Suc__n,axiom,
% 2.75/2.84 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat__add__right__cancel,axiom,
% 2.75/2.84 ! [V_n_2,V_k_2,V_m_2] :
% 2.75/2.84 ( 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)
% 2.75/2.84 <=> V_m_2 = V_n_2 ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat__add__left__cancel,axiom,
% 2.75/2.84 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.84 ( 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)
% 2.75/2.84 <=> V_m_2 = V_n_2 ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat__add__assoc,axiom,
% 2.75/2.84 ! [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)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat__add__left__commute,axiom,
% 2.75/2.84 ! [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)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat__add__commute,axiom,
% 2.75/2.84 ! [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) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__of__nat__le__iff,axiom,
% 2.75/2.84 ! [V_m_2,V_n_2] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
% 2.75/2.84 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_seq__suble,axiom,
% 2.75/2.84 ! [V_n_2,V_fa_2] :
% 2.75/2.84 ( c_SEQ_Osubseq(V_fa_2)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__of__nat__add,axiom,
% 2.75/2.84 ! [V_n,V_m] : hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_termination__basic__simps_I4_J,axiom,
% 2.75/2.84 ! [V_y,V_z,V_x] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_termination__basic__simps_I3_J,axiom,
% 2.75/2.84 ! [V_z,V_y,V_x] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_le__Suc__ex__iff,axiom,
% 2.75/2.84 ! [V_l_2,V_k_2] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 2.75/2.84 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_lift__Suc__mono__le,axiom,
% 2.75/2.84 ! [V_n_H_2,V_n_2,V_fa_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n)))
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_n_H_2)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_fa_2,V_n_2),hAPP(V_fa_2,V_n_H_2)) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__of__nat__inject,axiom,
% 2.75/2.84 ! [V_m_2,V_n_2] :
% 2.75/2.84 ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)
% 2.75/2.84 <=> V_n_2 = V_m_2 ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__add__left__mono,axiom,
% 2.75/2.84 ! [V_z,V_y,V_x] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 2.75/2.84 => 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)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__le__antisym,axiom,
% 2.75/2.84 ! [V_w,V_z] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 2.75/2.84 => V_z = V_w ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__le__trans,axiom,
% 2.75/2.84 ! [V_k,V_j,V_i] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__le__linear,axiom,
% 2.75/2.84 ! [V_w,V_z] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 2.75/2.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__le__refl,axiom,
% 2.75/2.84 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_decseq__def,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 2.75/2.84 <=> ! [B_m,B_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_incseq__def,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 2.75/2.84 <=> ! [B_m,B_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_monoseq__def,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_SEQ_Omonoseq(T_a,V_X_2)
% 2.75/2.84 <=> ( ! [B_m,B_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) )
% 2.75/2.84 | ! [B_m,B_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_monoseq__Suc,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_SEQ_Omonoseq(T_a,V_X_2)
% 2.75/2.84 <=> ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))
% 2.75/2.84 | ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n)) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__of__nat__Suc,axiom,
% 2.75/2.84 ! [V_n] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 2.75/2.84 ! [V_c,V_a,T_a] :
% 2.75/2.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.84 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 2.75/2.84 ! [V_d,V_c,V_a,T_a] :
% 2.75/2.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.84 => 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)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 2.75/2.84 ! [V_d,V_c,V_a,T_a] :
% 2.75/2.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.84 => 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) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 2.75/2.84 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.84 => 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)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 2.75/2.84 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.84 => 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) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_incseq__imp__monoseq,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 2.75/2.84 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_decseq__imp__monoseq,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 2.75/2.84 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_one__reorient,axiom,
% 2.75/2.84 ! [V_x_2,T_a] :
% 2.75/2.84 ( class_Groups_Oone(T_a)
% 2.75/2.84 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 2.75/2.84 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 2.75/2.84 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.84 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.84 => 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)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_incseq__SucI,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))
% 2.75/2.84 => c_SEQ_Oincseq(T_a,V_X_2) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat__le__real__less,axiom,
% 2.75/2.84 ! [V_m_2,V_n_2] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
% 2.75/2.84 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat__less__real__le,axiom,
% 2.75/2.84 ! [V_m_2,V_n_2] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 2.75/2.84 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_monoI2,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( ! [B_m,B_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) )
% 2.75/2.84 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_monoI1,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( ! [B_m,B_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 2.75/2.84 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) )
% 2.75/2.84 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_mono__SucI2,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n))
% 2.75/2.84 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_mono__SucI1,axiom,
% 2.75/2.84 ! [V_X_2,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))
% 2.75/2.84 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_real__of__nat__one,axiom,
% 2.75/2.84 hAPP(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) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 2.75/2.84 ! [V_i_2,V_n_2,V_inc_2,T_a] :
% 2.75/2.84 ( class_Rings_Osemiring__1(T_a)
% 2.75/2.84 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Nat_OSuc(V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__Suc__diff__eq2,axiom,
% 2.75/2.84 ! [V_m,V_j,V_k] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 2.75/2.84 => 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)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__zeroE,axiom,
% 2.75/2.84 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_lessI,axiom,
% 2.75/2.84 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_Suc__mono,axiom,
% 2.75/2.84 ! [V_n,V_m] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_le0,axiom,
% 2.75/2.84 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_zero__less__Suc,axiom,
% 2.75/2.84 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__Suc__1,axiom,
% 2.75/2.84 ! [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 ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 2.75/2.84 ! [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) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_Suc__diff__1,axiom,
% 2.75/2.84 ! [V_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.84 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_Suc__pred_H,axiom,
% 2.75/2.84 ! [V_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.84 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__add__0,axiom,
% 2.75/2.84 ! [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) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__is__0__eq,axiom,
% 2.75/2.84 ! [V_n_2,V_m_2] :
% 2.75/2.84 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.84 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__is__0__eq_H,axiom,
% 2.75/2.84 ! [V_n,V_m] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.84 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_gr0__conv__Suc,axiom,
% 2.75/2.84 ! [V_n_2] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 2.75/2.84 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__Suc0,axiom,
% 2.75/2.84 ! [V_n_2] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 2.75/2.84 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__Suc__eq__0__disj,axiom,
% 2.75/2.84 ! [V_n_2,V_m_2] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 2.75/2.84 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.84 | ? [B_j] :
% 2.75/2.84 ( V_m_2 = c_Nat_OSuc(B_j)
% 2.75/2.84 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_not__less0,axiom,
% 2.75/2.84 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__not__refl,axiom,
% 2.75/2.84 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_order__less__irrefl,axiom,
% 2.75/2.84 ! [V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Opreorder(T_a)
% 2.75/2.84 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_neq0__conv,axiom,
% 2.75/2.84 ! [V_n_2] :
% 2.75/2.84 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.84 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_nat__neq__iff,axiom,
% 2.75/2.84 ! [V_n_2,V_m_2] :
% 2.75/2.84 ( V_m_2 != V_n_2
% 2.75/2.84 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.84 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_linorder__neq__iff,axiom,
% 2.75/2.84 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.84 ( class_Orderings_Olinorder(T_a)
% 2.75/2.84 => ( V_x_2 != V_y_2
% 2.75/2.84 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.84 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_not__less__iff__gr__or__eq,axiom,
% 2.75/2.84 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.84 ( class_Orderings_Olinorder(T_a)
% 2.75/2.84 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.84 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 2.75/2.84 | V_x_2 = V_y_2 ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__0__eq__0,axiom,
% 2.75/2.84 ! [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) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_zero__reorient,axiom,
% 2.75/2.84 ! [V_x_2,T_a] :
% 2.75/2.84 ( class_Groups_Ozero(T_a)
% 2.75/2.84 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 2.75/2.84 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_zero__less__diff,axiom,
% 2.75/2.84 ! [V_m_2,V_n_2] :
% 2.75/2.84 ( 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))
% 2.75/2.84 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__nat__zero__code,axiom,
% 2.75/2.84 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__0__right,axiom,
% 2.75/2.84 ! [V_a,T_a] :
% 2.75/2.84 ( class_Groups_Ogroup__add(T_a)
% 2.75/2.84 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_minus__nat_Odiff__0,axiom,
% 2.75/2.84 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__self,axiom,
% 2.75/2.84 ! [V_a,T_a] :
% 2.75/2.84 ( class_Groups_Ogroup__add(T_a)
% 2.75/2.84 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__self__eq__0,axiom,
% 2.75/2.84 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_eq__iff__diff__eq__0,axiom,
% 2.75/2.84 ! [V_b_2,V_a_2,T_a] :
% 2.75/2.84 ( class_Groups_Oab__group__add(T_a)
% 2.75/2.84 => ( V_a_2 = V_b_2
% 2.75/2.84 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__iff__diff__less__0,axiom,
% 2.75/2.84 ! [V_b_2,V_a_2,T_a] :
% 2.75/2.84 ( class_Groups_Oordered__ab__group__add(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 2.75/2.84 <=> 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)) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_linorder__less__linear,axiom,
% 2.75/2.84 ! [V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Olinorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 | V_x = V_y
% 2.75/2.84 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_right__minus__eq,axiom,
% 2.75/2.84 ! [V_b_2,V_a_2,T_a] :
% 2.75/2.84 ( class_Groups_Ogroup__add(T_a)
% 2.75/2.84 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.84 <=> V_a_2 = V_b_2 ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__commute,axiom,
% 2.75/2.84 ! [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) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 2.75/2.84 ! [V_i_2,V_inc_2,T_a] :
% 2.75/2.84 ( class_Rings_Osemiring__1(T_a)
% 2.75/2.84 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_linorder__antisym__conv3,axiom,
% 2.75/2.84 ! [V_x_2,V_y_2,T_a] :
% 2.75/2.84 ( class_Orderings_Olinorder(T_a)
% 2.75/2.84 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 2.75/2.84 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.84 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_linorder__neqE,axiom,
% 2.75/2.84 ! [V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Olinorder(T_a)
% 2.75/2.84 => ( V_x != V_y
% 2.75/2.84 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_linorder__neqE__nat,axiom,
% 2.75/2.84 ! [V_y,V_x] :
% 2.75/2.84 ( V_x != V_y
% 2.75/2.84 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_Suc__pred,axiom,
% 2.75/2.84 ! [V_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.84 => 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 ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__Suc__less,axiom,
% 2.75/2.84 ! [V_i,V_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.84 => 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) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__less,axiom,
% 2.75/2.84 ! [V_m,V_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__irrefl__nat,axiom,
% 2.75/2.84 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_gr__implies__not0,axiom,
% 2.75/2.84 ! [V_n,V_m] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.84 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__not__refl2,axiom,
% 2.75/2.84 ! [V_m,V_n] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 2.75/2.84 => V_m != V_n ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__not__refl3,axiom,
% 2.75/2.84 ! [V_t,V_s] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 2.75/2.84 => V_s != V_t ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__imp__neq,axiom,
% 2.75/2.84 ! [V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 => V_x != V_y ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_order__less__not__sym,axiom,
% 2.75/2.84 ! [V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Opreorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_order__less__imp__not__less,axiom,
% 2.75/2.84 ! [V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Opreorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_order__less__imp__not__eq,axiom,
% 2.75/2.84 ! [V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 => V_x != V_y ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_order__less__imp__not__eq2,axiom,
% 2.75/2.84 ! [V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 => V_y != V_x ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_less__imp__diff__less,axiom,
% 2.75/2.84 ! [V_n,V_k,V_j] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_order__less__asym_H,axiom,
% 2.75/2.84 ! [V_b,V_a,T_a] :
% 2.75/2.84 ( class_Orderings_Opreorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.84 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_xt1_I9_J,axiom,
% 2.75/2.84 ! [V_a,V_b,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 2.75/2.84 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_ord__eq__less__trans,axiom,
% 2.75/2.84 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.84 ( class_Orderings_Oord(T_a)
% 2.75/2.84 => ( V_a = V_b
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_xt1_I1_J,axiom,
% 2.75/2.84 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( V_a = V_b
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_ord__less__eq__trans,axiom,
% 2.75/2.84 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.84 ( class_Orderings_Oord(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.84 => ( V_b = V_c
% 2.75/2.84 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_xt1_I2_J,axiom,
% 2.75/2.84 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 2.75/2.84 => ( V_b = V_c
% 2.75/2.84 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_order__less__trans,axiom,
% 2.75/2.84 ! [V_z,V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Opreorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_xt1_I10_J,axiom,
% 2.75/2.84 ! [V_z,V_x,V_y,T_a] :
% 2.75/2.84 ( class_Orderings_Oorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 2.75/2.84 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diff__less__mono2,axiom,
% 2.75/2.84 ! [V_l,V_n,V_m] :
% 2.75/2.84 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 2.75/2.84 => 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)) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_order__less__asym,axiom,
% 2.75/2.84 ! [V_y,V_x,T_a] :
% 2.75/2.84 ( class_Orderings_Opreorder(T_a)
% 2.75/2.84 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.84 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 2.75/2.84
% 2.75/2.84 fof(fact_diffs0__imp__equal,axiom,
% 2.75/2.84 ! [V_n,V_m] :
% 2.75/2.84 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.84 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 => V_m = V_n ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__eq__diff__eq,axiom,
% 2.75/2.85 ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Oab__group__add(T_a)
% 2.75/2.85 => ( 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)
% 2.75/2.85 => ( V_a_2 = V_b_2
% 2.75/2.85 <=> V_c_2 = V_da_2 ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__eq__diff__less,axiom,
% 2.75/2.85 ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add(T_a)
% 2.75/2.85 => ( 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)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_da_2) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_gr0I,axiom,
% 2.75/2.85 ! [V_n] :
% 2.75/2.85 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_linorder__cases,axiom,
% 2.75/2.85 ! [V_y,V_x,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.85 => ( V_x != V_y
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_nat__less__cases,axiom,
% 2.75/2.85 ! [V_P_2,V_n_2,V_m_2] :
% 2.75/2.85 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 2.75/2.85 => ( ( V_m_2 = V_n_2
% 2.75/2.85 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 2.75/2.85 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 2.75/2.85 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 2.75/2.85 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__less__mono,axiom,
% 2.75/2.85 ! [V_c,V_b,V_a] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 2.75/2.85 => 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)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__diff__iff,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__diff__conv,axiom,
% 2.75/2.85 ! [V_k_2,V_j_2,V_i_2] :
% 2.75/2.85 ( 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))
% 2.75/2.85 <=> 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) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__diff__inverse,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.75/2.85 ! [V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.75/2.85 ! [V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__pos__pos,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__neg__neg,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__less__Suc,axiom,
% 2.75/2.85 ! [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)) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__iff__diff__le__0,axiom,
% 2.75/2.85 ! [V_b_2,V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 2.75/2.85 <=> 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)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_nat__diff__split,axiom,
% 2.75/2.85 ! [V_b_2,V_a_2,V_P_2] :
% 2.75/2.85 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 2.75/2.85 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
% 2.75/2.85 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 2.75/2.85 & ! [B_d] :
% 2.75/2.85 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 2.75/2.85 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_nat__diff__split__asm,axiom,
% 2.75/2.85 ! [V_b_2,V_a_2,V_P_2] :
% 2.75/2.85 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 2.75/2.85 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
% 2.75/2.85 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 2.75/2.85 | ? [B_d] :
% 2.75/2.85 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 2.75/2.85 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_One__nat__def,axiom,
% 2.75/2.85 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__less__iff,axiom,
% 2.75/2.85 ! [V_m_2,V_n_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__gr__0,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( 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))
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 2.75/2.85 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__eq__if,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n )
% 2.75/2.85 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 => 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)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__pos__nonneg,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__nonneg__pos,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__strict__increasing,axiom,
% 2.75/2.85 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__strict__increasing2,axiom,
% 2.75/2.85 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__neg__nonpos,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__nonpos__neg,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__eq__diff__less__eq,axiom,
% 2.75/2.85 ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add(T_a)
% 2.75/2.85 => ( 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)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_da_2) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__add__cancel,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Ogroup__add(T_a)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__diff__cancel,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Ogroup__add(T_a)
% 2.75/2.85 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_linorder__not__less,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_linorder__not__le,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_linorder__le__less__linear,axiom,
% 2.75/2.85 ! [V_y,V_x,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 2.75/2.85 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_order__less__le,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 2.75/2.85 & V_x_2 != V_y_2 ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__le__not__le,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( class_Orderings_Opreorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 2.75/2.85 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_order__le__less,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.85 | V_x_2 = V_y_2 ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_leI,axiom,
% 2.75/2.85 ! [V_y,V_x,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_not__leE,axiom,
% 2.75/2.85 ! [V_x,V_y,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_linorder__antisym__conv1,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 2.75/2.85 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_order__neq__le__trans,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( V_a != V_b
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_xt1_I12_J,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( V_a != V_b
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_leD,axiom,
% 2.75/2.85 ! [V_x,V_y,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 2.75/2.85 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_order__less__imp__le,axiom,
% 2.75/2.85 ! [V_y,V_x,T_a] :
% 2.75/2.85 ( class_Orderings_Opreorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_linorder__antisym__conv2,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( class_Orderings_Olinorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 2.75/2.85 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_order__le__imp__less__or__eq,axiom,
% 2.75/2.85 ! [V_y,V_x,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.85 | V_x = V_y ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_order__le__neq__trans,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.85 => ( V_a != V_b
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_xt1_I11_J,axiom,
% 2.75/2.85 ! [V_a,V_b,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 2.75/2.85 => ( V_a != V_b
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_order__less__le__trans,axiom,
% 2.75/2.85 ! [V_z,V_y,V_x,T_a] :
% 2.75/2.85 ( class_Orderings_Opreorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_xt1_I7_J,axiom,
% 2.75/2.85 ! [V_z,V_x,V_y,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_order__le__less__trans,axiom,
% 2.75/2.85 ! [V_z,V_y,V_x,T_a] :
% 2.75/2.85 ( class_Orderings_Opreorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_xt1_I8_J,axiom,
% 2.75/2.85 ! [V_z,V_x,V_y,T_a] :
% 2.75/2.85 ( class_Orderings_Oorder(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__less__cancel__right,axiom,
% 2.75/2.85 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__less__cancel__left,axiom,
% 2.75/2.85 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__strict__right__mono,axiom,
% 2.75/2.85 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.85 => 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)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__strict__left__mono,axiom,
% 2.75/2.85 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.85 => 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)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__strict__mono,axiom,
% 2.75/2.85 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__less__imp__less__right,axiom,
% 2.75/2.85 ! [V_b,V_c,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__less__imp__less__left,axiom,
% 2.75/2.85 ! [V_b,V_a,V_c,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__Suc__Suc,axiom,
% 2.75/2.85 ! [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) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__diff__diff,axiom,
% 2.75/2.85 ! [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) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__add__inverse2,axiom,
% 2.75/2.85 ! [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 ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__add__inverse,axiom,
% 2.75/2.85 ! [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 ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__diff__left,axiom,
% 2.75/2.85 ! [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)) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__cancel,axiom,
% 2.75/2.85 ! [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) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__cancel2,axiom,
% 2.75/2.85 ! [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) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__diff__iff,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Nat_Odiff__diff__eq,axiom,
% 2.75/2.85 ! [V_n,V_m,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 2.75/2.85 => 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) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_eq__diff__iff,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 2.75/2.85 => ( 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)
% 2.75/2.85 <=> V_m_2 = V_n_2 ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__diff__cancel,axiom,
% 2.75/2.85 ! [V_n,V_i] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 2.75/2.85 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__le__mono,axiom,
% 2.75/2.85 ! [V_l,V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__le__mono2,axiom,
% 2.75/2.85 ! [V_l,V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__le__self,axiom,
% 2.75/2.85 ! [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) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_not__less__eq,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__Suc__eq,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 | V_m_2 = V_n_2 ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__less__eq,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_not__less__less__Suc__eq,axiom,
% 2.75/2.85 ! [V_m_2,V_n_2] :
% 2.75/2.85 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 2.75/2.85 <=> V_n_2 = V_m_2 ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__antisym,axiom,
% 2.75/2.85 ! [V_m,V_n] :
% 2.75/2.85 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 2.75/2.85 => V_m = V_n ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__SucI,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__lessI,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => ( c_Nat_OSuc(V_m) != V_n
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__trans__Suc,axiom,
% 2.75/2.85 ! [V_k,V_j,V_i] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__SucE,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => V_m = V_n ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__lessD,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__less__SucD,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__less__def,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 2.75/2.85 & V_x_2 != V_y_2 ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__eq__real__def,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 2.75/2.85 | V_x_2 = V_y_2 ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_termination__basic__simps_I1_J,axiom,
% 2.75/2.85 ! [V_z,V_y,V_x] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_termination__basic__simps_I2_J,axiom,
% 2.75/2.85 ! [V_y,V_z,V_x] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_not__add__less1,axiom,
% 2.75/2.85 ! [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) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_not__add__less2,axiom,
% 2.75/2.85 ! [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) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_nat__add__left__cancel__less,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.85 ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_trans__less__add1,axiom,
% 2.75/2.85 ! [V_m,V_j,V_i] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_trans__less__add2,axiom,
% 2.75/2.85 ! [V_m,V_j,V_i] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__less__mono1,axiom,
% 2.75/2.85 ! [V_k,V_j,V_i] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__less__mono,axiom,
% 2.75/2.85 ! [V_l,V_k,V_j,V_i] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 2.75/2.85 => 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)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__add__eq__less,axiom,
% 2.75/2.85 ! [V_n,V_m,V_l,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 2.75/2.85 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__lessD1,axiom,
% 2.75/2.85 ! [V_k,V_j,V_i] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_termination__basic__simps_I5_J,axiom,
% 2.75/2.85 ! [V_y,V_x] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__or__eq__imp__le,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 | V_m = V_n )
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__neq__implies__less,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => ( V_m != V_n
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__imp__le__nat,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__eq__less__or__eq,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 | V_m_2 = V_n_2 ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_nat__less__le,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 & V_m_2 != V_n_2 ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__0__left,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Groups_Omonoid__add(T_a)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__0,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_double__zero__sym,axiom,
% 2.75/2.85 ! [V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.75/2.85 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 2.75/2.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__0__right,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Groups_Omonoid__add(T_a)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add_Ocomm__neutral,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Groups_Ocomm__monoid__add(T_a)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__0__iff,axiom,
% 2.75/2.85 ! [V_a_2,V_b_2,T_a] :
% 2.75/2.85 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 2.75/2.85 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
% 2.75/2.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Zero__not__Suc,axiom,
% 2.75/2.85 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_nat_Osimps_I2_J,axiom,
% 2.75/2.85 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__not__Zero,axiom,
% 2.75/2.85 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_nat_Osimps_I3_J,axiom,
% 2.75/2.85 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Zero__neq__Suc,axiom,
% 2.75/2.85 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__neq__Zero,axiom,
% 2.75/2.85 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_plus__nat_Oadd__0,axiom,
% 2.75/2.85 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Nat_Oadd__0__right,axiom,
% 2.75/2.85 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__is__0,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__eq__self__zero,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 2.75/2.85 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__0__eq,axiom,
% 2.75/2.85 ! [V_n_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.75/2.85 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 2.75/2.85 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_subseq__def,axiom,
% 2.75/2.85 ! [V_fa_2] :
% 2.75/2.85 ( c_SEQ_Osubseq(V_fa_2)
% 2.75/2.85 <=> ! [B_m,B_n] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__less__le__mono,axiom,
% 2.75/2.85 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__le__less__mono,axiom,
% 2.75/2.85 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__diff__le,axiom,
% 2.75/2.85 ! [V_m,V_n] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__add__assoc2,axiom,
% 2.75/2.85 ! [V_i,V_j,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 2.75/2.85 => 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) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__diff__assoc2,axiom,
% 2.75/2.85 ! [V_i,V_j,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 2.75/2.85 => 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) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__add__assoc,axiom,
% 2.75/2.85 ! [V_i,V_j,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__imp__diff__is__add,axiom,
% 2.75/2.85 ! [V_k_2,V_j_2,V_i_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 2.75/2.85 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 2.75/2.85 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__add__diff__inverse2,axiom,
% 2.75/2.85 ! [V_m,V_n] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__diff__conv2,axiom,
% 2.75/2.85 ! [V_i_2,V_j_2,V_k_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> 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) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__diff__assoc,axiom,
% 2.75/2.85 ! [V_i,V_j,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 2.75/2.85 => 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) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__add__diff__inverse,axiom,
% 2.75/2.85 ! [V_m,V_n] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 2.75/2.85 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__add__diff,axiom,
% 2.75/2.85 ! [V_m,V_n,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__diff__conv,axiom,
% 2.75/2.85 ! [V_i_2,V_k_2,V_j_2] :
% 2.75/2.85 ( 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)
% 2.75/2.85 <=> 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__diff__right,axiom,
% 2.75/2.85 ! [V_i,V_j,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 2.75/2.85 => 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) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__add__Suc1,axiom,
% 2.75/2.85 ! [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))) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__add__Suc2,axiom,
% 2.75/2.85 ! [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))) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__iff__Suc__add,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__le__lessD,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__less__Suc__eq,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 2.75/2.85 <=> V_n_2 = V_m_2 ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__leI,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__imp__less__Suc,axiom,
% 2.75/2.85 ! [V_n,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__le__eq,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__Suc__eq__le,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__eq__Suc__le,axiom,
% 2.75/2.85 ! [V_m_2,V_n_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.75/2.85 ! [V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.75/2.85 ! [V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__nonneg__nonneg,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__nonneg__eq__0__iff,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 2.75/2.85 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.85 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.85 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__increasing,axiom,
% 2.75/2.85 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__increasing2,axiom,
% 2.75/2.85 ! [V_a,V_b,V_c,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__nonpos__nonpos,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.85 => 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)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__eq__plus1__left,axiom,
% 2.75/2.85 ! [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) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Suc__eq__plus1,axiom,
% 2.75/2.85 ! [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)) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__1,axiom,
% 2.75/2.85 hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_one__is__add,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( 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)
% 2.75/2.85 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.75/2.85 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.75/2.85 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__is__1,axiom,
% 2.75/2.85 ! [V_n_2,V_m_2] :
% 2.75/2.85 ( 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))
% 2.75/2.85 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.75/2.85 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.75/2.85 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_subseq__Suc__iff,axiom,
% 2.75/2.85 ! [V_fa_2] :
% 2.75/2.85 ( c_SEQ_Osubseq(V_fa_2)
% 2.75/2.85 <=> ! [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))) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_diff__Suc__diff__eq1,axiom,
% 2.75/2.85 ! [V_m,V_j,V_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_zero__less__two,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.85 => 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))) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 2.75/2.85 ! [V_x] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 2.75/2.85 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__add__one,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.85 => 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))) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_not__one__less__zero,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.85 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_zero__less__one,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_zero__le__one,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_not__one__le__zero,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.85 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_pos__add__strict,axiom,
% 2.75/2.85 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_even__less__0__iff,axiom,
% 2.75/2.85 ! [V_a_2,T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_d_I1_J,axiom,
% 2.75/2.85 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_rp,axiom,
% 2.75/2.85 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__ge__zero,axiom,
% 2.75/2.85 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__le__eq__diff,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 2.75/2.85 <=> 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__fun__def,axiom,
% 2.75/2.85 ! [V_ga_2,V_fa_2,T_a,T_b] :
% 2.75/2.85 ( class_Orderings_Oord(T_b)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 2.75/2.85 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2,V_ga_2)
% 2.75/2.85 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_ga_2,V_fa_2) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__zero__not__eq__one,axiom,
% 2.75/2.85 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__zero,axiom,
% 2.75/2.85 hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__zero__iff,axiom,
% 2.75/2.85 ! [V_n_2] :
% 2.75/2.85 ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.75/2.85 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_not__real__of__nat__less__zero,axiom,
% 2.75/2.85 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__diff,axiom,
% 2.75/2.85 ! [V_m,V_n] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 2.75/2.85 => hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_linorder__neqE__linordered__idom,axiom,
% 2.75/2.85 ! [V_y,V_x,T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.85 => ( V_x != V_y
% 2.75/2.85 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 2.75/2.85 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 2.75/2.85 ! [V_n_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 2.75/2.85 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__Suc__gt__zero,axiom,
% 2.75/2.85 ! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 2.75/2.85 ! [V_n_2] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_double__eq__0__iff,axiom,
% 2.75/2.85 ! [V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.75/2.85 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_one__neq__zero,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Rings_Ozero__neq__one(T_a)
% 2.75/2.85 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_zero__neq__one,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Rings_Ozero__neq__one(T_a)
% 2.75/2.85 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_ath,axiom,
% 2.75/2.85 ! [V_e,V_x,V_m] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_m,V_x)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_m,V_e))
% 2.75/2.85 => 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) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_Deriv_Oadd__diff__add,axiom,
% 2.75/2.85 ! [V_d,V_b,V_c,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oab__group__add(T_a)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_natceiling__eq,axiom,
% 2.75/2.85 ! [V_x,V_n] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),V_x)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.75/2.85 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_ex__least__nat__less,axiom,
% 2.75/2.85 ! [V_n_2,V_P_2] :
% 2.75/2.85 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 2.75/2.85 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 2.75/2.85 => ? [B_k] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)
% 2.75/2.85 & ! [B_i] :
% 2.75/2.85 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
% 2.75/2.85 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 2.75/2.85 & hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_expand__Suc,axiom,
% 2.75/2.85 ! [V_v] :
% 2.75/2.85 ( 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))
% 2.75/2.85 => 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))) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_psize__eq__0__iff,axiom,
% 2.75/2.85 ! [V_pa_2,T_a] :
% 2.75/2.85 ( class_Groups_Ozero(T_a)
% 2.75/2.85 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.85 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_abs__one,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.85 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_natceiling__zero,axiom,
% 2.75/2.85 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_number__of__reorient,axiom,
% 2.75/2.85 ! [V_x_2,V_wa_2,T_a] :
% 2.75/2.85 ( class_Int_Onumber(T_a)
% 2.75/2.85 => ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
% 2.75/2.85 <=> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_eq__number__of,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( ( class_Int_Onumber__ring(T_a)
% 2.75/2.85 & class_Int_Oring__char__0(T_a) )
% 2.75/2.85 => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
% 2.75/2.85 <=> V_x_2 = V_y_2 ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_natceiling__real__of__nat,axiom,
% 2.75/2.85 ! [V_n] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ).
% 2.75/2.85
% 2.75/2.85 fof(fact_abs__eq__0,axiom,
% 2.75/2.85 ! [V_a_2,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.85 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.85 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_abs__zero,axiom,
% 2.75/2.85 ! [T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.85 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_abs__le__D1,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.85 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_abs__ge__self,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.85 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_abs__add__abs,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_abs__minus__commute,axiom,
% 2.75/2.85 ! [V_b,V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_abs__idempotent,axiom,
% 2.75/2.85 ! [V_a,T_a] :
% 2.75/2.85 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.85 => 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) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_le__number__of,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( ( class_Int_Onumber__ring(T_a)
% 2.75/2.85 & class_Rings_Olinordered__idom(T_a) )
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_less__number__of,axiom,
% 2.75/2.85 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.85 ( ( class_Int_Onumber__ring(T_a)
% 2.75/2.85 & class_Rings_Olinordered__idom(T_a) )
% 2.75/2.85 => ( 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))
% 2.75/2.85 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__number__of__left,axiom,
% 2.75/2.85 ! [V_z,V_w,V_v,T_a] :
% 2.75/2.85 ( class_Int_Onumber__ring(T_a)
% 2.75/2.85 => 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) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_add__number__of__eq,axiom,
% 2.75/2.85 ! [V_w,V_v,T_a] :
% 2.75/2.85 ( class_Int_Onumber__ring(T_a)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.85 fof(fact_number__of__add,axiom,
% 2.75/2.85 ! [V_w,V_v,T_a] :
% 2.75/2.85 ( class_Int_Onumber__ring(T_a)
% 2.75/2.85 => 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)) ) ).
% 2.75/2.85
% 2.75/2.86 fof(fact_number__of__diff,axiom,
% 2.75/2.86 ! [V_w,V_v,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__real__of__nat__cancel,axiom,
% 2.75/2.86 ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__neg,axiom,
% 2.75/2.86 ! [V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 2.75/2.86 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zero__le__natceiling,axiom,
% 2.75/2.86 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__mono,axiom,
% 2.75/2.86 ! [V_y,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_real__natceiling__ge,axiom,
% 2.75/2.86 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(V_x))) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__one,axiom,
% 2.75/2.86 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__ge__zero,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__le__zero__iff,axiom,
% 2.75/2.86 ! [V_a_2,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => ( 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))
% 2.75/2.86 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__of__nonneg,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.86 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__not__less__zero,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zero__less__abs__iff,axiom,
% 2.75/2.86 ! [V_a_2,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
% 2.75/2.86 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__of__pos,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.86 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__triangle__ineq,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__triangle__ineq3,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__triangle__ineq2,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__triangle__ineq2__sym,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__diff__less__iff,axiom,
% 2.75/2.86 ! [V_ra_2,V_a_2,V_x_2,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.86 => ( 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)
% 2.75/2.86 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2)
% 2.75/2.86 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__number__of__eq__not__less,axiom,
% 2.75/2.86 ! [V_wa_2,V_v_2,T_a] :
% 2.75/2.86 ( ( class_Int_Onumber(T_a)
% 2.75/2.86 & class_Orderings_Olinorder(T_a) )
% 2.75/2.86 => ( 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))
% 2.75/2.86 <=> ~ 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)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_add__number__of__diff1,axiom,
% 2.75/2.86 ! [V_c,V_w,V_v,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => 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) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__le,axiom,
% 2.75/2.86 ! [V_a,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__le__eq,axiom,
% 2.75/2.86 ! [V_a_2,V_x_2] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__subtract,axiom,
% 2.75/2.86 ! [V_x,V_a] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a),V_x)
% 2.75/2.86 => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__triangle__ineq4,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__diff__triangle__ineq,axiom,
% 2.75/2.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.75/2.86 => 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)))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__add__one__not__less__self,axiom,
% 2.75/2.86 ! [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) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__add__one__gt__zero,axiom,
% 2.75/2.86 ! [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))) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__le__eq__one,axiom,
% 2.75/2.86 ! [V_x_2] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__add,axiom,
% 2.75/2.86 ! [V_a,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.86 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__add__one,axiom,
% 2.75/2.86 ! [V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_wr,axiom,
% 2.75/2.86 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_reals__Archimedean6,axiom,
% 2.75/2.86 ! [V_r] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 2.75/2.86 => ? [B_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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)
% 2.75/2.86 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__add__one,axiom,
% 2.75/2.86 ! [V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_lemma__interval,axiom,
% 2.75/2.86 ! [V_b,V_x,V_a] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)
% 2.75/2.86 => ? [B_d] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 2.75/2.86 & ! [B_y] :
% 2.75/2.86 ( 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,B_y)),B_d)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a,B_y)
% 2.75/2.86 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y,V_b) ) ) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_reals__Archimedean6a,axiom,
% 2.75/2.86 ! [V_r] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 2.75/2.86 => ? [B_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n),V_r)
% 2.75/2.86 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_n))) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_g_I1_J,axiom,
% 2.75/2.86 ! [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) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_odd__nonzero,axiom,
% 2.75/2.86 ! [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) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_int__one__le__iff__zero__less,axiom,
% 2.75/2.86 ! [V_za_2] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zle__add1__eq__le,axiom,
% 2.75/2.86 ! [V_za_2,V_wa_2] :
% 2.75/2.86 ( 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)))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zle__diff1__eq,axiom,
% 2.75/2.86 ! [V_za_2,V_wa_2] :
% 2.75/2.86 ( 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)))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zless__add1__eq,axiom,
% 2.75/2.86 ! [V_za_2,V_wa_2] :
% 2.75/2.86 ( 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)))
% 2.75/2.86 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
% 2.75/2.86 | V_wa_2 = V_za_2 ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_add1__zle__eq,axiom,
% 2.75/2.86 ! [V_za_2,V_wa_2] :
% 2.75/2.86 ( 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)
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_odd__less__0,axiom,
% 2.75/2.86 ! [V_za_2] :
% 2.75/2.86 ( 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))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__imp__0__less,axiom,
% 2.75/2.86 ! [V_z] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zless__imp__add1__zle,axiom,
% 2.75/2.86 ! [V_z,V_w] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 2.75/2.86 => 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) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_int__0__less__1,axiom,
% 2.75/2.86 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zabs__less__one__iff,axiom,
% 2.75/2.86 ! [V_za_2] :
% 2.75/2.86 ( 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))
% 2.75/2.86 <=> V_za_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__number__of__int__code,axiom,
% 2.75/2.86 ! [V_l_2,V_k_2] :
% 2.75/2.86 ( 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))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zless__linear,axiom,
% 2.75/2.86 ! [V_y,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 2.75/2.86 | V_x = V_y
% 2.75/2.86 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__bin__lemma,axiom,
% 2.75/2.86 ! [V_l_2,V_k_2] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
% 2.75/2.86 <=> 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__zless__mono,axiom,
% 2.75/2.86 ! [V_z,V_z_H,V_w,V_w_H] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 2.75/2.86 => 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)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__strict__right__mono,axiom,
% 2.75/2.86 ! [V_k,V_j,V_i] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zless__le,axiom,
% 2.75/2.86 ! [V_wa_2,V_za_2] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
% 2.75/2.86 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2)
% 2.75/2.86 & V_za_2 != V_wa_2 ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__0__right,axiom,
% 2.75/2.86 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__0,axiom,
% 2.75/2.86 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 2.75/2.86
% 2.75/2.86 fof(fact_plus__numeral__code_I9_J,axiom,
% 2.75/2.86 ! [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)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__eq__number__of__int__code,axiom,
% 2.75/2.86 ! [V_l_2,V_k_2] :
% 2.75/2.86 ( 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))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__number__of__eq,axiom,
% 2.75/2.86 ! [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) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zle__antisym,axiom,
% 2.75/2.86 ! [V_w,V_z] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 2.75/2.86 => V_z = V_w ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zle__trans,axiom,
% 2.75/2.86 ! [V_k,V_j,V_i] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__left__mono,axiom,
% 2.75/2.86 ! [V_k,V_j,V_i] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__assoc,axiom,
% 2.75/2.86 ! [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)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__left__commute,axiom,
% 2.75/2.86 ! [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)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zle__linear,axiom,
% 2.75/2.86 ! [V_w,V_z] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 2.75/2.86 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__commute,axiom,
% 2.75/2.86 ! [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) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zle__refl,axiom,
% 2.75/2.86 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__real__of__nat,axiom,
% 2.75/2.86 ! [V_n] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) = V_n ).
% 2.75/2.86
% 2.75/2.86 fof(fact_complex__mod__triangle__sub,axiom,
% 2.75/2.86 ! [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))) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__number__of__eq,axiom,
% 2.75/2.86 ! [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) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__zero,axiom,
% 2.75/2.86 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zero__le__natfloor,axiom,
% 2.75/2.86 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__mono,axiom,
% 2.75/2.86 ! [V_y,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__one,axiom,
% 2.75/2.86 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__neg,axiom,
% 2.75/2.86 ! [V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 2.75/2.86 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_real__natfloor__le,axiom,
% 2.75/2.86 ! [V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_x) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__natfloor,axiom,
% 2.75/2.86 ! [V_a,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x),V_a)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_lemma__NBseq__def,axiom,
% 2.75/2.86 ! [V_X_2,T_b] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_b)
% 2.75/2.86 => ( ? [B_K] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.86 & ! [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) )
% 2.75/2.86 <=> ? [B_N] :
% 2.75/2.86 ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_lemma__NBseq__def2,axiom,
% 2.75/2.86 ! [V_X_2,T_b] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_b)
% 2.75/2.86 => ( ? [B_K] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.86 & ! [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) )
% 2.75/2.86 <=> ? [B_N] :
% 2.75/2.86 ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__natfloor__eq,axiom,
% 2.75/2.86 ! [V_a_2,V_x_2] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2),V_x_2) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__natfloor__eq__one,axiom,
% 2.75/2.86 ! [V_x_2] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_real__natfloor__add__one__gt,axiom,
% 2.75/2.86 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__subtract,axiom,
% 2.75/2.86 ! [V_x,V_a] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a),V_x)
% 2.75/2.86 => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_real__natfloor__gt__diff__one,axiom,
% 2.75/2.86 ! [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)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__natfloor,axiom,
% 2.75/2.86 ! [V_n,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))
% 2.75/2.86 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__add,axiom,
% 2.75/2.86 ! [V_a,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.86 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 2.75/2.86 ! [V_n,V_z] :
% 2.75/2.86 ( 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)
% 2.75/2.86 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__eq,axiom,
% 2.75/2.86 ! [V_x,V_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),V_x)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.75/2.86 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__triangle__ineq3,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__diff__triangle__ineq,axiom,
% 2.75/2.86 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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)))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__triangle__ineq2,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__diff__ineq,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__triangle__ineq4,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_N1,axiom,
% 2.75/2.86 ! [B_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_N1____,B_n)
% 2.75/2.86 => 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____) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_number__of__is__id,axiom,
% 2.75/2.86 ! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k ).
% 2.75/2.86
% 2.75/2.86 fof(fact_real__norm__def,axiom,
% 2.75/2.86 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_int__0__neq__1,axiom,
% 2.75/2.86 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__minus__commute,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__norm__cancel,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__eq__zero,axiom,
% 2.75/2.86 ! [V_x_2,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.75/2.86 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__zero,axiom,
% 2.75/2.86 ! [T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__ge__zero,axiom,
% 2.75/2.86 ! [V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__not__less__zero,axiom,
% 2.75/2.86 ! [V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ~ 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__one,axiom,
% 2.75/2.86 ! [T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 2.75/2.86 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__number__of,axiom,
% 2.75/2.86 ! [V_w,T_a] :
% 2.75/2.86 ( ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 & class_RealVector_Oreal__normed__algebra__1(T_a) )
% 2.75/2.86 => 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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__le__zero__iff,axiom,
% 2.75/2.86 ! [V_x_2,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( 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))
% 2.75/2.86 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zero__less__norm__iff,axiom,
% 2.75/2.86 ! [V_x_2,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( 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))
% 2.75/2.86 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__triangle__ineq,axiom,
% 2.75/2.86 ! [V_y,V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => 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))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__add__less,axiom,
% 2.75/2.86 ! [V_s,V_y,V_r,V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 2.75/2.86 => 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)) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_complex__mod__triangle__ineq2,axiom,
% 2.75/2.86 ! [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)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 2.75/2.86 ! [V_y,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 2.75/2.86 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_fz_I2_J,axiom,
% 2.75/2.86 ! [B_e] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
% 2.75/2.86 => ? [B_N] :
% 2.75/2.86 ! [B_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n)
% 2.75/2.86 => 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) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 2.75/2.86 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 2.75/2.86
% 2.75/2.86 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,
% 2.75/2.86 ? [B_N] :
% 2.75/2.86 ! [B_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N,B_n)
% 2.75/2.86 => 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____) ) ).
% 2.75/2.86
% 2.75/2.86 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,
% 2.75/2.86 ~ ! [B_N1] :
% 2.75/2.86 ~ ! [B_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_N1,B_n)
% 2.75/2.86 => 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____) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__add__number__of,axiom,
% 2.75/2.86 ! [V_x,V_n] :
% 2.75/2.86 ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.86 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natfloor__add__number__of,axiom,
% 2.75/2.86 ! [V_x,V_n] :
% 2.75/2.86 ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.86 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_not__neg__0,axiom,
% 2.75/2.86 ~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_not__neg__1,axiom,
% 2.75/2.86 ~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_not__neg__eq__ge__0,axiom,
% 2.75/2.86 ! [V_x_2] :
% 2.75/2.86 ( ~ c_Nat__Numeral_Oneg(V_x_2)
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_neg__def,axiom,
% 2.75/2.86 ! [V_Z_2] :
% 2.75/2.86 ( c_Nat__Numeral_Oneg(V_Z_2)
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_Z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_neg__imp__number__of__eq__0,axiom,
% 2.75/2.86 ! [V_v] :
% 2.75/2.86 ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_eq__nat__number__of,axiom,
% 2.75/2.86 ! [V_v_H_2,V_v_2] :
% 2.75/2.86 ( 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)
% 2.75/2.86 <=> ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
% 2.75/2.86 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2))
% 2.75/2.86 => ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))
% 2.75/2.86 => c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 2.75/2.86 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H_2))
% 2.75/2.86 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_nat__number__of__add__left,axiom,
% 2.75/2.86 ! [V_k,V_v_H,V_v] :
% 2.75/2.86 ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k) )
% 2.75/2.86 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H))
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_k) )
% 2.75/2.86 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v_H))
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)),V_k) ) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_real__of__nat__number__of,axiom,
% 2.75/2.86 ! [V_v] :
% 2.75/2.86 ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 2.75/2.86 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_v) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__natfloor__eq__number__of,axiom,
% 2.75/2.86 ! [V_x_2,V_n_2] :
% 2.75/2.86 ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n_2))
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n_2),c_RComplete_Onatfloor(V_x_2))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n_2),V_x_2) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_natceiling__le__eq__number__of,axiom,
% 2.75/2.86 ! [V_x_2,V_n_2] :
% 2.75/2.86 ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n_2))
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n_2))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n_2)) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Suc__nat__number__of__add,axiom,
% 2.75/2.86 ! [V_n,V_v] :
% 2.75/2.86 ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) )
% 2.75/2.86 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)),V_n) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Suc__nat__number__of,axiom,
% 2.75/2.86 ! [V_v] :
% 2.75/2.86 ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 2.75/2.86 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.86 => c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_lemmaCauchy,axiom,
% 2.75/2.86 ! [V_X_2,V_M_2,T_a,T_b] :
% 2.75/2.86 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 2.75/2.86 & class_Orderings_Oord(T_a) )
% 2.75/2.86 => ( ! [B_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 2.75/2.86 => 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)) )
% 2.75/2.86 => ! [B_n] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 2.75/2.86 => 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)))) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_unimodular__reduce__norm,axiom,
% 2.75/2.86 ! [V_z] :
% 2.75/2.86 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 2.75/2.86 => ( 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))
% 2.75/2.86 | 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))
% 2.75/2.86 | 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))
% 2.75/2.86 | 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)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_complex__i__not__zero,axiom,
% 2.75/2.86 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_complex__i__not__one,axiom,
% 2.75/2.86 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_complex__i__not__number__of,axiom,
% 2.75/2.86 ! [V_w] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_succ__def,axiom,
% 2.75/2.86 ! [V_k] : c_Int_Osucc(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_number__of__succ,axiom,
% 2.75/2.86 ! [V_k,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_tsub__def,axiom,
% 2.75/2.86 ! [V_x,V_y] :
% 2.75/2.86 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 2.75/2.86 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 2.75/2.86 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 2.75/2.86 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Bseq__iff1a,axiom,
% 2.75/2.86 ! [V_X_2,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.75/2.86 <=> ? [B_N] :
% 2.75/2.86 ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Bseq__iff,axiom,
% 2.75/2.86 ! [V_X_2,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.75/2.86 <=> ? [B_N] :
% 2.75/2.86 ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_N))) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Bseq__def,axiom,
% 2.75/2.86 ! [V_X_2,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.75/2.86 <=> ? [B_K] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.86 & ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 2.75/2.86 ! [V_y,V_x] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_tsub__eq,axiom,
% 2.75/2.86 ! [V_x,V_y] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 2.75/2.86 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_BseqD,axiom,
% 2.75/2.86 ! [V_X_2,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.75/2.86 => ? [B_K] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.86 & ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_BseqI,axiom,
% 2.75/2.86 ! [V_X_2,V_K_2,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)
% 2.75/2.86 => ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
% 2.75/2.86 => c_SEQ_OBseq(T_a,V_X_2) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_nat__1__add__number__of,axiom,
% 2.75/2.86 ! [V_v] :
% 2.75/2.86 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 2.75/2.86 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_nat__number__of__add__1,axiom,
% 2.75/2.86 ! [V_v] :
% 2.75/2.86 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 2.75/2.86 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Pls__def,axiom,
% 2.75/2.86 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_add__Pls,axiom,
% 2.75/2.86 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k ).
% 2.75/2.86
% 2.75/2.86 fof(fact_add__Pls__right,axiom,
% 2.75/2.86 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 2.75/2.86
% 2.75/2.86 fof(fact_rel__simps_I19_J,axiom,
% 2.75/2.86 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_rel__simps_I2_J,axiom,
% 2.75/2.86 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_diff__bin__simps_I1_J,axiom,
% 2.75/2.86 ! [V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 2.75/2.86
% 2.75/2.86 fof(fact_number__of__Pls,axiom,
% 2.75/2.86 ! [T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_semiring__norm_I112_J,axiom,
% 2.75/2.86 ! [T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_add__numeral__0,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_add__numeral__0__right,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_nat__number__of__Pls,axiom,
% 2.75/2.86 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_semiring__norm_I113_J,axiom,
% 2.75/2.86 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_bin__less__0__simps_I1_J,axiom,
% 2.75/2.86 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zero__is__num__zero,axiom,
% 2.75/2.86 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_not__neg__number__of__Pls,axiom,
% 2.75/2.86 ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_eq__0__number__of,axiom,
% 2.75/2.86 ! [V_v_2] :
% 2.75/2.86 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_eq__number__of__0,axiom,
% 2.75/2.86 ! [V_v_2] :
% 2.75/2.86 ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__nat__number__of,axiom,
% 2.75/2.86 ! [V_v_H_2,V_v_2] :
% 2.75/2.86 ( 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))
% 2.75/2.86 <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
% 2.75/2.86 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) )
% 2.75/2.86 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__nat__number__of,axiom,
% 2.75/2.86 ! [V_v_H_2,V_v_2] :
% 2.75/2.86 ( 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))
% 2.75/2.86 <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__special_I3_J,axiom,
% 2.75/2.86 ! [V_x_2,T_a] :
% 2.75/2.86 ( ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 & class_Rings_Olinordered__idom(T_a) )
% 2.75/2.86 => ( 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))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__special_I1_J,axiom,
% 2.75/2.86 ! [V_y_2,T_a] :
% 2.75/2.86 ( ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 & class_Rings_Olinordered__idom(T_a) )
% 2.75/2.86 => ( 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))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__special_I3_J,axiom,
% 2.75/2.86 ! [V_x_2,T_a] :
% 2.75/2.86 ( ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 & class_Rings_Olinordered__idom(T_a) )
% 2.75/2.86 => ( 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))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__special_I1_J,axiom,
% 2.75/2.86 ! [V_y_2,T_a] :
% 2.75/2.86 ( ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 & class_Rings_Olinordered__idom(T_a) )
% 2.75/2.86 => ( 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))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__0__number__of,axiom,
% 2.75/2.86 ! [V_v_2] :
% 2.75/2.86 ( 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))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_add__nat__number__of,axiom,
% 2.75/2.86 ! [V_v_H,V_v] :
% 2.75/2.86 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.86 => 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) )
% 2.75/2.86 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.86 => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 2.75/2.86 => 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) )
% 2.75/2.86 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 2.75/2.86 => 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)) ) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_number__of2,axiom,
% 2.75/2.86 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,c_Int_OPls)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_nat__number__of__diff__1,axiom,
% 2.75/2.86 ! [V_v] :
% 2.75/2.86 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.86 => 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)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.75/2.86 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.86 => 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)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(V_v)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_Suc__diff__number__of,axiom,
% 2.75/2.86 ! [V_m,V_v] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v)
% 2.75/2.86 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(V_v))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_expi__zero,axiom,
% 2.75/2.86 c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_succ__pred,axiom,
% 2.75/2.86 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 2.75/2.86
% 2.75/2.86 fof(fact_le__iff__pred__less,axiom,
% 2.75/2.86 ! [V_l_2,V_k_2] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_pred__def,axiom,
% 2.75/2.86 ! [V_k] : c_Int_Opred(V_k) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_neg__number__of__pred__iff__0,axiom,
% 2.75/2.86 ! [V_v_2] :
% 2.75/2.86 ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(V_v_2)))
% 2.75/2.86 <=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_decr__lemma,axiom,
% 2.75/2.86 ! [V_z,V_x,V_d] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 2.75/2.86 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_incr__lemma,axiom,
% 2.75/2.86 ! [V_x,V_z,V_d] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 2.75/2.86 => c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__number__of__lemma,axiom,
% 2.75/2.86 ! [V_v,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => ( ( 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_v))
% 2.75/2.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(T_a,V_v) )
% 2.75/2.86 & ( ~ 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_v))
% 2.75/2.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zmult__zless__mono2__lemma,axiom,
% 2.75/2.86 ! [V_k,V_j,V_i] :
% 2.75/2.86 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 2.75/2.86 => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__right_Ozero,axiom,
% 2.75/2.86 ! [V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult_Ozero__right,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__left_Ozero,axiom,
% 2.75/2.86 ! [V_y,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult_Ozero__left,axiom,
% 2.75/2.86 ! [V_b,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__zero__left,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Rings_Omult__zero(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__zero__right,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Rings_Omult__zero(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__eq__0__iff,axiom,
% 2.75/2.86 ! [V_b_2,V_a_2,T_a] :
% 2.75/2.86 ( class_Rings_Oring__no__zero__divisors(T_a)
% 2.75/2.86 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.86 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.86 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_no__zero__divisors,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ono__zero__divisors(T_a)
% 2.75/2.86 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.86 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_divisors__zero,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ono__zero__divisors(T_a)
% 2.75/2.86 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.86 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.86 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__number__of__left,axiom,
% 2.75/2.86 ! [V_z,V_w,V_v,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_times__numeral__code_I5_J,axiom,
% 2.75/2.86 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_arith__simps_I32_J,axiom,
% 2.75/2.86 ! [V_w,V_v,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_number__of__mult,axiom,
% 2.75/2.86 ! [V_w,V_v,T_a] :
% 2.75/2.86 ( class_Int_Onumber__ring(T_a)
% 2.75/2.86 => c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(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)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_not__neg__int,axiom,
% 2.75/2.86 ! [V_n] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__int__eq,axiom,
% 2.75/2.86 ! [V_m] : c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__of__nat,axiom,
% 2.75/2.86 ! [V_n,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.86 => c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult_Oadd__right,axiom,
% 2.75/2.86 ! [V_b_H,V_b,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__right_Oadd,axiom,
% 2.75/2.86 ! [V_y,V_x,V_xa,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult_Oadd__left,axiom,
% 2.75/2.86 ! [V_b,V_a_H,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__left_Oadd,axiom,
% 2.75/2.86 ! [V_ya,V_y,V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__zmult__distrib,axiom,
% 2.75/2.86 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zadd__zmult__distrib2,axiom,
% 2.75/2.86 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_combine__common__factor,axiom,
% 2.75/2.86 ! [V_c,V_b,V_e,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Osemiring(T_a)
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__class_Odistrib,axiom,
% 2.75/2.86 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_crossproduct__eq,axiom,
% 2.75/2.86 ! [V_za_2,V_x_2,V_y_2,V_wa_2,T_a] :
% 2.75/2.86 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 2.75/2.86 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 2.75/2.86 <=> ( V_wa_2 = V_x_2
% 2.75/2.86 | V_y_2 = V_za_2 ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 2.75/2.86 ! [V_b,V_m,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 2.75/2.86 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_crossproduct__noteq,axiom,
% 2.75/2.86 ! [V_da_2,V_c_2,V_b_2,V_a_2,T_a] :
% 2.75/2.86 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 2.75/2.86 => ( ( V_a_2 != V_b_2
% 2.75/2.86 & V_c_2 != V_da_2 )
% 2.75/2.86 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_da_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_da_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 2.75/2.86 ! [V_z,V_y,V_x,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__mult__self,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_abs__mult,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.86 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_real__eq__of__nat,axiom,
% 2.75/2.86 c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_real__of__nat__def,axiom,
% 2.75/2.86 c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.75/2.86 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.86 ( class_Groups_Oab__semigroup__mult(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__eq__iff,axiom,
% 2.75/2.86 ! [V_n_2,V_m_2,T_a] :
% 2.75/2.86 ( class_Nat_Osemiring__char__0(T_a)
% 2.75/2.86 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)
% 2.75/2.86 <=> V_m_2 = V_n_2 ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__mult,axiom,
% 2.75/2.86 ! [V_n,V_m,T_a] :
% 2.75/2.86 ( class_Rings_Osemiring__1(T_a)
% 2.75/2.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 2.75/2.86 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 2.75/2.86 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 2.75/2.86 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 2.75/2.86 ! [V_rx,V_ly,V_lx,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 2.75/2.86 ! [V_rx,V_ly,V_lx,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 2.75/2.86 ! [V_ry,V_rx,V_lx,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 2.75/2.86 ! [V_ry,V_rx,V_lx,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zmult__assoc,axiom,
% 2.75/2.86 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zmult__commute,axiom,
% 2.75/2.86 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zdiff__zmult__distrib,axiom,
% 2.75/2.86 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zdiff__zmult__distrib2,axiom,
% 2.75/2.86 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__mult,axiom,
% 2.75/2.86 ! [V_y,V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 2.75/2.86 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__of__nat,axiom,
% 2.75/2.86 ! [V_n,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 2.75/2.86 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__mult__ineq,axiom,
% 2.75/2.86 ! [V_y,V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__left_Odiff,axiom,
% 2.75/2.86 ! [V_ya,V_y,V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult_Odiff__left,axiom,
% 2.75/2.86 ! [V_b,V_a_H,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__right_Odiff,axiom,
% 2.75/2.86 ! [V_y,V_x,V_xa,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult_Odiff__right,axiom,
% 2.75/2.86 ! [V_b_H,V_b,V_a,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_norm__mult__less,axiom,
% 2.75/2.86 ! [V_s,V_y,V_r,V_x,T_a] :
% 2.75/2.86 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 2.75/2.86 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zmult__1__right,axiom,
% 2.75/2.86 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zmult__1,axiom,
% 2.75/2.86 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__1__left,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__1,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Groups_Ocomm__monoid__mult(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__1__right,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult_Ocomm__neutral,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Groups_Ocomm__monoid__mult(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.86 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__Pls,axiom,
% 2.75/2.86 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__0__le__iff,axiom,
% 2.75/2.86 ! [V_n,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zero__le__imp__of__nat,axiom,
% 2.75/2.86 ! [V_m,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__less__0__iff,axiom,
% 2.75/2.86 ! [V_m,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.86 => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__0,axiom,
% 2.75/2.86 ! [T_a] :
% 2.75/2.86 ( class_Rings_Osemiring__1(T_a)
% 2.75/2.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__less__imp__less,axiom,
% 2.75/2.86 ! [V_n,V_m,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
% 2.75/2.86 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_less__imp__of__nat__less,axiom,
% 2.75/2.86 ! [V_n,V_m,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.86 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__less__iff,axiom,
% 2.75/2.86 ! [V_n_2,V_m_2,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__le__iff,axiom,
% 2.75/2.86 ! [V_n_2,V_m_2,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))
% 2.75/2.86 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__add,axiom,
% 2.75/2.86 ! [V_n,V_m,T_a] :
% 2.75/2.86 ( class_Rings_Osemiring__1(T_a)
% 2.75/2.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_of__nat__1,axiom,
% 2.75/2.86 ! [T_a] :
% 2.75/2.86 ( class_Rings_Osemiring__1(T_a)
% 2.75/2.86 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 2.75/2.86 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_int__0,axiom,
% 2.75/2.86 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_int__eq__0__conv,axiom,
% 2.75/2.86 ! [V_n_2] :
% 2.75/2.86 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.75/2.86 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zero__le__square,axiom,
% 2.75/2.86 ! [V_a,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__ring(T_a)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_zero__le__mult__iff,axiom,
% 2.75/2.86 ! [V_b_2,V_a_2,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))
% 2.75/2.86 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 2.75/2.86 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 2.75/2.86 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.86 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__le__0__iff,axiom,
% 2.75/2.86 ! [V_b_2,V_a_2,T_a] :
% 2.75/2.86 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.86 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 2.75/2.86 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 2.75/2.86 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.86 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__nonneg__nonneg,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__nonneg__nonpos,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__nonneg__nonpos2,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.86 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.86 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 2.75/2.86
% 2.75/2.86 fof(fact_mult__nonpos__nonneg,axiom,
% 2.75/2.86 ! [V_b,V_a,T_a] :
% 2.75/2.86 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__nonpos__nonpos,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__right__mono,axiom,
% 2.75/2.87 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__semiring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__left__mono,axiom,
% 2.75/2.87 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__semiring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__mult__left__mono,axiom,
% 2.75/2.87 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__comm__semiring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__right__mono__neg,axiom,
% 2.75/2.87 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__left__mono__neg,axiom,
% 2.75/2.87 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__mono_H,axiom,
% 2.75/2.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__semiring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__mono,axiom,
% 2.75/2.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__semiring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_split__mult__pos__le,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring(T_a)
% 2.75/2.87 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 2.75/2.87 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_split__mult__neg__le,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.75/2.87 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 2.75/2.87 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_not__square__less__zero,axiom,
% 2.75/2.87 ! [V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring(T_a)
% 2.75/2.87 => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__cancel__right__disj,axiom,
% 2.75/2.87 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
% 2.75/2.87 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 2.75/2.87 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 2.75/2.87 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__cancel__left__disj,axiom,
% 2.75/2.87 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 2.75/2.87 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 2.75/2.87 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 2.75/2.87 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__cancel__left__pos,axiom,
% 2.75/2.87 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__pos__pos,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__pos__neg,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__pos__neg2,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__less__mult__pos,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__less__mult__pos2,axiom,
% 2.75/2.87 ! [V_a,V_b,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__cancel__left__neg,axiom,
% 2.75/2.87 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__neg__pos,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__neg__neg,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__strict__right__mono,axiom,
% 2.75/2.87 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__strict__left__mono,axiom,
% 2.75/2.87 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__mult__strict__left__mono,axiom,
% 2.75/2.87 ! [V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__strict__right__mono__neg,axiom,
% 2.75/2.87 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__strict__left__mono__neg,axiom,
% 2.75/2.87 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 2.75/2.87 ! [V_P_2] :
% 2.75/2.87 ( ! [B_x] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_x)
% 2.75/2.87 => hBOOL(hAPP(V_P_2,B_x)) )
% 2.75/2.87 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 2.75/2.87 ! [V_P_2] :
% 2.75/2.87 ( ? [B_x] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_x)
% 2.75/2.87 & hBOOL(hAPP(V_P_2,B_x)) )
% 2.75/2.87 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 2.75/2.87 ! [V_z] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__zle__int,axiom,
% 2.75/2.87 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__less__0__conv,axiom,
% 2.75/2.87 ! [V_k] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_sum__squares__eq__zero__iff,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_add__scale__eq__noteq,axiom,
% 2.75/2.87 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 2.75/2.87 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 2.75/2.87 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 => ( ( V_a = V_b
% 2.75/2.87 & V_c != V_d )
% 2.75/2.87 => c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zless__int,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I3_J,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zle__int,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_less__1__mult,axiom,
% 2.75/2.87 ! [V_n,V_m,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_left__distrib__number__of,axiom,
% 2.75/2.87 ! [V_v,V_b,V_a,T_b] :
% 2.75/2.87 ( ( class_Int_Onumber(T_b)
% 2.75/2.87 & class_Rings_Osemiring(T_b) )
% 2.75/2.87 => hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_right__distrib__number__of,axiom,
% 2.75/2.87 ! [V_c,V_b,V_v,T_b] :
% 2.75/2.87 ( ( class_Int_Onumber(T_b)
% 2.75/2.87 & class_Rings_Osemiring(T_b) )
% 2.75/2.87 => hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zle__iff__zadd,axiom,
% 2.75/2.87 ! [V_za_2,V_wa_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2)
% 2.75/2.87 <=> ? [B_n] : V_za_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 2.75/2.87 ! [V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_y)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zadd__int,axiom,
% 2.75/2.87 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zadd__int__left,axiom,
% 2.75/2.87 ! [V_z,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_z) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_eq__add__iff2,axiom,
% 2.75/2.87 ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.75/2.87 ( class_Rings_Oring(T_a)
% 2.75/2.87 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2)
% 2.75/2.87 <=> V_c_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_da_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_eq__add__iff1,axiom,
% 2.75/2.87 ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.75/2.87 ( class_Rings_Oring(T_a)
% 2.75/2.87 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2)
% 2.75/2.87 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2) = V_da_2 ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__diff__mult,axiom,
% 2.75/2.87 ! [V_b,V_a,V_y,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Oring(T_a)
% 2.75/2.87 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult_Oprod__diff__prod,axiom,
% 2.75/2.87 ! [V_b,V_a,V_y,V_x,T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.87 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 2.75/2.87 ! [V_m,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 2.75/2.87 ! [V_a,V_m,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 2.75/2.87 ! [V_m,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_right__diff__distrib__number__of,axiom,
% 2.75/2.87 ! [V_c,V_b,V_v,T_b] :
% 2.75/2.87 ( ( class_Int_Onumber(T_b)
% 2.75/2.87 & class_Rings_Oring(T_b) )
% 2.75/2.87 => hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_left__diff__distrib__number__of,axiom,
% 2.75/2.87 ! [V_v,V_b,V_a,T_b] :
% 2.75/2.87 ( ( class_Int_Onumber(T_b)
% 2.75/2.87 & class_Rings_Oring(T_b) )
% 2.75/2.87 => hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 2.75/2.87 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__1,axiom,
% 2.75/2.87 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_abs__mult__less,axiom,
% 2.75/2.87 ! [V_d,V_b,V_c,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 2.75/2.87 ! [V_y,V_x] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zmult__zless__mono2,axiom,
% 2.75/2.87 ! [V_k,V_j,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_abs__zmult__eq__1,axiom,
% 2.75/2.87 ! [V_n,V_m] :
% 2.75/2.87 ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 2.75/2.87 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 2.75/2.87 ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x,V_y)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_of__nat__Suc,axiom,
% 2.75/2.87 ! [V_m,T_a] :
% 2.75/2.87 ( class_Rings_Osemiring__1(T_a)
% 2.75/2.87 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Nat_OSuc(V_m)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_of__nat__diff,axiom,
% 2.75/2.87 ! [V_m,V_n,T_a] :
% 2.75/2.87 ( class_Rings_Oring__1(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 2.75/2.87 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__le__cancel__left__pos,axiom,
% 2.75/2.87 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__le__cancel__left__neg,axiom,
% 2.75/2.87 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__strict__mono,axiom,
% 2.75/2.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__strict__mono_H,axiom,
% 2.75/2.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__le__imp__less,axiom,
% 2.75/2.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__le__less__imp__less,axiom,
% 2.75/2.87 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__right__less__imp__less,axiom,
% 2.75/2.87 ! [V_b,V_c,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__imp__less__right,axiom,
% 2.75/2.87 ! [V_b,V_c,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__left__less__imp__less,axiom,
% 2.75/2.87 ! [V_b,V_a,V_c,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__imp__less__left,axiom,
% 2.75/2.87 ! [V_b,V_a,V_c,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__right__le__imp__le,axiom,
% 2.75/2.87 ! [V_b,V_c,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__left__le__imp__le,axiom,
% 2.75/2.87 ! [V_b,V_a,V_c,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__le__0__conv,axiom,
% 2.75/2.87 ! [V_n_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_sum__squares__le__zero__iff,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
% 2.75/2.87 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_sum__squares__ge__zero,axiom,
% 2.75/2.87 ! [V_y,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring(T_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__Suc0__eq__1,axiom,
% 2.75/2.87 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_not__sum__squares__lt__zero,axiom,
% 2.75/2.87 ! [V_y,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring(T_a)
% 2.75/2.87 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_sum__squares__gt__zero__iff,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
% 2.75/2.87 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__right__le__one__le,axiom,
% 2.75/2.87 ! [V_y,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__left__le__one__le,axiom,
% 2.75/2.87 ! [V_y,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_le__add__iff1,axiom,
% 2.75/2.87 ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2),V_da_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_le__add__iff2,axiom,
% 2.75/2.87 ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_da_2)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_less__add__iff2,axiom,
% 2.75/2.87 ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_da_2)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_less__add__iff1,axiom,
% 2.75/2.87 ! [V_da_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_da_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2),V_da_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zless__iff__Suc__zadd,axiom,
% 2.75/2.87 ! [V_za_2,V_wa_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
% 2.75/2.87 <=> ? [B_n] : V_za_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(B_n))) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__Suc,axiom,
% 2.75/2.87 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_m)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__squared__diff__one__factored,axiom,
% 2.75/2.87 ! [V_x,T_a] :
% 2.75/2.87 ( class_Rings_Oring__1(T_a)
% 2.75/2.87 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_abs__eq__mult,axiom,
% 2.75/2.87 ! [V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oordered__ring__abs(T_a)
% 2.75/2.87 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
% 2.75/2.87 & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 2.75/2.87 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_abs__mult__pos,axiom,
% 2.75/2.87 ! [V_y,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zdiff__int,axiom,
% 2.75/2.87 ! [V_m,V_n] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 2.75/2.87 => c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_pos__zmult__eq__1__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)
% 2.75/2.87 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 2.75/2.87 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 2.75/2.87 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_of__nat__0__less__iff,axiom,
% 2.75/2.87 ! [V_n_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__less__int__conv,axiom,
% 2.75/2.87 ! [V_n_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_convex__bound__le,axiom,
% 2.75/2.87 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__1(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 2.75/2.87 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__nat__number__of,axiom,
% 2.75/2.87 ! [V_v] :
% 2.75/2.87 ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.87 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 2.75/2.87 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.87 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_of__nat__number__of__eq,axiom,
% 2.75/2.87 ! [V_v,T_a] :
% 2.75/2.87 ( class_Int_Onumber__ring(T_a)
% 2.75/2.87 => ( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.87 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Ozero__class_Ozero(T_a) )
% 2.75/2.87 & ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v))
% 2.75/2.87 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(T_a,V_v) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_convex__bound__lt,axiom,
% 2.75/2.87 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 2.75/2.87 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zdiff__int__split,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,V_P_2] :
% 2.75/2.87 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x_2,V_y_2))))
% 2.75/2.87 <=> ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_y_2,V_x_2)
% 2.75/2.87 => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 2.75/2.87 & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
% 2.75/2.87 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_self__quotient__aux2,axiom,
% 2.75/2.87 ! [V_q,V_r,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 2.75/2.87 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_self__quotient__aux1,axiom,
% 2.75/2.87 ! [V_q,V_r,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 2.75/2.87 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 2.75/2.87 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 2.75/2.87 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__right__cancel,axiom,
% 2.75/2.87 ! [V_b_2,V_a_2,V_c_2] :
% 2.75/2.87 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.75/2.87 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)
% 2.75/2.87 <=> V_a_2 = V_b_2 ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__left__cancel,axiom,
% 2.75/2.87 ! [V_b_2,V_a_2,V_c_2] :
% 2.75/2.87 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.75/2.87 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)
% 2.75/2.87 <=> V_a_2 = V_b_2 ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__0,axiom,
% 2.75/2.87 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__0__right,axiom,
% 2.75/2.87 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__is__0,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 2.75/2.87 <=> ( V_m_2 = V_n_2
% 2.75/2.87 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__cancel2,axiom,
% 2.75/2.87 ! [V_n_2,V_k_2,V_m_2] :
% 2.75/2.87 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
% 2.75/2.87 <=> ( V_m_2 = V_n_2
% 2.75/2.87 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_add__mult__distrib,axiom,
% 2.75/2.87 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_add__mult__distrib2,axiom,
% 2.75/2.87 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__add__mult__distrib,axiom,
% 2.75/2.87 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__of__nat__mult,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__assoc,axiom,
% 2.75/2.87 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__commute,axiom,
% 2.75/2.87 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__assoc,axiom,
% 2.75/2.87 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__commute,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__int__eq,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
% 2.75/2.87 <=> V_m_2 = V_n_2 ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zmult__int,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__mult,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__le__mono,axiom,
% 2.75/2.87 ! [V_l,V_k,V_j,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__le__mono2,axiom,
% 2.75/2.87 ! [V_k,V_j,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__le__mono1,axiom,
% 2.75/2.87 ! [V_k,V_j,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_le__cube,axiom,
% 2.75/2.87 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_le__square,axiom,
% 2.75/2.87 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Suc__mult__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
% 2.75/2.87 <=> V_m_2 = V_n_2 ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_diff__mult__distrib,axiom,
% 2.75/2.87 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_diff__mult__distrib2,axiom,
% 2.75/2.87 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2] :
% 2.75/2.87 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
% 2.75/2.87 <=> V_x_2 = V_y_2 ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 2.75/2.87 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__1,axiom,
% 2.75/2.87 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__1,axiom,
% 2.75/2.87 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__1__eq__mult__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 2.75/2.87 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 2.75/2.87 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__1__right,axiom,
% 2.75/2.87 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__eq__1__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 2.75/2.87 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 2.75/2.87 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_le__mult__natfloor,axiom,
% 2.75/2.87 ! [V_b,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__eq__1__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.75/2.87 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.75/2.87 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__0__less__mult__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
% 2.75/2.87 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 2.75/2.87 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 2.75/2.87 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 2.75/2.87 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__cancel2,axiom,
% 2.75/2.87 ! [V_n_2,V_k_2,V_m_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
% 2.75/2.87 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 2.75/2.87 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__mono1,axiom,
% 2.75/2.87 ! [V_k,V_j,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__less__mono2,axiom,
% 2.75/2.87 ! [V_k,V_j,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__less__mono2,axiom,
% 2.75/2.87 ! [V_y,V_x,V_z] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__order,axiom,
% 2.75/2.87 ! [V_y,V_x] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__less__iff1,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,V_za_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Suc__mult__less__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__Suc__right,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__Suc,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Suc__mult__le__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__eq__self__implies__10,axiom,
% 2.75/2.87 ! [V_n,V_m] :
% 2.75/2.87 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 2.75/2.87 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 2.75/2.87 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__two__squares__add__zero__iff,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2] :
% 2.75/2.87 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.75/2.87 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.75/2.87 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_expi__add,axiom,
% 2.75/2.87 ! [V_b,V_a] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_n__less__m__mult__n,axiom,
% 2.75/2.87 ! [V_m,V_n] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_n__less__n__mult__m,axiom,
% 2.75/2.87 ! [V_m,V_n] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_one__less__mult,axiom,
% 2.75/2.87 ! [V_m,V_n] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__le__cancel__iff2,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,V_za_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__mult__le__cancel__iff1,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,V_za_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_one__le__mult__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
% 2.75/2.87 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
% 2.75/2.87 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__le__cancel2,axiom,
% 2.75/2.87 ! [V_n_2,V_k_2,V_m_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
% 2.75/2.87 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__le__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 2.75/2.87 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_rabs__ratiotest__lemma,axiom,
% 2.75/2.87 ! [V_y,V_x,V_c] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
% 2.75/2.87 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_norm__ratiotest__lemma,axiom,
% 2.75/2.87 ! [V_y,V_x,V_c,T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
% 2.75/2.87 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__eq__if,axiom,
% 2.75/2.87 ! [V_n,V_m] :
% 2.75/2.87 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.75/2.87 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__nat__number__of,axiom,
% 2.75/2.87 ! [V_v_H,V_v] :
% 2.75/2.87 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.75/2.87 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__number__of__mult__left,axiom,
% 2.75/2.87 ! [V_k,V_v_H,V_v] :
% 2.75/2.87 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.75/2.87 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_q__pos__lemma,axiom,
% 2.75/2.87 ! [V_r_H,V_q_H,V_b_H] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_q__neg__lemma,axiom,
% 2.75/2.87 ! [V_r_H,V_q_H,V_b_H] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_unique__quotient__lemma,axiom,
% 2.75/2.87 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zdiv__mono2__lemma,axiom,
% 2.75/2.87 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 2.75/2.87 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_unique__quotient__lemma__neg,axiom,
% 2.75/2.87 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__less__add__iff2,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__less__add__iff1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 2.75/2.87 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 | V_m_2 = V_n_2 ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_left__add__mult__distrib,axiom,
% 2.75/2.87 ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__less__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__eq__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 2.75/2.87 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 2.75/2.87 <=> V_m_2 = V_n_2 ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__mult__le__cancel1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_k_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__eq__add__iff2,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 2.75/2.87 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
% 2.75/2.87 <=> V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__diff__add__eq2,axiom,
% 2.75/2.87 ! [V_n,V_m,V_u,V_j,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 2.75/2.87 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__le__add__iff2,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__eq__add__iff1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 2.75/2.87 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
% 2.75/2.87 <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_n_2 ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__diff__add__eq1,axiom,
% 2.75/2.87 ! [V_n,V_m,V_u,V_i,V_j] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
% 2.75/2.87 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__le__add__iff1,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_not__real__square__gt__zero,axiom,
% 2.75/2.87 ! [V_x_2] :
% 2.75/2.87 ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))
% 2.75/2.87 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__left_Opos__bounded,axiom,
% 2.75/2.87 ! [V_y,T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.87 => ? [B_K] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.87 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult_Opos__bounded,axiom,
% 2.75/2.87 ! [T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.87 => ? [B_K] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.87 & ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__right_Opos__bounded,axiom,
% 2.75/2.87 ! [V_x,T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.87 => ? [B_K] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.87 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_decr__mult__lemma,axiom,
% 2.75/2.87 ! [V_k_2,V_P_2,V_da_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_da_2)
% 2.75/2.87 => ( ! [B_x] :
% 2.75/2.87 ( hBOOL(hAPP(V_P_2,B_x))
% 2.75/2.87 => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_da_2))) )
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 2.75/2.87 => ! [B_x] :
% 2.75/2.87 ( hBOOL(hAPP(V_P_2,B_x))
% 2.75/2.87 => hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_da_2)))) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_incr__mult__lemma,axiom,
% 2.75/2.87 ! [V_k_2,V_P_2,V_da_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_da_2)
% 2.75/2.87 => ( ! [B_x] :
% 2.75/2.87 ( hBOOL(hAPP(V_P_2,B_x))
% 2.75/2.87 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_da_2))) )
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 2.75/2.87 => ! [B_x] :
% 2.75/2.87 ( hBOOL(hAPP(V_P_2,B_x))
% 2.75/2.87 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_da_2)))) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__less__imp__eq__int,axiom,
% 2.75/2.87 ! [V_k] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 2.75/2.87 => ? [B_n] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_n)
% 2.75/2.87 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult_Ononneg__bounded,axiom,
% 2.75/2.87 ! [T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.87 => ? [B_K] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.87 & ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__left_Ononneg__bounded,axiom,
% 2.75/2.87 ! [V_y,T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.87 => ? [B_K] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.87 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_mult__right_Ononneg__bounded,axiom,
% 2.75/2.87 ! [V_x,T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.75/2.87 => ? [B_K] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 2.75/2.87 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 2.75/2.87 ! [V_n,V_x] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_cis__real__of__nat__Suc__mult,axiom,
% 2.75/2.87 ! [V_a,V_n] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a))) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 2.75/2.87 ! [V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_norm__power,axiom,
% 2.75/2.87 ! [V_n,V_x,T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 2.75/2.87 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_norm__power__ineq,axiom,
% 2.75/2.87 ! [V_n,V_x,T_a] :
% 2.75/2.87 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 2.75/2.87 ! [V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 2.75/2.87 ! [V_q,V_p,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 2.75/2.87 ! [V_q,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 2.75/2.87 ! [V_q,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 2.75/2.87 ! [V_q,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 2.75/2.87 ! [V_q,V_p,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 2.75/2.87 ! [V_q,V_y,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__eq__0__iff__number__of,axiom,
% 2.75/2.87 ! [V_wa_2,V_a_2,T_a] :
% 2.75/2.87 ( ( class_Power_Opower(T_a)
% 2.75/2.87 & class_Rings_Omult__zero(T_a)
% 2.75/2.87 & class_Rings_Ono__zero__divisors(T_a)
% 2.75/2.87 & class_Rings_Ozero__neq__one(T_a) )
% 2.75/2.87 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_cis__mult,axiom,
% 2.75/2.87 ! [V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_cis__zero,axiom,
% 2.75/2.87 c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_realpow__Suc__le__self,axiom,
% 2.75/2.87 ! [V_n,V_r,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__0__left__number__of,axiom,
% 2.75/2.87 ! [V_w,T_a] :
% 2.75/2.87 ( ( class_Power_Opower(T_a)
% 2.75/2.87 & class_Rings_Osemiring__0(T_a) )
% 2.75/2.87 => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a) )
% 2.75/2.87 & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_realpow__two__diff,axiom,
% 2.75/2.87 ! [V_y,V_x,T_a] :
% 2.75/2.87 ( class_Rings_Ocomm__ring__1(T_a)
% 2.75/2.87 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_realpow__minus__mult,axiom,
% 2.75/2.87 ! [V_x,V_n,T_a] :
% 2.75/2.87 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_realpow__num__eq__if,axiom,
% 2.75/2.87 ! [V_m,V_n,T_a] :
% 2.75/2.87 ( class_Power_Opower(T_a)
% 2.75/2.87 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 2.75/2.87 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__strict__mono,axiom,
% 2.75/2.87 ! [V_n,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zpower__int,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__power,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 2.75/2.87 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__one__le__power,axiom,
% 2.75/2.87 ! [V_n,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__less__power__nat__eq,axiom,
% 2.75/2.87 ! [V_n_2,V_x_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
% 2.75/2.87 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 2.75/2.87 ! [V_n,V_x] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__zero__less__power__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_x_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
% 2.75/2.87 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 2.75/2.87 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__power__less__imp__less,axiom,
% 2.75/2.87 ! [V_n,V_m,V_i] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__Suc__0,axiom,
% 2.75/2.87 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 2.75/2.87 ! [V_m_2,V_x_2] :
% 2.75/2.87 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.75/2.87 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__real__of__nat,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_real__of__nat__power,axiom,
% 2.75/2.87 ! [V_n,V_m] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zpower__zadd__distrib,axiom,
% 2.75/2.87 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zpower__zpower,axiom,
% 2.75/2.87 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__less__power__nat__eq__number__of,axiom,
% 2.75/2.87 ! [V_wa_2,V_x_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))
% 2.75/2.87 <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__le__zpower__abs,axiom,
% 2.75/2.87 ! [V_n,V_x] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_natfloor__power,axiom,
% 2.75/2.87 ! [V_n,V_x] :
% 2.75/2.87 ( V_x = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))
% 2.75/2.87 => c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_DeMoivre,axiom,
% 2.75/2.87 ! [V_n,V_a] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__eq__if,axiom,
% 2.75/2.87 ! [V_p,V_m] :
% 2.75/2.87 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 2.75/2.87 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__less__zpower__abs__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_x_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))
% 2.75/2.87 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.75/2.87 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_field__power__not__zero,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 2.75/2.87 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__commutes,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__mult__distrib,axiom,
% 2.75/2.87 ! [V_n,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Groups_Ocomm__monoid__mult(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__one,axiom,
% 2.75/2.87 ! [V_n,T_a] :
% 2.75/2.87 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__abs,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.87 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_of__nat__power,axiom,
% 2.75/2.87 ! [V_n,V_m,T_a] :
% 2.75/2.87 ( class_Rings_Osemiring__1(T_a)
% 2.75/2.87 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__mult,axiom,
% 2.75/2.87 ! [V_n,V_m,V_a,T_a] :
% 2.75/2.87 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__one__right,axiom,
% 2.75/2.87 ! [V_a,T_a] :
% 2.75/2.87 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__le__power,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__mono,axiom,
% 2.75/2.87 ! [V_n,V_b,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__less__power,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_one__le__power,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__inject__exp,axiom,
% 2.75/2.87 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
% 2.75/2.87 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
% 2.75/2.87 <=> V_m_2 = V_n_2 ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__eq__0__iff,axiom,
% 2.75/2.87 ! [V_n_2,V_a_2,T_a] :
% 2.75/2.87 ( ( class_Power_Opower(T_a)
% 2.75/2.87 & class_Rings_Omult__zero(T_a)
% 2.75/2.87 & class_Rings_Ono__zero__divisors(T_a)
% 2.75/2.87 & class_Rings_Ozero__neq__one(T_a) )
% 2.75/2.87 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.87 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__0__Suc,axiom,
% 2.75/2.87 ! [V_n,T_a] :
% 2.75/2.87 ( ( class_Power_Opower(T_a)
% 2.75/2.87 & class_Rings_Osemiring__0(T_a) )
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__Suc,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Power_Opower(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__Suc2,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__0,axiom,
% 2.75/2.87 ! [V_a,T_a] :
% 2.75/2.87 ( class_Power_Opower(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__add,axiom,
% 2.75/2.87 ! [V_n,V_m,V_a,T_a] :
% 2.75/2.87 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__less__imp__less__base,axiom,
% 2.75/2.87 ! [V_b,V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__inject__base,axiom,
% 2.75/2.87 ! [V_b,V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => V_a = V_b ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__le__imp__le__base,axiom,
% 2.75/2.87 ! [V_b,V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__less__power__Suc,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__gt1__lemma,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__0__left,axiom,
% 2.75/2.87 ! [V_n,T_a] :
% 2.75/2.87 ( ( class_Power_Opower(T_a)
% 2.75/2.87 & class_Rings_Osemiring__0(T_a) )
% 2.75/2.87 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 2.75/2.87 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zero__le__power__abs,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__idom(T_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__gt1,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__strict__increasing,axiom,
% 2.75/2.87 ! [V_a,V_N,V_n,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__less__imp__less__exp,axiom,
% 2.75/2.87 ! [V_n,V_m,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__strict__increasing__iff,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__increasing,axiom,
% 2.75/2.87 ! [V_a,V_N,V_n,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__Suc__less,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__Suc__less__one,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__strict__decreasing,axiom,
% 2.75/2.87 ! [V_a,V_N,V_n,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__eq__imp__eq__base,axiom,
% 2.75/2.87 ! [V_b,V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.87 => V_a = V_b ) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__decreasing,axiom,
% 2.75/2.87 ! [V_a,V_N,V_n,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__le__imp__le__exp,axiom,
% 2.75/2.87 ! [V_n,V_m,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
% 2.75/2.87 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__increasing__iff,axiom,
% 2.75/2.87 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_one__less__power,axiom,
% 2.75/2.87 ! [V_n,V_a,T_a] :
% 2.75/2.87 ( class_Rings_Olinordered__semidom(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.87 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_lemma__realpow__diff,axiom,
% 2.75/2.87 ! [V_y,V_n,V_p,T_a] :
% 2.75/2.87 ( class_Groups_Omonoid__mult(T_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
% 2.75/2.87 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_reduce__poly__simple,axiom,
% 2.75/2.87 ! [V_n,V_b] :
% 2.75/2.87 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 2.75/2.87 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.87 => ? [B_z] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power__power__power,axiom,
% 2.75/2.87 ! [T_a] :
% 2.75/2.87 ( class_Power_Opower(T_a)
% 2.75/2.87 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power_Opower_Opower__0,axiom,
% 2.75/2.87 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 2.75/2.87
% 2.75/2.87 fof(fact_power_Opower_Opower__Suc,axiom,
% 2.75/2.87 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_reals__Archimedean4,axiom,
% 2.75/2.87 ! [V_x,V_y] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 2.75/2.87 => ? [B_n] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n)),V_y),V_x)
% 2.75/2.87 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_n))),V_y)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_int__power__div__base,axiom,
% 2.75/2.87 ! [V_k,V_m] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 2.75/2.87 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zdiv__mono1__neg,axiom,
% 2.75/2.87 ! [V_b,V_a_H,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => 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)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zdiv__mono1,axiom,
% 2.75/2.87 ! [V_b,V_a_H,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 2.75/2.87 => 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)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_div__neg__neg__trivial,axiom,
% 2.75/2.87 ! [V_b,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 2.75/2.87 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zdiv__mono2__neg,axiom,
% 2.75/2.87 ! [V_b,V_b_H,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 2.75/2.87 => 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)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_div__nonpos__pos__le0,axiom,
% 2.75/2.87 ! [V_b,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 2.75/2.87 => 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)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 2.75/2.87 ! [V_a_2,V_b_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => ( 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))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_div__pos__pos__trivial,axiom,
% 2.75/2.87 ! [V_b,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 2.75/2.87 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_div__nonneg__neg__le0,axiom,
% 2.75/2.87 ! [V_b,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.87 => 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)) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_zdiv__mono2,axiom,
% 2.75/2.87 ! [V_b,V_b_H,V_a] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 2.75/2.87 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 2.75/2.87 => 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)) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 2.75/2.87 ! [V_b_2,V_a_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)
% 2.75/2.87 => ( 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))
% 2.75/2.87 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_a_2)
% 2.75/2.87 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 2.75/2.87 ! [V_i_2,V_k_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 2.75/2.87 => ( 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))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) ) ) ).
% 2.75/2.87
% 2.75/2.87 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 2.75/2.87 ! [V_a_2,V_b_2] :
% 2.75/2.87 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 2.75/2.87 => ( 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))
% 2.75/2.87 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ) ).
% 2.75/2.87
% 2.75/2.88 fof(fact_zdiv__eq__0__iff,axiom,
% 2.75/2.88 ! [V_k_2,V_i_2] :
% 2.75/2.88 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.75/2.88 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.75/2.88 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)
% 2.75/2.88 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) )
% 2.75/2.88 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.88 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2) ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_int__div__less__self,axiom,
% 2.75/2.88 ! [V_k,V_x] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
% 2.75/2.88 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_zdiv__zmult2__eq,axiom,
% 2.75/2.88 ! [V_b,V_a,V_c] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__self1,axiom,
% 2.75/2.88 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__self2,axiom,
% 2.75/2.88 ! [V_c,V_a,V_b,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__add__self2,axiom,
% 2.75/2.88 ! [V_a,V_b,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => 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)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__add__self1,axiom,
% 2.75/2.88 ! [V_a,V_b,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => 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)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__mult1,axiom,
% 2.75/2.88 ! [V_b,V_a,V_c,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__mult2,axiom,
% 2.75/2.88 ! [V_b,V_a,V_c,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__self1__is__id,axiom,
% 2.75/2.88 ! [V_a,V_b,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__self2__is__id,axiom,
% 2.75/2.88 ! [V_a,V_b,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__mult1__if,axiom,
% 2.75/2.88 ! [V_b,V_a,V_c,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 2.75/2.88 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_zdiv__self,axiom,
% 2.75/2.88 ! [V_a] :
% 2.75/2.88 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__self,axiom,
% 2.75/2.88 ! [V_a,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_zdiv__zero,axiom,
% 2.75/2.88 ! [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) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__0,axiom,
% 2.75/2.88 ! [V_a,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__by__0,axiom,
% 2.75/2.88 ! [V_a,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 2.75/2.88 ! [V_y,V_x] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 2.75/2.88 => 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)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 2.75/2.88 ! [V_a_2,V_b_2] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
% 2.75/2.88 => ( 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))
% 2.75/2.88 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 2.75/2.88 ! [V_a_2,V_b_2] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.88 => ( 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))
% 2.75/2.88 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__neg__pos__less0,axiom,
% 2.75/2.88 ! [V_b,V_a] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 2.75/2.88 => 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)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__by__1,axiom,
% 2.75/2.88 ! [V_a,T_a] :
% 2.75/2.88 ( class_Divides_Osemiring__div(T_a)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_divmod__int__rel__div__eq,axiom,
% 2.75/2.88 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 2.75/2.88 ( V_a_1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y),V_r_1)
% 2.75/2.88 => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1)
% 2.75/2.88 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1) ) )
% 2.75/2.88 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1)
% 2.75/2.88 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
% 2.75/2.88 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_split__zdiv,axiom,
% 2.75/2.88 ! [V_k_2,V_n_2,V_P_2] :
% 2.75/2.88 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
% 2.75/2.88 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.75/2.88 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 2.75/2.88 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 2.75/2.88 => ! [B_i] :
% 2.75/2.88 ( ? [B_j] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)
% 2.75/2.88 & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
% 2.75/2.88 & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) )
% 2.75/2.88 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 2.75/2.88 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.88 => ! [B_i] :
% 2.75/2.88 ( ? [B_j] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 2.75/2.88 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 2.75/2.88 & V_n_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j) )
% 2.75/2.88 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_DeMoivre2,axiom,
% 2.75/2.88 ! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_a)) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_realpow__pos__nth__unique,axiom,
% 2.75/2.88 ! [V_a,V_n] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 2.75/2.88 => ? [B_x] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x)
% 2.75/2.88 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
% 2.75/2.88 & ! [B_y] :
% 2.75/2.88 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)
% 2.75/2.88 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a )
% 2.75/2.88 => B_y = B_x ) ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_nat__mult__div__cancel__disj,axiom,
% 2.75/2.88 ! [V_n,V_m,V_k] :
% 2.75/2.88 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.75/2.88 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult2__eq,axiom,
% 2.75/2.88 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__less,axiom,
% 2.75/2.88 ! [V_n,V_m] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__1,axiom,
% 2.75/2.88 ! [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 ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__le__dividend,axiom,
% 2.75/2.88 ! [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) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__le__mono,axiom,
% 2.75/2.88 ! [V_k,V_n,V_m] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.88 => 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)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 2.75/2.88 ! [V_y,V_x] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x,V_y)) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_zdiv__int,axiom,
% 2.75/2.88 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__less__dividend,axiom,
% 2.75/2.88 ! [V_m,V_n] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 2.75/2.88 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_nat__mult__div__cancel1,axiom,
% 2.75/2.88 ! [V_n,V_m,V_k] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__self__is__m,axiom,
% 2.75/2.88 ! [V_m,V_n] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__mult__self1__is__m,axiom,
% 2.75/2.88 ! [V_m,V_n] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__le__mono2,axiom,
% 2.75/2.88 ! [V_k,V_n,V_m] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 2.75/2.88 => 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)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_complex__mod__rcis,axiom,
% 2.75/2.88 ! [V_a,V_r] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_rcis__zero__mod,axiom,
% 2.75/2.88 ! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_cis__rcis__eq,axiom,
% 2.75/2.88 ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__if,axiom,
% 2.75/2.88 ! [V_m,V_n] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.88 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.88 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.75/2.88 & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.88 => 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)) ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_div__geq,axiom,
% 2.75/2.88 ! [V_m,V_n] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.88 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 2.75/2.88 => 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)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_split__div,axiom,
% 2.75/2.88 ! [V_k_2,V_n_2,V_P_2] :
% 2.75/2.88 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
% 2.75/2.88 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.88 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 2.75/2.88 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.88 => ! [B_i,B_j] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)
% 2.75/2.88 => ( V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
% 2.75/2.88 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_split__div__lemma,axiom,
% 2.75/2.88 ! [V_m_2,V_q_2,V_n_2] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 2.75/2.88 => ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2),V_m_2)
% 2.75/2.88 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2))) )
% 2.75/2.88 <=> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_split__div_H,axiom,
% 2.75/2.88 ! [V_n_2,V_m_2,V_P_2] :
% 2.75/2.88 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
% 2.75/2.88 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.75/2.88 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 2.75/2.88 | ? [B_q] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q),V_m_2)
% 2.75/2.88 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q)))
% 2.75/2.88 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_le__div__geq,axiom,
% 2.75/2.88 ! [V_m,V_n] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 2.75/2.88 => 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)) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_rcis__mult,axiom,
% 2.75/2.88 ! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b)) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_realpow__pos__nth,axiom,
% 2.75/2.88 ! [V_a,V_n] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 2.75/2.88 => ? [B_r] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)
% 2.75/2.88 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a ) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_natfloor__div__nat,axiom,
% 2.75/2.88 ! [V_y,V_x] :
% 2.75/2.88 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
% 2.75/2.88 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y)
% 2.75/2.88 => c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_real__of__nat__div4,axiom,
% 2.75/2.88 ! [V_x,V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_x))) ).
% 2.75/2.88
% 2.75/2.88 fof(fact_nonzero__power__divide,axiom,
% 2.75/2.88 ! [V_n,V_a,V_b,T_a] :
% 2.75/2.88 ( class_Fields_Ofield(T_a)
% 2.75/2.88 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.75/2.88 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ).
% 2.75/2.88
% 2.75/2.88 %----Arity declarations (273)
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Oidom(T_1)
% 2.75/2.88 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 2.75/2.88 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.75/2.88 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__ring(T_1)
% 2.75/2.88 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 2.75/2.88 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 2.75/2.88 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 2.75/2.88 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 2.75/2.88 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 2.75/2.88 class_Rings_Oidom(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 2.75/2.88 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_fun__Orderings_Opreorder,axiom,
% 2.75/2.88 ! [T_2,T_1] :
% 2.75/2.88 ( class_Orderings_Opreorder(T_1)
% 2.75/2.88 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_fun__Orderings_Oorder,axiom,
% 2.75/2.88 ! [T_2,T_1] :
% 2.75/2.88 ( class_Orderings_Oorder(T_1)
% 2.75/2.88 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_fun__Orderings_Oord,axiom,
% 2.75/2.88 ! [T_2,T_1] :
% 2.75/2.88 ( class_Orderings_Oord(T_1)
% 2.75/2.88 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.75/2.88 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 2.75/2.88 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 2.75/2.88 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 2.75/2.88 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 2.75/2.88 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 2.75/2.88 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 2.75/2.88 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 2.75/2.88 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 2.75/2.88 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 2.75/2.88 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 2.75/2.88 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 2.75/2.88 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 2.75/2.88 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 2.75/2.88 class_Orderings_Opreorder(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 2.75/2.88 class_Orderings_Olinorder(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 2.75/2.88 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 2.75/2.88 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 2.75/2.88 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 2.75/2.88 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 2.75/2.88 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 2.75/2.88 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 2.75/2.88 class_Rings_Omult__zero(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 2.75/2.88 class_Orderings_Oorder(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 2.75/2.88 class_Int_Oring__char__0(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 2.75/2.88 class_Int_Onumber__ring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 2.75/2.88 class_Rings_Osemiring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 2.75/2.88 class_Orderings_Oord(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 2.75/2.88 class_Rings_Oring__1(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Power_Opower,axiom,
% 2.75/2.88 class_Power_Opower(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 2.75/2.88 class_Groups_Ozero(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Rings_Oring,axiom,
% 2.75/2.88 class_Rings_Oring(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Int_Onumber,axiom,
% 2.75/2.88 class_Int_Onumber(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Int__Oint__Groups_Oone,axiom,
% 2.75/2.88 class_Groups_Oone(tc_Int_Oint) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.75/2.88 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 2.75/2.88 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 2.75/2.88 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 2.75/2.88 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 2.75/2.88 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 2.75/2.88 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 2.75/2.88 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 2.75/2.88 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 2.75/2.88 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 2.75/2.88 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 2.75/2.88 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 2.75/2.88 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 2.75/2.88 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 2.75/2.88 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 2.75/2.88 class_Orderings_Oorder(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 2.75/2.88 class_Rings_Osemiring(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 2.75/2.88 class_Orderings_Oord(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Power_Opower,axiom,
% 2.75/2.88 class_Power_Opower(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 2.75/2.88 class_Groups_Ozero(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 2.75/2.88 class_Int_Onumber(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 2.75/2.88 class_Groups_Oone(tc_Nat_Onat) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 2.75/2.88 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 2.75/2.88 class_Orderings_Oorder(tc_HOL_Obool) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 2.75/2.88 class_Orderings_Oord(tc_HOL_Obool) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.75/2.88 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 2.75/2.88 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 2.75/2.88 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 2.75/2.88 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 2.75/2.88 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 2.75/2.88 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 2.75/2.88 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 2.75/2.88 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 2.75/2.88 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 2.75/2.88 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 2.75/2.88 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 2.75/2.88 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 2.75/2.88 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 2.75/2.88 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 2.75/2.88 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 2.75/2.88 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Nat_Osemiring__char__0,axiom,
% 2.75/2.88 class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 2.75/2.88 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 2.75/2.88 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 2.75/2.88 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 2.75/2.88 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 2.75/2.88 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 2.75/2.88 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 2.75/2.88 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 2.75/2.88 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
% 2.75/2.88 class_Rings_Osemiring__1(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 2.75/2.88 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 2.75/2.88 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 2.75/2.88 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 2.75/2.88 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 2.75/2.88 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
% 2.75/2.88 class_Int_Onumber__ring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 2.75/2.88 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 2.75/2.88 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 2.75/2.88 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 2.75/2.88 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 2.75/2.88 class_Power_Opower(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 2.75/2.88 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 2.75/2.88 class_Rings_Oring(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Int_Onumber,axiom,
% 2.75/2.88 class_Int_Onumber(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 2.75/2.88 class_Groups_Oone(tc_RealDef_Oreal) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.75/2.88 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 2.75/2.88 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 2.75/2.88 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 2.75/2.88 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 2.75/2.88 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 2.75/2.88 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 2.75/2.88 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 2.75/2.88 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 2.75/2.88 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 2.75/2.88 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 2.75/2.88 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Nat_Osemiring__char__0,axiom,
% 2.75/2.88 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 2.75/2.88 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 2.75/2.88 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 2.75/2.88 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 2.75/2.88 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 2.75/2.88 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
% 2.75/2.88 class_Rings_Osemiring__1(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 2.75/2.88 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 2.75/2.88 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 2.75/2.88 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 2.75/2.88 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
% 2.75/2.88 class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 2.75/2.88 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 2.75/2.88 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 2.75/2.88 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 2.75/2.88 class_Power_Opower(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 2.75/2.88 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 2.75/2.88 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
% 2.75/2.88 class_Int_Onumber(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 2.75/2.88 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Oidom(T_1)
% 2.75/2.88 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 2.75/2.88 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Oidom(T_1)
% 2.75/2.88 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Oidom(T_1)
% 2.75/2.88 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 2.75/2.88 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.75/2.88 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.75/2.88 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Ocomm__monoid__add(T_1)
% 2.75/2.88 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Oidom(T_1)
% 2.75/2.88 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Ocomm__monoid__add(T_1)
% 2.75/2.88 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.75/2.88 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Fields_Ofield(T_1)
% 2.75/2.88 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.75/2.88 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Nat_Osemiring__char__0,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Oab__group__add(T_1)
% 2.75/2.88 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.75/2.88 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.75/2.88 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__ring__1(T_1)
% 2.75/2.88 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Ocomm__monoid__add(T_1)
% 2.75/2.88 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Osemiring__1,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.75/2.88 => class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.75/2.88 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Oab__group__add(T_1)
% 2.75/2.88 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.75/2.88 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Int_Onumber__ring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__ring__1(T_1)
% 2.75/2.88 => class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.75/2.88 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Olinordered__idom(T_1)
% 2.75/2.88 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__ring__1(T_1)
% 2.75/2.88 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.75/2.88 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Groups_Ozero(T_1)
% 2.75/2.88 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__ring(T_1)
% 2.75/2.88 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Int_Onumber,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__ring__1(T_1)
% 2.75/2.88 => class_Int_Onumber(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 2.75/2.88 ! [T_1] :
% 2.75/2.88 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.75/2.88 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 2.75/2.88
% 2.75/2.88 %----Conjectures (1)
% 2.75/2.88 fof(conj_0,conjecture,
% 2.75/2.88 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ).
% 2.75/2.88
% 2.75/2.88 %------------------------------------------------------------------------------
% 2.75/2.88 %-------------------------------------------
% 2.75/2.88 % Proof found
% 2.75/2.88 % SZS status Theorem for theBenchmark
% 2.75/2.88 % SZS output start Proof
% 2.75/2.89 %ClaNum:2003(EqnAxiom:303)
% 2.75/2.89 %VarNum:8892(SingletonVarNum:3146)
% 2.75/2.89 %MaxLitNum:7
% 2.75/2.89 %MaxfuncDepth:6
% 2.75/2.89 %SharedTerms:306
% 2.75/2.89 %goalClause: 708
% 2.75/2.89 %singleGoalClaCount:1
% 2.75/2.89 [305]P1(a108)
% 2.75/2.89 [306]P9(a109)
% 2.75/2.89 [307]P9(a110)
% 2.75/2.89 [308]P9(a1)
% 2.75/2.89 [309]P9(a14)
% 2.75/2.89 [310]P10(a109)
% 2.75/2.89 [311]P10(a110)
% 2.75/2.89 [312]P10(a1)
% 2.75/2.89 [313]P11(a109)
% 2.75/2.89 [314]P11(a110)
% 2.75/2.89 [315]P11(a1)
% 2.75/2.89 [316]P29(a109)
% 2.75/2.89 [317]P29(a110)
% 2.75/2.89 [318]P29(a1)
% 2.75/2.89 [319]P37(a109)
% 2.75/2.89 [320]P37(a110)
% 2.75/2.89 [321]P37(a1)
% 2.75/2.89 [322]P37(a14)
% 2.75/2.89 [323]P38(a109)
% 2.75/2.89 [324]P38(a110)
% 2.75/2.89 [325]P38(a1)
% 2.75/2.89 [326]P38(a14)
% 2.75/2.89 [327]P12(a109)
% 2.75/2.89 [328]P12(a110)
% 2.75/2.89 [329]P12(a1)
% 2.75/2.89 [330]P12(a15)
% 2.75/2.89 [331]P13(a109)
% 2.75/2.89 [332]P13(a110)
% 2.75/2.89 [333]P13(a1)
% 2.75/2.89 [334]P13(a15)
% 2.75/2.89 [335]P14(a109)
% 2.75/2.89 [336]P14(a110)
% 2.75/2.89 [337]P14(a1)
% 2.75/2.89 [338]P14(a15)
% 2.75/2.89 [339]P39(a109)
% 2.75/2.89 [340]P39(a110)
% 2.75/2.89 [341]P39(a1)
% 2.75/2.89 [342]P39(a15)
% 2.75/2.89 [343]P20(a109)
% 2.75/2.89 [344]P20(a110)
% 2.75/2.89 [345]P20(a1)
% 2.75/2.89 [346]P20(a15)
% 2.75/2.89 [347]P49(a109)
% 2.75/2.89 [348]P49(a110)
% 2.75/2.89 [349]P49(a1)
% 2.75/2.89 [350]P49(a15)
% 2.75/2.89 [351]P30(a109)
% 2.75/2.89 [352]P30(a110)
% 2.75/2.89 [353]P30(a1)
% 2.75/2.89 [354]P30(a15)
% 2.75/2.89 [355]P21(a110)
% 2.75/2.89 [356]P21(a1)
% 2.75/2.89 [357]P21(a15)
% 2.75/2.89 [358]P15(a110)
% 2.75/2.89 [359]P15(a1)
% 2.75/2.89 [360]P15(a15)
% 2.75/2.89 [361]P27(a110)
% 2.75/2.89 [362]P27(a1)
% 2.75/2.89 [363]P24(a110)
% 2.75/2.89 [364]P24(a1)
% 2.75/2.89 [365]P31(a109)
% 2.75/2.89 [366]P31(a110)
% 2.75/2.89 [367]P31(a1)
% 2.75/2.89 [368]P32(a109)
% 2.75/2.89 [369]P32(a110)
% 2.75/2.89 [370]P32(a1)
% 2.75/2.89 [371]P25(a109)
% 2.75/2.89 [372]P25(a110)
% 2.75/2.89 [373]P25(a1)
% 2.75/2.89 [374]P25(a15)
% 2.75/2.89 [375]P22(a109)
% 2.75/2.89 [376]P22(a110)
% 2.75/2.89 [377]P22(a1)
% 2.75/2.89 [378]P22(a15)
% 2.75/2.89 [379]P73(a109)
% 2.75/2.89 [380]P73(a110)
% 2.75/2.89 [381]P73(a1)
% 2.75/2.89 [382]P73(a15)
% 2.75/2.89 [383]P50(a109)
% 2.75/2.89 [384]P50(a110)
% 2.75/2.89 [385]P50(a1)
% 2.75/2.89 [386]P51(a110)
% 2.75/2.89 [387]P51(a1)
% 2.75/2.89 [388]P74(a109)
% 2.75/2.89 [389]P74(a110)
% 2.75/2.89 [390]P74(a1)
% 2.75/2.89 [391]P74(a15)
% 2.75/2.89 [392]P33(a109)
% 2.75/2.89 [393]P33(a110)
% 2.75/2.89 [394]P33(a1)
% 2.75/2.89 [395]P33(a15)
% 2.75/2.89 [396]P34(a110)
% 2.75/2.89 [397]P34(a1)
% 2.75/2.89 [398]P34(a15)
% 2.75/2.89 [399]P35(a110)
% 2.75/2.89 [400]P35(a1)
% 2.75/2.89 [401]P35(a15)
% 2.75/2.89 [402]P28(a110)
% 2.75/2.89 [403]P28(a1)
% 2.75/2.89 [404]P40(a110)
% 2.75/2.89 [405]P40(a15)
% 2.75/2.89 [406]P41(a110)
% 2.75/2.89 [407]P41(a15)
% 2.75/2.89 [408]P42(a110)
% 2.75/2.89 [409]P42(a15)
% 2.75/2.89 [410]P56(a109)
% 2.75/2.89 [411]P56(a110)
% 2.75/2.89 [412]P56(a1)
% 2.75/2.89 [413]P56(a15)
% 2.75/2.89 [414]P61(a110)
% 2.75/2.89 [415]P61(a1)
% 2.75/2.89 [416]P61(a15)
% 2.75/2.89 [417]P62(a109)
% 2.75/2.89 [418]P62(a110)
% 2.75/2.89 [419]P62(a1)
% 2.75/2.89 [420]P62(a15)
% 2.75/2.89 [421]P71(a109)
% 2.75/2.89 [422]P71(a110)
% 2.75/2.89 [423]P71(a1)
% 2.75/2.89 [424]P71(a15)
% 2.75/2.89 [425]P45(a109)
% 2.75/2.89 [426]P45(a110)
% 2.75/2.89 [427]P45(a1)
% 2.75/2.89 [428]P45(a15)
% 2.75/2.89 [429]P18(a109)
% 2.75/2.89 [430]P18(a110)
% 2.75/2.89 [431]P18(a1)
% 2.75/2.89 [432]P18(a15)
% 2.75/2.89 [433]P36(a109)
% 2.75/2.89 [434]P36(a110)
% 2.75/2.89 [435]P36(a1)
% 2.75/2.89 [436]P36(a15)
% 2.75/2.89 [437]P44(a110)
% 2.75/2.89 [438]P44(a15)
% 2.75/2.89 [439]P26(a109)
% 2.75/2.89 [440]P26(a110)
% 2.75/2.89 [441]P26(a1)
% 2.75/2.89 [442]P26(a15)
% 2.75/2.89 [443]P23(a109)
% 2.75/2.89 [444]P23(a110)
% 2.75/2.89 [445]P23(a1)
% 2.75/2.89 [446]P23(a15)
% 2.75/2.89 [447]P54(a110)
% 2.75/2.89 [448]P54(a1)
% 2.75/2.89 [449]P55(a110)
% 2.75/2.89 [450]P55(a1)
% 2.75/2.89 [451]P63(a109)
% 2.75/2.89 [452]P63(a110)
% 2.75/2.89 [453]P63(a1)
% 2.75/2.89 [454]P64(a110)
% 2.75/2.89 [455]P64(a1)
% 2.75/2.89 [456]P66(a109)
% 2.75/2.89 [457]P66(a110)
% 2.75/2.89 [458]P66(a1)
% 2.75/2.89 [459]P65(a109)
% 2.75/2.89 [460]P65(a110)
% 2.75/2.89 [461]P65(a1)
% 2.75/2.89 [462]P57(a109)
% 2.75/2.89 [463]P57(a110)
% 2.75/2.89 [464]P57(a1)
% 2.75/2.89 [465]P52(a109)
% 2.75/2.89 [466]P52(a110)
% 2.75/2.89 [467]P52(a1)
% 2.75/2.89 [468]P68(a110)
% 2.75/2.89 [469]P68(a1)
% 2.75/2.89 [470]P68(a15)
% 2.75/2.89 [471]P69(a110)
% 2.75/2.89 [472]P69(a1)
% 2.75/2.89 [473]P69(a15)
% 2.75/2.89 [474]P58(a109)
% 2.75/2.89 [475]P58(a110)
% 2.75/2.89 [476]P58(a1)
% 2.75/2.89 [477]P67(a110)
% 2.75/2.89 [478]P67(a1)
% 2.75/2.89 [479]P59(a110)
% 2.75/2.89 [480]P59(a1)
% 2.75/2.89 [481]P60(a110)
% 2.75/2.89 [482]P60(a1)
% 2.75/2.89 [483]P43(a109)
% 2.75/2.89 [484]P43(a110)
% 2.75/2.89 [485]P43(a1)
% 2.75/2.89 [486]P43(a15)
% 2.75/2.89 [487]P72(a109)
% 2.75/2.89 [488]P72(a110)
% 2.75/2.89 [489]P72(a1)
% 2.75/2.89 [490]P72(a15)
% 2.75/2.89 [491]P46(a110)
% 2.75/2.89 [492]P46(a1)
% 2.75/2.89 [493]P46(a15)
% 2.75/2.89 [494]P70(a110)
% 2.75/2.89 [495]P70(a1)
% 2.75/2.89 [496]P70(a15)
% 2.75/2.89 [497]P16(a109)
% 2.75/2.89 [498]P16(a1)
% 2.75/2.89 [499]P17(a110)
% 2.75/2.89 [500]P17(a15)
% 2.75/2.89 [501]P53(a110)
% 2.75/2.89 [502]P53(a1)
% 2.75/2.89 [503]P53(a15)
% 2.75/2.89 [504]P19(a109)
% 2.75/2.89 [505]P19(a110)
% 2.75/2.89 [506]P19(a1)
% 2.75/2.89 [507]P19(a15)
% 2.75/2.89 [508]P48(a109)
% 2.75/2.89 [509]P48(a110)
% 2.75/2.89 [510]P48(a1)
% 2.75/2.89 [511]P48(a15)
% 2.75/2.89 [512]P47(a110)
% 2.75/2.89 [513]P47(a1)
% 2.75/2.89 [514]P47(a15)
% 2.75/2.89 [686]~P3(a1,a13,a13)
% 2.75/2.89 [304]E(f2(a1),a13)
% 2.75/2.89 [516]E(f16(a109),f17(a110))
% 2.75/2.89 [524]E(f18(a1,a13),f2(a1))
% 2.75/2.89 [525]E(f18(a109,a13),f2(a109))
% 2.75/2.89 [554]P2(a110,f2(a110),a116)
% 2.75/2.89 [555]P3(a110,f2(a110),a112)
% 2.75/2.89 [567]P2(a1,f2(a1),f3(a1))
% 2.75/2.89 [569]P3(a1,f2(a1),f3(a1))
% 2.75/2.89 [575]P2(a110,f26(a15,a118),a116)
% 2.75/2.89 [576]P2(a1,f2(a1),f18(a1,a13))
% 2.75/2.89 [677]~E(f3(a15),a6)
% 2.75/2.89 [678]~E(f2(a15),a6)
% 2.75/2.89 [679]~E(f3(a110),f2(a110))
% 2.75/2.89 [680]~E(f3(a1),f2(a1))
% 2.75/2.89 [681]~P4(f3(a1))
% 2.75/2.89 [682]~P4(f2(a1))
% 2.75/2.89 [684]~P4(f18(a1,a13))
% 2.75/2.89 [689]~P3(a1,a13,f2(a1))
% 2.75/2.89 [517]E(f19(f3(a110)),f3(a109))
% 2.75/2.89 [518]E(f19(f2(a110)),f2(a109))
% 2.75/2.89 [519]E(f24(f3(a110)),f3(a109))
% 2.75/2.89 [520]E(f24(f2(a110)),f2(a109))
% 2.75/2.89 [521]E(f4(f2(a15)),f3(a15))
% 2.75/2.89 [529]E(f25(f16(a109),f3(a109)),f3(a110))
% 2.75/2.89 [530]E(f25(f16(a109),f2(a109)),f2(a110))
% 2.75/2.89 [531]E(f25(f17(a1),f3(a109)),f3(a1))
% 2.75/2.89 [532]E(f25(f17(a1),f2(a109)),f2(a1))
% 2.75/2.89 [533]E(f5(f3(a110),f2(a110)),f3(a15))
% 2.75/2.89 [654]P2(a109,f12(a109,a113,a115),f25(a108,f12(a109,a113,a115)))
% 2.75/2.89 [588]E(f25(f16(a109),f12(a109,f2(a109),f3(a109))),f3(a110))
% 2.75/2.89 [589]E(f25(f17(a1),f12(a109,f2(a109),f3(a109))),f3(a1))
% 2.75/2.89 [708]~P2(a110,f25(f16(a109),f12(a109,f12(a109,a113,a115),f3(a109))),f25(f16(a109),f12(a109,f25(a108,f12(a109,a113,a115)),f3(a109))))
% 2.75/2.89 [548]P2(a109,x5481,x5481)
% 2.75/2.89 [549]P2(a110,x5491,x5491)
% 2.75/2.89 [550]P2(a1,x5501,x5501)
% 2.75/2.89 [688]~P3(a109,x6881,x6881)
% 2.75/2.89 [522]E(f18(a1,x5221),x5221)
% 2.75/2.89 [534]E(f7(a110,x5341),f26(a110,x5341))
% 2.75/2.89 [545]E(f12(a1,x5451,a13),x5451)
% 2.75/2.89 [546]E(f10(a1,x5461,a13),x5461)
% 2.75/2.89 [547]E(f12(a1,a13,x5471),x5471)
% 2.75/2.89 [557]E(f10(a109,x5571,x5571),f2(a109))
% 2.75/2.89 [559]P2(a109,f2(a109),x5591)
% 2.75/2.89 [683]~E(f18(a15,x6831),a6)
% 2.75/2.89 [692]~P3(a109,x6921,f2(a109))
% 2.75/2.89 [526]E(f5(f2(a110),x5261),f2(a15))
% 2.75/2.89 [537]E(f19(f18(a110,x5371)),f18(a109,x5371))
% 2.75/2.89 [538]E(f24(f18(a110,x5381)),f18(a109,x5381))
% 2.75/2.89 [541]E(f25(f25(f11(a109),x5411),f3(a109)),x5411)
% 2.75/2.89 [542]E(f25(f25(f11(a1),x5421),f3(a1)),x5421)
% 2.75/2.89 [544]E(f25(f25(f11(a109),x5441),f2(a109)),f2(a109))
% 2.75/2.89 [560]E(f12(a109,x5601,f2(a109)),x5601)
% 2.75/2.89 [561]E(f12(a1,x5611,f2(a1)),x5611)
% 2.75/2.89 [562]E(f10(a109,x5621,f2(a109)),x5621)
% 2.75/2.89 [563]E(f12(a109,f2(a109),x5631),x5631)
% 2.75/2.89 [564]E(f12(a1,f2(a1),x5641),x5641)
% 2.75/2.89 [565]E(f10(a109,f2(a109),x5651),f2(a109))
% 2.75/2.89 [566]E(f8(a1,f2(a1),x5661),f2(a1))
% 2.75/2.89 [577]P2(a110,f26(a15,f117(x5771)),a116)
% 2.75/2.89 [578]P2(a110,f2(a110),f25(f16(a109),x5781))
% 2.75/2.89 [580]P2(a1,f2(a1),f25(f17(a1),x5801))
% 2.75/2.89 [584]P2(a110,x5841,f25(f16(a109),f19(x5841)))
% 2.75/2.89 [598]P3(a109,x5981,f12(a109,x5981,f3(a109)))
% 2.75/2.89 [599]P3(a109,f2(a109),f12(a109,x5991,f3(a109)))
% 2.75/2.89 [600]E(f12(a1,f10(a1,x6001,f3(a1)),f3(a1)),x6001)
% 2.75/2.89 [605]P3(a110,f10(a110,x6051,f3(a110)),f25(f16(a109),f24(x6051)))
% 2.75/2.89 [606]P3(a110,f2(a110),f12(a110,f3(a110),f7(a110,x6061)))
% 2.75/2.89 [626]P3(a110,x6261,f12(a110,f25(f16(a109),f24(x6261)),f3(a110)))
% 2.75/2.89 [685]~P4(f25(f17(a1),x6851))
% 2.75/2.89 [694]~E(f12(a109,x6941,f3(a109)),x6941)
% 2.75/2.89 [700]~E(f12(a109,x7001,f3(a109)),f2(a109))
% 2.75/2.89 [701]~P3(a110,f25(f16(a109),x7011),f2(a110))
% 2.75/2.89 [702]~P3(a1,f25(f17(a1),x7021),f2(a1))
% 2.75/2.89 [705]~P2(a109,f12(a109,x7051,f3(a109)),x7051)
% 2.75/2.89 [707]~P3(a110,f12(a110,f7(a110,x7071),f3(a110)),x7071)
% 2.75/2.89 [535]E(f19(f25(f16(a109),x5351)),x5351)
% 2.75/2.89 [536]E(f24(f25(f16(a109),x5361)),x5361)
% 2.75/2.89 [539]E(f25(f25(f11(a1),a13),x5391),a13)
% 2.75/2.89 [551]E(f25(f25(f11(a109),f3(a109)),x5511),x5511)
% 2.75/2.89 [552]E(f25(f25(f11(a110),f3(a110)),x5521),x5521)
% 2.75/2.89 [553]E(f25(f25(f11(a1),f3(a1)),x5531),x5531)
% 2.75/2.89 [556]E(f25(f25(f11(a109),f2(a109)),x5561),f2(a109))
% 2.75/2.89 [571]E(f7(a110,f25(f16(a109),x5711)),f25(f16(a109),x5711))
% 2.75/2.89 [572]E(f7(a1,f25(f17(a1),x5721)),f25(f17(a1),x5721))
% 2.75/2.89 [590]P2(a109,x5901,f25(f25(f11(a109),x5901),x5901))
% 2.75/2.89 [602]E(f8(a109,x6021,f12(a109,f2(a109),f3(a109))),x6021)
% 2.75/2.89 [608]E(f12(a1,f3(a1),f25(f17(a1),x6081)),f25(f17(a1),f12(a109,x6081,f3(a109))))
% 2.75/2.89 [609]E(f12(a110,f25(f16(a109),x6091),f3(a110)),f25(f16(a109),f12(a109,x6091,f3(a109))))
% 2.75/2.89 [632]P3(a110,f2(a110),f25(f16(a109),f12(a109,x6321,f3(a109))))
% 2.75/2.89 [706]~E(f12(a1,f12(a1,f3(a1),x7061),x7061),f2(a1))
% 2.75/2.89 [643]P2(a109,x6431,f25(f25(f11(a109),x6431),f25(f25(f11(a109),x6431),x6431)))
% 2.75/2.89 [648]E(f25(f25(f22(a109),f12(a109,f2(a109),f3(a109))),x6481),f12(a109,f2(a109),f3(a109)))
% 2.75/2.89 [585]E(f12(a109,x5851,x5852),f12(a109,x5852,x5851))
% 2.75/2.89 [586]E(f12(a1,x5861,x5862),f12(a1,x5862,x5861))
% 2.75/2.89 [591]P2(a109,x5911,f12(a109,x5912,x5911))
% 2.75/2.89 [592]P2(a109,x5921,f12(a109,x5921,x5922))
% 2.75/2.89 [593]P2(a109,f10(a109,x5931,x5932),x5931)
% 2.75/2.89 [594]P2(a109,f8(a109,x5941,x5942),x5941)
% 2.75/2.89 [703]~P3(a109,f12(a109,x7031,x7032),x7032)
% 2.75/2.89 [704]~P3(a109,f12(a109,x7041,x7042),x7041)
% 2.75/2.89 [543]E(f26(a15,f5(x5431,x5432)),f7(a110,x5431))
% 2.75/2.89 [595]E(f10(a109,f12(a109,x5951,x5952),x5952),x5951)
% 2.75/2.89 [596]E(f10(a109,f12(a109,x5961,x5962),x5961),x5962)
% 2.75/2.89 [597]E(f10(a109,x5971,f12(a109,x5971,x5972)),f2(a109))
% 2.75/2.89 [603]E(f25(f25(f11(a15),f4(x6031)),f4(x6032)),f4(f12(a15,x6031,x6032)))
% 2.75/2.89 [607]E(f12(a1,f18(a1,x6071),f18(a1,x6072)),f18(a1,f12(a1,x6071,x6072)))
% 2.75/2.89 [629]P3(a109,f10(a109,x6291,x6292),f12(a109,x6291,f3(a109)))
% 2.75/2.89 [655]P3(a109,x6551,f12(a109,f12(a109,x6552,x6551),f3(a109)))
% 2.75/2.89 [656]P3(a109,x6561,f12(a109,f12(a109,x6561,x6562),f3(a109)))
% 2.75/2.89 [672]P2(a110,f26(a15,x6721),f12(a110,f26(a15,f12(a15,x6721,x6722)),f26(a15,x6722)))
% 2.75/2.89 [673]P2(a110,f10(a110,f26(a15,f12(a15,x6731,x6732)),f26(a15,x6731)),f26(a15,x6732))
% 2.75/2.89 [581]E(f25(f25(f11(a109),x5811),x5812),f25(f25(f11(a109),x5812),x5811))
% 2.75/2.89 [582]E(f25(f25(f11(a110),x5821),x5822),f25(f25(f11(a110),x5822),x5821))
% 2.75/2.89 [583]E(f25(f25(f11(a1),x5831),x5832),f25(f25(f11(a1),x5832),x5831))
% 2.75/2.89 [604]E(f20(f25(f17(a1),x6041),f25(f17(a1),x6042)),f25(f17(a1),f10(a109,x6041,x6042)))
% 2.75/2.89 [616]P2(a1,f2(a1),f25(f25(f22(a1),f7(a1,x6161)),x6162))
% 2.75/2.89 [617]E(f12(a110,f25(f16(a109),x6171),f25(f16(a109),x6172)),f25(f16(a109),f12(a109,x6171,x6172)))
% 2.75/2.89 [620]E(f12(a1,f25(f17(a1),x6201),f25(f17(a1),x6202)),f25(f17(a1),f12(a109,x6201,x6202)))
% 2.75/2.89 [621]E(f8(a1,f25(f17(a1),x6211),f25(f17(a1),x6212)),f25(f17(a1),f8(a109,x6211,x6212)))
% 2.75/2.89 [628]E(f25(f25(f11(a15),f5(f3(a110),x6281)),f5(f3(a110),x6282)),f5(f3(a110),f12(a110,x6281,x6282)))
% 2.75/2.89 [642]E(f12(a109,f12(a109,x6421,f3(a109)),x6422),f12(a109,f12(a109,x6421,x6422),f3(a109)))
% 2.75/2.89 [644]E(f10(a109,f10(a109,x6441,f3(a109)),x6442),f10(a109,x6441,f12(a109,x6442,f3(a109))))
% 2.75/2.89 [645]E(f12(a109,f12(a109,x6451,f3(a109)),x6452),f12(a109,x6451,f12(a109,x6452,f3(a109))))
% 2.75/2.89 [669]P2(a110,f25(f16(a109),f8(a109,x6691,x6692)),f27(a110,f25(f16(a109),x6691),f25(f16(a109),x6692)))
% 2.75/2.89 [612]E(f25(f25(f22(a110),f25(f16(a109),x6121)),x6122),f25(f16(a109),f25(f25(f22(a109),x6121),x6122)))
% 2.75/2.89 [614]E(f25(f25(f22(a1),f25(f17(a1),x6141)),x6142),f25(f17(a1),f25(f25(f22(a109),x6141),x6142)))
% 2.75/2.89 [615]E(f25(f25(f11(a1),f18(a1,x6151)),f18(a1,x6152)),f18(a1,f25(f25(f11(a1),x6151),x6152)))
% 2.75/2.89 [622]E(f25(f25(f11(a110),f25(f16(a109),x6221)),f25(f16(a109),x6222)),f25(f16(a109),f25(f25(f11(a109),x6221),x6222)))
% 2.75/2.89 [625]E(f25(f25(f11(a1),f25(f17(a1),x6251)),f25(f17(a1),x6252)),f25(f17(a1),f25(f25(f11(a109),x6251),x6252)))
% 2.75/2.89 [630]E(f25(f25(f11(a109),x6301),f12(a109,x6302,f3(a109))),f12(a109,x6301,f25(f25(f11(a109),x6301),x6302)))
% 2.75/2.89 [661]E(f25(f25(f11(a109),f12(a109,x6611,f3(a109))),x6612),f12(a109,x6612,f25(f25(f11(a109),x6611),x6612)))
% 2.75/2.89 [649]E(f5(f3(a110),f25(f25(f11(a110),f25(f16(a109),x6491)),x6492)),f25(f25(f22(a15),f5(f3(a110),x6492)),x6491))
% 2.75/2.89 [676]E(f25(f25(f11(a15),f5(f3(a110),x6761)),f5(f3(a110),f25(f25(f11(a110),f25(f16(a109),x6762)),x6761))),f5(f3(a110),f25(f25(f11(a110),f25(f16(a109),f12(a109,x6762,f3(a109)))),x6761)))
% 2.75/2.89 [633]E(f12(a109,x6331,f12(a109,x6332,x6333)),f12(a109,x6332,f12(a109,x6331,x6333)))
% 2.75/2.89 [634]E(f12(a1,x6341,f12(a1,x6342,x6343)),f12(a1,x6342,f12(a1,x6341,x6343)))
% 2.75/2.89 [635]E(f12(a109,f12(a109,x6351,x6352),x6353),f12(a109,x6351,f12(a109,x6352,x6353)))
% 2.75/2.89 [636]E(f12(a1,f12(a1,x6361,x6362),x6363),f12(a1,x6361,f12(a1,x6362,x6363)))
% 2.75/2.89 [637]E(f10(a109,f10(a109,x6371,x6372),x6373),f10(a109,x6371,f12(a109,x6372,x6373)))
% 2.75/2.89 [638]E(f10(a109,f10(a109,x6381,x6382),x6383),f10(a109,f10(a109,x6381,x6383),x6382))
% 2.75/2.89 [639]E(f10(a109,f12(a109,x6391,x6392),f12(a109,x6393,x6392)),f10(a109,x6391,x6393))
% 2.75/2.89 [640]E(f10(a109,f12(a109,x6401,x6402),f12(a109,x6401,x6403)),f10(a109,x6402,x6403))
% 2.75/2.89 [671]E(f10(a109,f10(a109,f12(a109,x6711,f3(a109)),x6712),f12(a109,x6713,f3(a109))),f10(a109,f10(a109,x6711,x6712),x6713))
% 2.75/2.89 [631]E(f8(a109,x6311,f25(f25(f11(a109),x6312),x6313)),f8(a109,f8(a109,x6311,x6312),x6313))
% 2.75/2.89 [657]E(f12(a109,f25(f25(f11(a109),x6571),x6572),f25(f25(f11(a109),x6571),x6573)),f25(f25(f11(a109),x6571),f12(a109,x6572,x6573)))
% 2.75/2.89 [658]E(f10(a109,f25(f25(f11(a109),x6581),x6582),f25(f25(f11(a109),x6581),x6583)),f25(f25(f11(a109),x6581),f10(a109,x6582,x6583)))
% 2.75/2.89 [659]E(f12(a1,f25(f25(f11(a1),x6591),x6592),f25(f25(f11(a1),x6591),x6593)),f25(f25(f11(a1),x6591),f12(a1,x6592,x6593)))
% 2.75/2.89 [660]E(f10(a1,f25(f25(f11(a1),x6601),x6602),f25(f25(f11(a1),x6601),x6603)),f25(f25(f11(a1),x6601),f10(a1,x6602,x6603)))
% 2.75/2.89 [663]E(f25(f25(f11(a1),f25(f25(f22(a1),x6631),x6632)),f25(f25(f22(a1),x6631),x6633)),f25(f25(f22(a1),x6631),f12(a109,x6632,x6633)))
% 2.75/2.89 [664]E(f12(a109,f25(f25(f11(a109),x6641),x6642),f25(f25(f11(a109),x6643),x6642)),f25(f25(f11(a109),f12(a109,x6641,x6643)),x6642))
% 2.75/2.89 [665]E(f10(a109,f25(f25(f11(a109),x6651),x6652),f25(f25(f11(a109),x6653),x6652)),f25(f25(f11(a109),f10(a109,x6651,x6653)),x6652))
% 2.75/2.89 [666]E(f12(a110,f25(f25(f11(a110),x6661),x6662),f25(f25(f11(a110),x6663),x6662)),f25(f25(f11(a110),f12(a110,x6661,x6663)),x6662))
% 2.75/2.89 [667]E(f12(a1,f25(f25(f11(a1),x6671),x6672),f25(f25(f11(a1),x6673),x6672)),f25(f25(f11(a1),f12(a1,x6671,x6673)),x6672))
% 2.75/2.89 [668]E(f10(a1,f25(f25(f11(a1),x6681),x6682),f25(f25(f11(a1),x6683),x6682)),f25(f25(f11(a1),f10(a1,x6681,x6683)),x6682))
% 2.75/2.89 [670]E(f12(a1,f25(f17(a1),x6701),f12(a1,f25(f17(a1),x6702),x6703)),f12(a1,f25(f17(a1),f12(a109,x6701,x6702)),x6703))
% 2.75/2.89 [650]E(f25(f25(f11(a109),f25(f25(f11(a109),x6501),x6502)),x6503),f25(f25(f11(a109),x6501),f25(f25(f11(a109),x6502),x6503)))
% 2.75/2.89 [651]E(f25(f25(f11(a110),f25(f25(f11(a110),x6511),x6512)),x6513),f25(f25(f11(a110),x6511),f25(f25(f11(a110),x6512),x6513)))
% 2.75/2.89 [652]E(f25(f25(f11(a1),f25(f25(f11(a1),x6521),x6522)),x6523),f25(f25(f11(a1),x6521),f25(f25(f11(a1),x6522),x6523)))
% 2.75/2.89 [653]E(f25(f25(f22(a1),f25(f25(f22(a1),x6531),x6532)),x6533),f25(f25(f22(a1),x6531),f25(f25(f11(a109),x6532),x6533)))
% 2.75/2.89 [662]E(f5(f25(f25(f22(a110),x6621),x6622),f25(f25(f11(a110),f25(f16(a109),x6622)),x6623)),f25(f25(f22(a15),f5(x6621,x6623)),x6622))
% 2.75/2.89 [627]E(f25(f25(f23(x6271,x6272,x6273),x6274),f2(a109)),x6272)
% 2.75/2.89 [647]E(f5(f25(f25(f11(a110),x6471),x6472),f12(a110,x6473,x6474)),f25(f25(f11(a15),f5(x6471,x6473)),f5(x6472,x6474)))
% 2.75/2.89 [675]E(f12(a109,f25(f25(f11(a109),x6751),x6752),f12(a109,f25(f25(f11(a109),x6753),x6752),x6754)),f12(a109,f25(f25(f11(a109),f12(a109,x6751,x6753)),x6752),x6754))
% 2.75/2.89 [674]E(f25(f25(f23(x6741,x6742,x6743),x6744),f12(a109,x6745,f3(a109))),f25(f25(x6743,x6744),f25(f25(f23(x6741,x6742,x6743),x6744),x6745)))
% 2.75/2.89 [709]~P51(x7091)+P9(f111(x7091))
% 2.75/2.89 [710]~P51(x7101)+P10(f111(x7101))
% 2.75/2.89 [711]~P51(x7111)+P11(f111(x7111))
% 2.75/2.89 [712]~P51(x7121)+P29(f111(x7121))
% 2.75/2.89 [713]~P51(x7131)+P37(f111(x7131))
% 2.75/2.89 [714]~P51(x7141)+P38(f111(x7141))
% 2.75/2.89 [715]~P19(x7151)+P12(f111(x7151))
% 2.75/2.89 [716]~P19(x7161)+P13(f111(x7161))
% 2.75/2.89 [717]~P22(x7171)+P14(f111(x7171))
% 2.75/2.89 [718]~P39(x7181)+P39(f111(x7181))
% 2.75/2.89 [719]~P39(x7191)+P20(f111(x7191))
% 2.75/2.89 [720]~P39(x7201)+P49(f111(x7201))
% 2.75/2.89 [721]~P30(x7211)+P30(f111(x7211))
% 2.75/2.89 [722]~P15(x7221)+P21(f111(x7221))
% 2.75/2.89 [723]~P15(x7231)+P15(f111(x7231))
% 2.75/2.89 [724]~P51(x7241)+P27(f111(x7241))
% 2.75/2.89 [725]~P51(x7251)+P24(f111(x7251))
% 2.75/2.89 [726]~P51(x7261)+P31(f111(x7261))
% 2.75/2.89 [727]~P51(x7271)+P32(f111(x7271))
% 2.75/2.89 [728]~P22(x7281)+P25(f111(x7281))
% 2.75/2.89 [729]~P22(x7291)+P22(f111(x7291))
% 2.75/2.89 [730]~P53(x7301)+P73(f111(x7301))
% 2.75/2.89 [731]~P51(x7311)+P50(f111(x7311))
% 2.75/2.89 [732]~P51(x7321)+P51(f111(x7321))
% 2.75/2.89 [733]~P39(x7331)+P74(f111(x7331))
% 2.75/2.89 [734]~P46(x7341)+P33(f111(x7341))
% 2.75/2.89 [735]~P46(x7351)+P34(f111(x7351))
% 2.75/2.89 [736]~P51(x7361)+P35(f111(x7361))
% 2.75/2.89 [737]~P51(x7371)+P28(f111(x7371))
% 2.75/2.89 [738]~P48(x7381)+P56(f111(x7381))
% 2.75/2.89 [739]~P53(x7391)+P61(f111(x7391))
% 2.75/2.89 [740]~P53(x7401)+P62(f111(x7401))
% 2.75/2.89 [741]~P48(x7411)+P71(f111(x7411))
% 2.75/2.89 [742]~P48(x7421)+P45(f111(x7421))
% 2.75/2.89 [743]~P48(x7431)+P18(f111(x7431))
% 2.75/2.89 [744]~P51(x7441)+P36(f111(x7441))
% 2.75/2.89 [745]~P39(x7451)+P26(f111(x7451))
% 2.75/2.89 [746]~P39(x7461)+P23(f111(x7461))
% 2.75/2.89 [747]~P51(x7471)+P54(f111(x7471))
% 2.75/2.89 [748]~P51(x7481)+P55(f111(x7481))
% 2.75/2.89 [749]~P51(x7491)+P63(f111(x7491))
% 2.75/2.89 [750]~P51(x7501)+P64(f111(x7501))
% 2.75/2.89 [751]~P51(x7511)+P66(f111(x7511))
% 2.75/2.89 [752]~P51(x7521)+P65(f111(x7521))
% 2.75/2.89 [753]~P51(x7531)+P57(f111(x7531))
% 2.75/2.89 [754]~P51(x7541)+P52(f111(x7541))
% 2.75/2.89 [755]~P47(x7551)+P68(f111(x7551))
% 2.75/2.89 [756]~P46(x7561)+P69(f111(x7561))
% 2.75/2.89 [757]~P51(x7571)+P58(f111(x7571))
% 2.75/2.89 [758]~P51(x7581)+P67(f111(x7581))
% 2.75/2.89 [759]~P51(x7591)+P59(f111(x7591))
% 2.75/2.89 [760]~P51(x7601)+P60(f111(x7601))
% 2.75/2.89 [761]~P39(x7611)+P43(f111(x7611))
% 2.75/2.89 [762]~P48(x7621)+P72(f111(x7621))
% 2.75/2.89 [763]~P46(x7631)+P46(f111(x7631))
% 2.75/2.89 [764]~P53(x7641)+P70(f111(x7641))
% 2.75/2.89 [765]~P17(x7651)+P16(f111(x7651))
% 2.75/2.89 [766]~P53(x7661)+P53(f111(x7661))
% 2.75/2.89 [767]~P19(x7671)+P19(f111(x7671))
% 2.75/2.89 [768]~P48(x7681)+P48(f111(x7681))
% 2.75/2.89 [769]~P47(x7691)+P47(f111(x7691))
% 2.75/2.89 [771]~P74(x7711)+~E(f3(x7711),f2(x7711))
% 2.75/2.89 [773]~P34(x7731)+E(f18(x7731,a13),f2(x7731))
% 2.75/2.89 [806]E(f18(a109,x8061),f2(a109))+~P4(f18(a1,x8061))
% 2.75/2.89 [807]E(x8071,f2(a1))+E(f8(a1,x8071,x8071),f3(a1))
% 2.75/2.89 [811]E(x8111,f2(a109))+P3(a109,f2(a109),x8111)
% 2.75/2.89 [814]P4(x8141)+P2(a1,f2(a1),x8141)
% 2.75/2.89 [820]~P4(x8201)+P3(a1,x8201,f2(a1))
% 2.75/2.89 [845]~P42(x8451)+P2(a110,f2(a110),f28(x8451))
% 2.75/2.89 [846]~P42(x8461)+P3(a110,f2(a110),f29(x8461))
% 2.75/2.89 [852]P1(x8521)+P3(a109,f30(x8521),f49(x8521))
% 2.75/2.89 [863]~P50(x8631)+P2(x8631,f2(x8631),f3(x8631))
% 2.75/2.89 [864]~P50(x8641)+P3(x8641,f2(x8641),f3(x8641))
% 2.75/2.89 [868]P2(a1,x8681,a13)+~E(f18(a109,x8681),f2(a109))
% 2.75/2.89 [885]~E(x8851,f2(a1))+P3(a1,f7(a1,x8851),f3(a1))
% 2.75/2.89 [912]E(x9121,f2(a109))+~P2(a109,x9121,f2(a109))
% 2.75/2.89 [913]P4(x9131)+~P3(a1,x9131,f2(a1))
% 2.75/2.89 [920]E(f19(x9201),f2(a109))+~P2(a110,x9201,f2(a110))
% 3.00/2.89 [921]E(f24(x9211),f2(a109))+~P2(a110,x9211,f2(a110))
% 3.00/2.89 [922]~P4(x9221)+~P2(a1,f2(a1),x9221)
% 3.00/2.89 [924]~P2(a1,x9241,a13)+E(f18(a109,x9241),f2(a109))
% 3.00/2.89 [962]~P50(x9621)+~P2(x9621,f3(x9621),f2(x9621))
% 3.00/2.89 [963]~P50(x9631)+~P3(x9631,f3(x9631),f2(x9631))
% 3.00/2.89 [996]E(x9961,f2(a1))+~P3(a1,f7(a1,x9961),f3(a1))
% 3.00/2.89 [1027]~P3(a1,f2(a1),x10271)+P2(a1,f3(a1),x10271)
% 3.00/2.89 [1028]~P2(a1,f3(a1),x10281)+P3(a1,f2(a1),x10281)
% 3.00/2.89 [1055]~P2(a110,x10551,f3(a110))+P2(a109,f19(x10551),f3(a109))
% 3.00/2.89 [1056]~P2(a110,f3(a110),x10561)+P2(a109,f3(a109),f24(x10561))
% 3.00/2.89 [1057]~P3(a1,f2(a1),x10571)+P3(a109,f2(a109),f88(x10571))
% 3.00/2.89 [1062]~P2(a109,f19(x10621),f3(a109))+P2(a110,x10621,f3(a110))
% 3.00/2.89 [1063]~P2(a109,f3(a109),f24(x10631))+P2(a110,f3(a110),x10631)
% 3.00/2.89 [1066]~P3(a1,a13,x10661)+P3(a109,f2(a109),f18(a109,x10661))
% 3.00/2.89 [1093]P3(a1,a13,x10931)+~P3(a109,f2(a109),f18(a109,x10931))
% 3.00/2.89 [774]~E(x7741,f2(a109))+E(f25(f16(a109),x7741),f2(a110))
% 3.00/2.89 [775]~E(x7751,f2(a109))+E(f25(f17(a1),x7751),f2(a1))
% 3.00/2.89 [776]~P41(x7761)+E(f26(x7761,f3(x7761)),f3(a110))
% 3.00/2.89 [777]~P40(x7771)+E(f26(x7771,f2(x7771)),f2(a110))
% 3.00/2.89 [778]~P51(x7781)+E(f7(x7781,f3(x7781)),f3(x7781))
% 3.00/2.89 [779]~P28(x7791)+E(f7(x7791,f2(x7791)),f2(x7791))
% 3.00/2.89 [782]~P49(x7821)+E(f25(f17(x7821),f3(a109)),f3(x7821))
% 3.00/2.89 [783]~P49(x7831)+E(f25(f17(x7831),f2(a109)),f2(x7831))
% 3.00/2.89 [784]E(x7841,f2(a109))+~E(f25(f16(a109),x7841),f2(a110))
% 3.00/2.89 [785]E(x7851,f2(a109))+~E(f25(f17(a1),x7851),f2(a1))
% 3.00/2.89 [875]~P43(x8751)+E(f23(x8751,f3(x8751),f11(x8751)),f22(x8751))
% 3.00/2.89 [877]E(f25(f16(a109),f18(a109,x8771)),f18(a110,x8771))+P4(f18(a1,x8771))
% 3.00/2.89 [878]P4(f18(a1,x8781))+E(f25(f17(a1),f18(a109,x8781)),f18(a1,x8781))
% 3.00/2.89 [888]~P4(f18(a1,x8881))+E(f25(f16(a109),f18(a109,x8881)),f2(a110))
% 3.00/2.89 [889]~P4(f18(a1,x8891))+E(f25(f17(a1),f18(a109,x8891)),f2(a1))
% 3.00/2.89 [916]~E(x9161,f2(a109))+P2(a110,f25(f16(a109),x9161),f2(a110))
% 3.00/2.89 [917]~E(x9171,f2(a109))+P2(a1,f25(f17(a1),x9171),f2(a1))
% 3.00/2.89 [964]~P3(a1,f2(a1),x9641)+E(f25(f17(a1),f88(x9641)),x9641)
% 3.00/2.89 [987]~P4(f18(a1,x9871))+E(f12(a109,f18(a109,x9871),f3(a109)),f3(a109))
% 3.00/2.89 [1023]E(x10231,f2(a109))+~P2(a110,f25(f16(a109),x10231),f2(a110))
% 3.00/2.89 [1024]E(x10241,f2(a109))+~P2(a1,f25(f17(a1),x10241),f2(a1))
% 3.00/2.89 [1058]~P3(a109,f2(a109),x10581)+E(f12(a109,f43(x10581),f3(a109)),x10581)
% 3.00/2.89 [1070]~P3(a1,x10701,a13)+E(f12(a109,f3(a109),f18(a109,x10701)),f3(a109))
% 3.00/2.89 [1071]~P3(a1,x10711,a13)+E(f12(a109,f18(a109,x10711),f3(a109)),f3(a109))
% 3.00/2.89 [1072]~P2(a1,x10721,a13)+E(f10(a109,f18(a109,x10721),f3(a109)),f2(a109))
% 3.00/2.89 [1094]~P3(a109,f2(a109),x10941)+P3(a110,f2(a110),f25(f16(a109),x10941))
% 3.00/2.89 [1095]~P3(a109,f2(a109),x10951)+P3(a1,f2(a1),f25(f17(a1),x10951))
% 3.00/2.89 [1134]~P2(a110,f2(a110),x11341)+P3(a110,x11341,f25(f16(a109),f57(x11341)))
% 3.00/2.89 [1135]~P2(a110,f2(a110),x11351)+P2(a110,f25(f16(a109),f24(x11351)),x11351)
% 3.00/2.89 [1136]~P2(a110,f2(a110),x11361)+P2(a110,f25(f16(a109),f58(x11361)),x11361)
% 3.00/2.89 [1152]P3(a109,f2(a109),x11521)+~P3(a110,f2(a110),f25(f16(a109),x11521))
% 3.00/2.89 [1153]P3(a109,f2(a109),x11531)+~P3(a1,f2(a1),f25(f17(a1),x11531))
% 3.00/2.89 [1157]~P50(x11571)+P3(x11571,f2(x11571),f12(x11571,f3(x11571),f3(x11571)))
% 3.00/2.89 [1175]P1(x11751)+~P3(a109,f25(x11751,f30(x11751)),f25(x11751,f49(x11751)))
% 3.00/2.89 [1300]~P2(a1,f2(a1),x13001)+P3(a1,f2(a1),f12(a1,f3(a1),x13001))
% 3.00/2.89 [1303]~P3(a109,f2(a109),x13031)+E(f12(a109,f10(a109,x13031,f3(a109)),f3(a109)),x13031)
% 3.00/2.89 [1328]E(x13281,f2(a109))+~P3(a109,x13281,f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1692]~P3(a109,f2(a109),x16921)+E(f12(a109,f10(a109,x16921,f12(a109,f2(a109),f3(a109))),f3(a109)),x16921)
% 3.00/2.89 [1038]E(x10381,f2(a110))+P3(a110,f2(a110),f25(f25(f11(a110),x10381),x10381))
% 3.00/2.89 [1215]P4(f18(a1,x12151))+E(f12(a109,f18(a109,x12151),f3(a109)),f18(a109,f12(a1,x12151,f3(a1))))
% 3.00/2.89 [1237]~E(x12371,f2(a110))+~P3(a110,f2(a110),f25(f25(f11(a110),x12371),x12371))
% 3.00/2.89 [1296]P3(a1,x12961,a13)+E(f12(a109,f3(a109),f18(a109,x12961)),f18(a109,f12(a1,x12961,f3(a1))))
% 3.00/2.89 [1297]P3(a1,x12971,a13)+E(f12(a109,f18(a109,x12971),f3(a109)),f18(a109,f12(a1,x12971,f3(a1))))
% 3.00/2.89 [1298]P2(a1,x12981,a13)+E(f10(a109,f18(a109,x12981),f3(a109)),f18(a109,f10(a1,x12981,f3(a1))))
% 3.00/2.89 [1316]~P2(a110,f2(a110),x13161)+E(f19(f12(a110,x13161,f3(a110))),f12(a109,f19(x13161),f3(a109)))
% 3.00/2.89 [1317]~P2(a110,f2(a110),x13171)+E(f24(f12(a110,x13171,f3(a110))),f12(a109,f24(x13171),f3(a109)))
% 3.00/2.89 [1334]~E(f18(a109,x13341),f2(a109))+P4(f18(a1,f10(a1,x13341,f3(a1))))
% 3.00/2.89 [1577]E(f18(a109,x15771),f2(a109))+~P4(f18(a1,f10(a1,x15771,f3(a1))))
% 3.00/2.89 [1600]~P2(a110,f2(a110),x16001)+P3(a110,x16001,f25(f16(a109),f12(a109,f58(x16001),f3(a109))))
% 3.00/2.89 [1601]~P2(a110,f2(a110),x16011)+P2(a110,f25(f16(a109),f10(a109,f57(x16011),f3(a109))),x16011)
% 3.00/2.89 [1689]~P3(a1,x16891,f2(a1))+P3(a1,f12(a1,f12(a1,f3(a1),x16891),x16891),f2(a1))
% 3.00/2.89 [1807]P1(x18071)+~P3(a109,f25(x18071,f55(x18071)),f25(x18071,f12(a109,f55(x18071),f3(a109))))
% 3.00/2.89 [1850]P3(a1,x18501,f2(a1))+~P3(a1,f12(a1,f12(a1,f3(a1),x18501),x18501),f2(a1))
% 3.00/2.89 [1792]~P2(a109,a113,x17921)+P3(a110,f26(a15,f10(a15,f117(f25(a108,x17921)),a119)),a112)
% 3.00/2.89 [1793]~P2(a109,a62,x17931)+P3(a110,f26(a15,f10(a15,f117(f25(a108,x17931)),a119)),a112)
% 3.00/2.89 [1794]~P2(a109,a73,x17941)+P3(a110,f26(a15,f10(a15,f117(f25(a108,x17941)),a119)),a112)
% 3.00/2.89 [804]~E(x8041,x8042)+P2(a109,x8041,x8042)
% 3.00/2.89 [805]~E(x8051,x8052)+P2(a110,x8051,x8052)
% 3.00/2.89 [818]~P9(x8181)+P2(x8181,x8182,x8182)
% 3.00/2.89 [896]~E(x8961,x8962)+~P3(a109,x8961,x8962)
% 3.00/2.89 [897]~E(x8971,x8972)+~P3(a110,x8971,x8972)
% 3.00/2.89 [898]~E(x8981,x8982)+~P3(a1,x8981,x8982)
% 3.00/2.89 [914]~P3(x9141,x9142,x9142)+~P9(x9141)
% 3.00/2.89 [952]P2(a109,x9522,x9521)+P2(a109,x9521,x9522)
% 3.00/2.89 [953]P2(a110,x9532,x9531)+P2(a110,x9531,x9532)
% 3.00/2.89 [954]P2(a1,x9542,x9541)+P2(a1,x9541,x9542)
% 3.00/2.89 [1006]~P3(a109,x10061,x10062)+P2(a109,x10061,x10062)
% 3.00/2.89 [1008]~P3(a110,x10081,x10082)+P2(a110,x10081,x10082)
% 3.00/2.89 [1009]~P3(a1,x10091,x10092)+P2(a1,x10091,x10092)
% 3.00/2.89 [786]~P9(x7862)+P9(f114(x7861,x7862))
% 3.00/2.89 [787]~P37(x7872)+P37(f114(x7871,x7872))
% 3.00/2.89 [788]~P38(x7882)+P38(f114(x7881,x7882))
% 3.00/2.89 [809]E(f12(a109,x8091,x8092),x8092)+~E(x8091,f2(a109))
% 3.00/2.89 [817]~E(x8172,f2(a1))+E(f8(a1,x8171,x8172),f2(a1))
% 3.00/2.89 [827]~P21(x8271)+E(f10(x8271,x8272,x8272),f2(x8271))
% 3.00/2.89 [851]P2(a1,x8512,x8511)+E(f20(x8511,x8512),f2(a1))
% 3.00/2.89 [890]~P1(x8902)+P2(a109,x8901,f25(x8902,x8901))
% 3.00/2.89 [899]~P28(x8991)+P2(x8991,x8992,f7(x8991,x8992))
% 3.00/2.89 [900]~E(f12(a109,x9002,x9001),x9002)+E(x9001,f2(a109))
% 3.00/2.89 [902]~P40(x9021)+P2(a110,f2(a110),f26(x9021,x9022))
% 3.00/2.89 [903]~P42(x9032)+P2(a110,f2(a110),f91(x9031,x9032))
% 3.00/2.89 [904]~P42(x9042)+P2(a110,f2(a110),f92(x9041,x9042))
% 3.00/2.89 [905]~P42(x9052)+P3(a110,f2(a110),f50(x9051,x9052))
% 3.00/2.89 [906]~P42(x9062)+P3(a110,f2(a110),f87(x9061,x9062))
% 3.00/2.89 [908]~P3(a109,x9082,x9081)+~E(x9081,f2(a109))
% 3.00/2.89 [909]E(x9091,f2(a109))+~E(f12(a109,x9092,x9091),f2(a109))
% 3.00/2.89 [910]E(x9101,f2(a109))+~E(f12(a109,x9101,x9102),f2(a109))
% 3.00/2.89 [915]~P28(x9151)+P2(x9151,f2(x9151),f7(x9151,x9152))
% 3.00/2.89 [1001]~P40(x10011)+~P3(a110,f26(x10011,x10012),f2(a110))
% 3.00/2.89 [1013]~P2(a109,x10131,x10132)+E(f10(a109,x10131,x10132),f2(a109))
% 3.00/2.89 [1014]~P3(a109,x10141,x10142)+E(f8(a109,x10141,x10142),f2(a109))
% 3.00/2.89 [1021]P2(a109,x10211,x10212)+~E(f10(a109,x10211,x10212),f2(a109))
% 3.00/2.89 [1025]~P28(x10251)+~P3(x10251,f7(x10251,x10252),f2(x10251))
% 3.00/2.89 [1035]~P2(a110,x10351,x10352)+P2(a109,f19(x10351),f19(x10352))
% 3.00/2.89 [1036]~P2(a110,x10361,x10362)+P2(a109,f24(x10361),f24(x10362))
% 3.00/2.89 [1049]~P2(a1,x10492,x10491)+E(f10(a1,x10491,x10492),f20(x10491,x10492))
% 3.00/2.89 [1110]~P2(a1,x11101,a13)+P2(a109,f18(a109,x11101),f18(a109,x11102))
% 3.00/2.89 [1126]~P2(a1,x11261,x11262)+P2(a109,f18(a109,x11261),f18(a109,x11262))
% 3.00/2.89 [1127]~P2(a1,x11271,x11272)+P2(a1,f18(a1,x11271),f18(a1,x11272))
% 3.00/2.89 [1128]~P3(a1,x11281,x11282)+P3(a1,f18(a1,x11281),f18(a1,x11282))
% 3.00/2.89 [1176]P2(a1,x11761,x11762)+~P2(a1,f18(a1,x11761),f18(a1,x11762))
% 3.00/2.89 [1177]P3(a1,x11771,x11772)+~P3(a109,f18(a109,x11771),f18(a109,x11772))
% 3.00/2.89 [1178]P3(a1,x11781,x11782)+~P3(a1,f18(a1,x11781),f18(a1,x11782))
% 3.00/2.89 [1268]~P3(a109,x12682,x12681)+P3(a109,f2(a109),f10(a109,x12681,x12682))
% 3.00/2.89 [1269]~P2(a110,x12691,x12692)+P2(a110,f10(a110,x12691,x12692),f2(a110))
% 3.00/2.89 [1270]~P3(a1,x12701,x12702)+P3(a1,f10(a1,x12701,x12702),f2(a1))
% 3.00/2.89 [1375]P3(a109,x13751,x13752)+~P3(a109,f2(a109),f10(a109,x13752,x13751))
% 3.00/2.89 [1376]P2(a110,x13761,x13762)+~P2(a110,f10(a110,x13761,x13762),f2(a110))
% 3.00/2.89 [1377]P3(a1,x13771,x13772)+~P3(a1,f10(a1,x13771,x13772),f2(a1))
% 3.00/2.89 [799]E(x7991,x7992)+~E(f25(f16(a109),x7991),f25(f16(a109),x7992))
% 3.00/2.89 [801]E(x8011,x8012)+~E(f25(f17(a1),x8011),f25(f17(a1),x8012))
% 3.00/2.89 [808]~P40(x8081)+E(f7(a110,f26(x8081,x8082)),f26(x8081,x8082))
% 3.00/2.89 [816]~P28(x8161)+E(f7(x8161,f7(x8161,x8162)),f7(x8161,x8162))
% 3.00/2.89 [821]~P39(x8211)+E(f25(f25(f22(x8211),x8212),f3(a109)),x8212)
% 3.00/2.89 [822]~P26(x8221)+E(f25(f25(f22(x8221),x8222),f3(a109)),x8222)
% 3.00/2.89 [828]~P39(x8281)+E(f25(f25(f11(x8281),x8282),f3(x8281)),x8282)
% 3.00/2.89 [829]~P26(x8291)+E(f25(f25(f11(x8291),x8292),f3(x8291)),x8292)
% 3.00/2.89 [830]~P23(x8301)+E(f25(f25(f11(x8301),x8302),f3(x8301)),x8302)
% 3.00/2.89 [831]~P39(x8311)+E(f25(f25(f22(x8311),x8312),f2(a109)),f3(x8311))
% 3.00/2.89 [832]~P43(x8321)+E(f25(f25(f22(x8321),x8322),f2(a109)),f3(x8321))
% 3.00/2.89 [834]~P39(x8341)+E(f12(x8341,x8342,f2(x8341)),x8342)
% 3.00/2.89 [835]~P25(x8351)+E(f12(x8351,x8352,f2(x8351)),x8352)
% 3.00/2.89 [836]~P22(x8361)+E(f12(x8361,x8362,f2(x8361)),x8362)
% 3.00/2.89 [837]~P21(x8371)+E(f10(x8371,x8372,f2(x8371)),x8372)
% 3.00/2.89 [838]~P16(x8381)+E(f8(x8381,x8382,f3(x8381)),x8382)
% 3.00/2.89 [839]~P39(x8391)+E(f12(x8391,f2(x8391),x8392),x8392)
% 3.00/2.89 [840]~P25(x8401)+E(f12(x8401,f2(x8401),x8402),x8402)
% 3.00/2.89 [841]~P22(x8411)+E(f12(x8411,f2(x8411),x8412),x8412)
% 3.00/2.89 [847]~P39(x8471)+E(f25(f25(f11(x8471),x8472),f2(x8471)),f2(x8471))
% 3.00/2.89 [849]~P42(x8491)+E(f25(f25(f11(x8491),x8492),f2(x8491)),f2(x8491))
% 3.00/2.89 [850]~P56(x8501)+E(f25(f25(f11(x8501),x8502),f2(x8501)),f2(x8501))
% 3.00/2.89 [855]~P16(x8551)+E(f8(x8551,x8552,f2(x8551)),f2(x8551))
% 3.00/2.89 [856]~P16(x8561)+E(f8(x8561,f2(x8561),x8562),f2(x8561))
% 3.00/2.89 [886]~P34(x8861)+E(f12(x8861,x8862,f18(x8861,a13)),x8862)
% 3.00/2.89 [887]~P34(x8871)+E(f12(x8871,f18(x8871,a13),x8872),x8872)
% 3.00/2.89 [948]~P50(x9481)+P2(x9481,f2(x9481),f25(f17(x9481),x9482))
% 3.00/2.89 [995]E(x9951,x9952)+~E(f25(x9951,f42(x9952,x9951)),f25(x9952,f42(x9952,x9951)))
% 3.00/2.89 [1029]P3(a109,f2(a109),x10291)+~E(x10291,f12(a109,x10292,f3(a109)))
% 3.00/2.89 [1069]~P50(x10691)+~P3(x10691,f25(f17(x10691),x10692),f2(x10691))
% 3.00/2.89 [1074]~P2(a109,x10741,x10742)+E(f12(a109,x10741,f53(x10742,x10741)),x10742)
% 3.00/2.89 [1075]~P2(a109,x10751,x10752)+E(f12(a109,x10751,f56(x10752,x10751)),x10752)
% 3.00/2.89 [1076]~E(x10761,x10762)+P3(a109,x10761,f12(a109,x10762,f3(a109)))
% 3.00/2.89 [1077]~E(x10771,x10772)+P3(a1,x10771,f12(a1,x10772,f3(a1)))
% 3.00/2.89 [1080]~E(x10801,f2(a109))+P3(a109,x10801,f12(a109,x10802,f3(a109)))
% 3.00/2.89 [1117]~P50(x11171)+P3(x11171,x11172,f12(x11171,x11172,f3(x11171)))
% 3.00/2.89 [1146]~P3(a1,x11461,a13)+E(f12(a109,f18(a109,x11461),f18(a109,x11462)),f18(a109,x11462))
% 3.00/2.89 [1149]P2(a109,x11491,f24(x11492))+~P2(a110,f25(f16(a109),x11491),x11492)
% 3.00/2.89 [1150]P2(a109,f19(x11501),x11502)+~P2(a110,x11501,f25(f16(a109),x11502))
% 3.00/2.89 [1156]~P3(a1,x11561,a13)+E(f25(f25(f11(a109),f18(a109,x11561)),f18(a109,x11562)),f2(a109))
% 3.00/2.89 [1161]~P2(a109,x11611,x11612)+P2(a110,f25(f16(a109),x11611),f25(f16(a109),x11612))
% 3.00/2.89 [1163]~P2(a109,x11631,x11632)+P2(a1,f25(f17(a1),x11631),f25(f17(a1),x11632))
% 3.00/2.89 [1164]~P3(a109,x11641,x11642)+P3(a110,f25(f16(a109),x11641),f25(f16(a109),x11642))
% 3.00/2.89 [1166]~P3(a109,x11661,x11662)+P3(a1,f25(f17(a1),x11661),f25(f17(a1),x11662))
% 3.00/2.89 [1180]P3(a109,x11802,x11801)+E(f12(a109,x11801,f10(a109,x11802,x11801)),x11802)
% 3.00/2.89 [1187]P3(a109,x11871,x11872)+P3(a109,x11872,f12(a109,x11871,f3(a109)))
% 3.00/2.89 [1188]P2(a109,x11881,x11882)+P2(a109,f12(a109,x11882,f3(a109)),x11881)
% 3.00/2.89 [1238]P2(a109,x12381,x12382)+~P2(a110,f25(f16(a109),x12381),f25(f16(a109),x12382))
% 3.00/2.89 [1240]P2(a109,x12401,x12402)+~P2(a1,f25(f17(a1),x12401),f25(f17(a1),x12402))
% 3.00/2.89 [1241]P3(a109,x12411,x12412)+~P3(a110,f25(f16(a109),x12411),f25(f16(a109),x12412))
% 3.00/2.89 [1243]P3(a109,x12431,x12432)+~P3(a1,f25(f17(a1),x12431),f25(f17(a1),x12432))
% 3.00/2.89 [1264]~P2(a109,x12641,x12642)+E(f12(a109,x12641,f10(a109,x12642,x12641)),x12642)
% 3.00/2.89 [1265]~P2(a109,x12652,x12651)+E(f10(a109,x12651,f10(a109,x12651,x12652)),x12652)
% 3.00/2.89 [1266]~P2(a109,x12662,x12661)+E(f12(a109,f10(a109,x12661,x12662),x12662),x12661)
% 3.00/2.89 [1275]~P3(a1,x12751,x12752)+P2(a1,x12751,f10(a1,x12752,f3(a1)))
% 3.00/2.89 [1277]~P2(a109,x12771,x12772)+P3(a109,x12771,f12(a109,x12772,f3(a109)))
% 3.00/2.89 [1280]~P2(a1,x12801,x12802)+P3(a1,x12801,f12(a1,x12802,f3(a1)))
% 3.00/2.89 [1281]~P3(a1,x12811,x12812)+P3(a1,x12811,f12(a1,x12812,f3(a1)))
% 3.00/2.89 [1284]~P3(a109,x12841,x12842)+P2(a109,f12(a109,x12841,f3(a109)),x12842)
% 3.00/2.89 [1286]~P3(a1,x12861,x12862)+P2(a1,f12(a1,x12861,f3(a1)),x12862)
% 3.00/2.89 [1287]~P2(a1,x12871,x12872)+P3(a1,f10(a1,x12871,f3(a1)),x12872)
% 3.00/2.89 [1362]~P3(a109,x13621,x13622)+E(f12(a109,f12(a109,x13621,f54(x13622,x13621)),f3(a109)),x13622)
% 3.00/2.89 [1374]~P4(f18(a1,x13741))+E(f12(a109,f12(a109,f18(a109,x13741),x13742),f3(a109)),f12(a109,f3(a109),x13742))
% 3.00/2.89 [1380]P2(a109,x13801,x13802)+~P3(a109,x13801,f12(a109,x13802,f3(a109)))
% 3.00/2.89 [1381]P2(a1,x13811,x13812)+~P3(a1,x13811,f12(a1,x13812,f3(a1)))
% 3.00/2.89 [1382]P3(a1,x13821,x13822)+~P2(a1,x13821,f10(a1,x13822,f3(a1)))
% 3.00/2.89 [1384]P2(a1,x13841,x13842)+~P3(a1,f10(a1,x13841,f3(a1)),x13842)
% 3.00/2.89 [1387]P3(a109,x13871,x13872)+~P2(a109,f12(a109,x13871,f3(a109)),x13872)
% 3.00/2.89 [1389]P3(a1,x13891,x13892)+~P2(a1,f12(a1,x13891,f3(a1)),x13892)
% 3.00/2.89 [1461]~P3(a109,x14611,x14612)+~P3(a109,x14612,f12(a109,x14611,f3(a109)))
% 3.00/2.89 [1462]~P2(a109,x14621,x14622)+~P2(a109,f12(a109,x14622,f3(a109)),x14621)
% 3.00/2.89 [1466]~P2(a109,x14661,x14662)+P3(a110,f25(f16(a109),x14661),f12(a110,f25(f16(a109),x14662),f3(a110)))
% 3.00/2.89 [1467]~P3(a109,x14671,x14672)+P2(a110,f12(a110,f25(f16(a109),x14671),f3(a110)),f25(f16(a109),x14672))
% 3.00/2.89 [1502]P3(a110,x15021,f25(f16(a109),x15022))+~P2(a109,f12(a109,f24(x15021),f3(a109)),x15022)
% 3.00/2.89 [1635]E(x16351,f2(a109))+E(f12(a109,f12(a109,f10(a109,x16351,f3(a109)),x16352),f3(a109)),f12(a109,x16351,x16352))
% 3.00/2.89 [1684]P2(a109,x16841,x16842)+~P3(a110,f25(f16(a109),x16841),f12(a110,f25(f16(a109),x16842),f3(a110)))
% 3.00/2.89 [1685]P3(a109,x16851,x16852)+~P2(a110,f12(a110,f25(f16(a109),x16851),f3(a110)),f25(f16(a109),x16852))
% 3.00/2.89 [1693]P2(a109,x16931,x16932)+~P2(a109,f12(a109,x16931,f3(a109)),f12(a109,x16932,f3(a109)))
% 3.00/2.89 [1695]P3(a109,x16951,x16952)+~P3(a109,f12(a109,x16951,f3(a109)),f12(a109,x16952,f3(a109)))
% 3.00/2.89 [795]~E(x7952,f2(a109))+E(f25(f25(f11(a109),x7951),x7952),f2(a109))
% 3.00/2.89 [797]~E(x7971,f2(a109))+E(f25(f25(f11(a109),x7971),x7972),f2(a109))
% 3.00/2.89 [798]~E(x7982,f2(a109))+E(f25(f25(f22(a109),x7981),x7982),f3(a109))
% 3.00/2.89 [859]~P39(x8591)+E(f25(f25(f11(x8591),f3(x8591)),x8592),x8592)
% 3.00/2.89 [860]~P26(x8601)+E(f25(f25(f11(x8601),f3(x8601)),x8602),x8602)
% 3.00/2.89 [861]~P23(x8611)+E(f25(f25(f11(x8611),f3(x8611)),x8612),x8612)
% 3.00/2.89 [869]~P39(x8691)+E(f25(f25(f11(x8691),f2(x8691)),x8692),f2(x8691))
% 3.00/2.89 [871]~P42(x8711)+E(f25(f25(f11(x8711),f2(x8711)),x8712),f2(x8711))
% 3.00/2.89 [872]~P56(x8721)+E(f25(f25(f11(x8721),f2(x8721)),x8722),f2(x8721))
% 3.00/2.89 [873]~P26(x8731)+E(f25(f25(f22(x8731),f3(x8731)),x8732),f3(x8731))
% 3.00/2.89 [874]~P41(x8741)+E(f26(x8741,f25(f17(x8741),x8742)),f25(f17(a110),x8742))
% 3.00/2.89 [876]~P51(x8761)+E(f7(x8761,f25(f17(x8761),x8762)),f25(f17(x8761),x8762))
% 3.00/2.89 [881]E(x8811,f3(a109))+~E(f25(f25(f11(a109),x8812),x8811),f3(a109))
% 3.00/2.89 [882]E(x8821,f3(a109))+~E(f25(f25(f11(a109),x8821),x8822),f3(a109))
% 3.00/2.89 [958]~E(x9582,f2(a109))+E(f25(f25(f22(a109),x9581),x9582),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1061]~E(x10612,f2(a109))+P3(a109,f2(a109),f25(f25(f22(a109),x10611),x10612))
% 3.00/2.89 [1064]P2(a1,f2(a1),f79(x10641))+P75(f25(x10641,f25(f17(a1),x10642)))
% 3.00/2.89 [1067]~P75(f25(x10671,f79(x10671)))+P75(f25(x10671,f25(f17(a1),x10672)))
% 3.00/2.89 [1088]~P54(x10881)+P2(x10881,f2(x10881),f25(f25(f11(x10881),x10882),x10882))
% 3.00/2.89 [1142]~P51(x11421)+E(f25(f25(f11(x11421),f7(x11421,x11422)),f7(x11421,x11422)),f25(f25(f11(x11421),x11422),x11422))
% 3.00/2.89 [1144]P75(f25(x11441,f81(x11441)))+~P75(f25(x11441,f25(f17(a1),x11442)))
% 3.00/2.89 [1158]~E(x11581,f12(a109,f2(a109),f3(a109)))+E(f25(f25(f22(a109),x11581),x11582),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1179]P2(a1,f2(a1),f81(x11791))+~P75(f25(x11791,f25(f17(a1),x11792)))
% 3.00/2.89 [1190]~P34(x11901)+E(f12(x11901,f3(x11901),f18(x11901,x11902)),f18(x11901,f12(a1,x11902,f3(a1))))
% 3.00/2.89 [1199]~P2(a1,x11991,x11992)+E(f12(a1,x11991,f25(f17(a1),f84(x11992,x11991))),x11992)
% 3.00/2.89 [1206]E(x12061,f12(a109,f2(a109),f3(a109)))+~E(f25(f25(f11(a109),x12062),x12061),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1207]E(x12071,f12(a109,f2(a109),f3(a109)))+~E(f25(f25(f11(a109),x12071),x12072),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1230]~P2(a1,f2(a1),x12301)+P2(a1,f2(a1),f25(f25(f22(a1),x12301),x12302))
% 3.00/2.89 [1232]~P3(a109,f2(a109),x12321)+P3(a109,f2(a109),f25(f25(f22(a109),x12321),x12322))
% 3.00/2.89 [1235]~P49(x12351)+E(f12(x12351,f3(x12351),f25(f17(x12351),x12352)),f25(f17(x12351),f12(a109,x12352,f3(a109))))
% 3.00/2.89 [1263]E(x12631,f2(a1))+P3(a1,f2(a1),f25(f25(f22(a1),f7(a1,x12631)),x12632))
% 3.00/2.89 [1267]~E(x12672,f2(a109))+P3(a1,f2(a1),f25(f25(f22(a1),f7(a1,x12671)),x12672))
% 3.00/2.89 [1314]~P54(x13141)+~P3(x13141,f25(f25(f11(x13141),x13142),x13142),f2(x13141))
% 3.00/2.89 [1349]P3(a109,f2(a109),x13491)+~P3(a109,f2(a109),f25(f25(f11(a109),x13492),x13491))
% 3.00/2.89 [1350]P3(a109,f2(a109),x13501)+~P3(a109,f2(a109),f25(f25(f11(a109),x13501),x13502))
% 3.00/2.89 [1410]~P2(a109,x14102,x14101)+E(f10(a110,f25(f16(a109),x14101),f25(f16(a109),x14102)),f25(f16(a109),f10(a109,x14101,x14102)))
% 3.00/2.89 [1411]~P2(a109,x14112,x14111)+E(f10(a1,f25(f17(a1),x14111),f25(f17(a1),x14112)),f25(f17(a1),f10(a109,x14111,x14112)))
% 3.00/2.89 [1441]~P1(x14411)+P3(a109,f25(x14411,x14412),f25(x14411,f12(a109,x14412,f3(a109))))
% 3.00/2.89 [1688]~P3(a109,f2(a109),x16881)+P3(a109,f10(a109,x16881,f12(a109,x16882,f3(a109))),x16881)
% 3.00/2.89 [1745]~P2(a109,f12(a109,f2(a109),f3(a109)),x17451)+P2(a109,f12(a109,f2(a109),f3(a109)),f25(f25(f22(a109),x17451),x17452))
% 3.00/2.89 [1809]P2(a109,f12(a109,f2(a109),f3(a109)),x18091)+~P2(a109,f12(a109,f2(a109),f3(a109)),f25(f25(f11(a109),x18092),x18091))
% 3.00/2.89 [1810]P2(a109,f12(a109,f2(a109),f3(a109)),x18101)+~P2(a109,f12(a109,f2(a109),f3(a109)),f25(f25(f11(a109),x18101),x18102))
% 3.00/2.89 [1811]~P69(x18111)+E(f25(f25(f11(x18111),f12(x18111,x18112,f3(x18111))),f10(x18111,x18112,f3(x18111))),f10(x18111,f25(f25(f11(x18111),x18112),x18112),f3(x18111)))
% 3.00/2.89 [1111]E(f7(a1,x11111),f3(a1))+~E(f7(a1,f25(f25(f11(a1),x11111),x11112)),f3(a1))
% 3.00/2.89 [1143]~E(f25(f16(a109),f24(x11431)),x11431)+E(f24(f25(f25(f22(a110),x11431),x11432)),f25(f25(f22(a109),f24(x11431)),x11432))
% 3.00/2.89 [1220]~P3(a109,f2(a109),x12202)+E(f8(a109,f25(f25(f11(a109),x12201),x12202),x12202),x12201)
% 3.00/2.89 [1221]~P3(a109,f2(a109),x12211)+E(f8(a109,f25(f25(f11(a109),x12211),x12212),x12211),x12212)
% 3.00/2.89 [1326]P3(a1,x13261,a13)+E(f25(f25(f11(a109),f18(a109,x13261)),f18(a109,x13262)),f18(a109,f25(f25(f11(a1),x13261),x13262)))
% 3.00/2.89 [1404]~P2(a110,f2(a110),x14041)+E(f19(f12(a110,x14041,f25(f16(a109),x14042))),f12(a109,f19(x14041),x14042))
% 3.00/2.89 [1405]~P2(a110,f2(a110),x14051)+E(f24(f12(a110,x14051,f25(f16(a109),x14052))),f12(a109,f24(x14051),x14052))
% 3.00/2.89 [1531]~P2(a110,f25(f16(a109),x15312),x15311)+E(f19(f10(a110,x15311,f25(f16(a109),x15312))),f10(a109,f19(x15311),x15312))
% 3.00/2.89 [1532]~P2(a110,f25(f16(a109),x15322),x15321)+E(f24(f10(a110,x15321,f25(f16(a109),x15322))),f10(a109,f24(x15321),x15322))
% 3.00/2.89 [1545]E(x15451,f2(a110))+~E(f12(a110,f25(f25(f11(a110),x15452),x15452),f25(f25(f11(a110),x15451),x15451)),f2(a110))
% 3.00/2.89 [1546]E(x15461,f2(a110))+~E(f12(a110,f25(f25(f11(a110),x15461),x15461),f25(f25(f11(a110),x15462),x15462)),f2(a110))
% 3.00/2.89 [1548]~P39(x15481)+E(f12(x15481,x15482,x15482),f25(f25(f11(x15481),f12(x15481,f3(x15481),f3(x15481))),x15482))
% 3.00/2.89 [1582]E(x15821,f2(a109))+E(f25(f25(f11(a109),x15822),f25(f25(f22(a109),x15822),f10(a109,x15821,f3(a109)))),f25(f25(f22(a109),x15822),x15821))
% 3.00/2.89 [1710]~P3(a1,x17101,x17102)+E(f12(a1,x17101,f25(f17(a1),f12(a109,f85(x17102,x17101),f3(a109)))),x17102)
% 3.00/2.89 [1746]P4(f18(a1,x17461))+E(f12(a109,f12(a109,f18(a109,x17461),x17462),f3(a109)),f12(a109,f18(a109,f12(a1,x17461,f3(a1))),x17462))
% 3.00/2.89 [1786]~P3(a1,a13,x17862)+E(f10(a109,f12(a109,x17861,f3(a109)),f18(a109,x17862)),f10(a109,x17861,f18(a109,f10(a1,x17862,f3(a1)))))
% 3.00/2.89 [1948]~P2(a110,f2(a110),x19482)+P2(a110,f12(a110,f25(f25(f11(a110),f25(f16(a109),x19481)),x19482),f3(a110)),f25(f25(f22(a110),f12(a110,x19482,f3(a110))),x19481))
% 3.00/2.89 [1845]E(x18451,f2(a109))+E(f12(a109,x18452,f25(f25(f11(a109),f10(a109,x18451,f3(a109))),x18452)),f25(f25(f11(a109),x18451),x18452))
% 3.00/2.89 [965]~P39(x9651)+E(f12(x9651,x9652,x9653),f12(x9651,x9653,x9652))
% 3.00/2.89 [1011]P2(a109,x10111,x10112)+~E(x10112,f12(a109,x10111,x10113))
% 3.00/2.89 [1078]E(x10781,x10782)+~E(f12(a109,x10783,x10781),f12(a109,x10783,x10782))
% 3.00/2.89 [1079]E(x10791,x10792)+~E(f12(a109,x10791,x10793),f12(a109,x10792,x10793))
% 3.00/2.89 [1249]~P2(a109,x12491,x12493)+P2(a109,x12491,f12(a109,x12492,x12493))
% 3.00/2.89 [1251]~P2(a109,x12511,x12512)+P2(a109,x12511,f12(a109,x12512,x12513))
% 3.00/2.89 [1253]~P3(a109,x12531,x12533)+P3(a109,x12531,f12(a109,x12532,x12533))
% 3.00/2.89 [1255]~P3(a109,x12551,x12552)+P3(a109,x12551,f12(a109,x12552,x12553))
% 3.00/2.89 [1256]~P3(a109,x12561,x12563)+P3(a109,f10(a109,x12561,x12562),x12563)
% 3.00/2.89 [1367]P2(a109,x13671,x13672)+~P2(a109,f12(a109,x13673,x13671),x13672)
% 3.00/2.89 [1368]P2(a109,x13681,x13682)+~P2(a109,f12(a109,x13681,x13683),x13682)
% 3.00/2.89 [1369]P3(a109,x13691,x13692)+~P3(a109,f12(a109,x13691,x13693),x13692)
% 3.00/2.89 [1470]~P2(a109,x14702,x14703)+P2(a109,f12(a109,x14701,x14702),f12(a109,x14701,x14703))
% 3.00/2.89 [1471]~P2(a109,x14711,x14713)+P2(a109,f12(a109,x14711,x14712),f12(a109,x14713,x14712))
% 3.00/2.89 [1472]~P2(a109,x14723,x14722)+P2(a109,f10(a109,x14721,x14722),f10(a109,x14721,x14723))
% 3.00/2.89 [1473]~P2(a109,x14731,x14733)+P2(a109,f10(a109,x14731,x14732),f10(a109,x14733,x14732))
% 3.00/2.89 [1474]~P2(a109,x14741,x14743)+P2(a109,f8(a109,x14741,x14742),f8(a109,x14743,x14742))
% 3.00/2.89 [1475]~P2(a110,x14752,x14753)+P2(a110,f12(a110,x14751,x14752),f12(a110,x14751,x14753))
% 3.00/2.89 [1476]~P2(a1,x14762,x14763)+P2(a1,f12(a1,x14761,x14762),f12(a1,x14761,x14763))
% 3.00/2.89 [1477]~P3(a109,x14772,x14773)+P3(a109,f12(a109,x14771,x14772),f12(a109,x14771,x14773))
% 3.00/2.89 [1478]~P3(a109,x14781,x14783)+P3(a109,f12(a109,x14781,x14782),f12(a109,x14783,x14782))
% 3.00/2.89 [1479]~P3(a1,x14791,x14793)+P3(a1,f12(a1,x14791,x14792),f12(a1,x14793,x14792))
% 3.00/2.89 [1578]~P2(a109,f10(a109,x15781,x15783),x15782)+P2(a109,x15781,f12(a109,x15782,x15783))
% 3.00/2.89 [1579]~P3(a109,f12(a109,x15791,x15793),x15792)+P3(a109,x15791,f10(a109,x15792,x15793))
% 3.00/2.89 [1580]~P2(a109,x15801,f12(a109,x15803,x15802))+P2(a109,f10(a109,x15801,x15802),x15803)
% 3.00/2.89 [1581]~P3(a109,x15811,f10(a109,x15813,x15812))+P3(a109,f12(a109,x15811,x15812),x15813)
% 3.00/2.89 [1686]P2(a109,x16861,x16862)+~P2(a109,f12(a109,x16863,x16861),f12(a109,x16863,x16862))
% 3.00/2.89 [1687]P3(a109,x16871,x16872)+~P3(a109,f12(a109,x16873,x16871),f12(a109,x16873,x16872))
% 3.00/2.89 [1083]~P21(x10831)+E(f12(x10831,f10(x10831,x10832,x10833),x10833),x10832)
% 3.00/2.89 [1084]~P21(x10841)+E(f10(x10841,f12(x10841,x10842,x10843),x10843),x10842)
% 3.00/2.89 [1218]~P34(x12181)+E(f10(x12181,f18(x12181,x12182),f18(x12181,x12183)),f18(x12181,f10(a1,x12182,x12183)))
% 3.00/2.89 [1219]~P34(x12191)+E(f12(x12191,f18(x12191,x12192),f18(x12191,x12193)),f18(x12191,f12(a1,x12192,x12193)))
% 3.00/2.89 [1292]~P28(x12921)+E(f7(x12921,f10(x12921,x12922,x12923)),f7(x12921,f10(x12921,x12923,x12922)))
% 3.00/2.89 [1293]~P40(x12931)+E(f26(x12931,f10(x12931,x12932,x12933)),f26(x12931,f10(x12931,x12933,x12932)))
% 3.00/2.89 [1305]~P49(x13051)+E(f21(x13051,x13052,f2(a109),x13053),x13053)
% 3.00/2.89 [1379]P3(a109,x13791,x13792)+~E(x13792,f12(a109,f12(a109,x13791,x13793),f3(a109)))
% 3.00/2.89 [1421]~P76(x14211,x14213,x14212)+P75(f25(x14211,f8(a1,x14212,x14213)))
% 3.00/2.89 [1571]~P2(a109,x15712,x15713)+E(f10(a109,f12(a109,x15711,x15712),x15713),f10(a109,x15711,f10(a109,x15713,x15712)))
% 3.00/2.89 [1572]~P2(a109,x15723,x15722)+E(f10(a109,f12(a109,x15721,x15722),x15723),f12(a109,x15721,f10(a109,x15722,x15723)))
% 3.00/2.89 [1574]~P2(a109,x15743,x15741)+E(f10(a109,f12(a109,x15741,x15742),x15743),f12(a109,f10(a109,x15741,x15743),x15742))
% 3.00/2.89 [1628]P76(x16281,x16282,x16283)+~P75(f25(x16281,f8(a1,x16283,x16282)))
% 3.00/2.89 [1651]~P2(a109,x16513,x16512)+P2(a109,x16511,f10(a109,f12(a109,x16512,x16511),x16513))
% 3.00/2.89 [1716]~P40(x17161)+P2(a110,f26(x17161,f12(x17161,x17162,x17163)),f12(a110,f26(x17161,x17162),f26(x17161,x17163)))
% 3.00/2.89 [1717]~P40(x17171)+P2(a110,f26(x17171,f10(x17171,x17172,x17173)),f12(a110,f26(x17171,x17172),f26(x17171,x17173)))
% 3.00/2.89 [1718]~P40(x17181)+P2(a110,f10(a110,f26(x17181,x17182),f26(x17181,x17183)),f26(x17181,f12(x17181,x17182,x17183)))
% 3.00/2.89 [1719]~P40(x17191)+P2(a110,f10(a110,f26(x17191,x17192),f26(x17191,x17193)),f26(x17191,f10(x17191,x17192,x17193)))
% 3.00/2.89 [1729]~P28(x17291)+P2(x17291,f7(x17291,f12(x17291,x17292,x17293)),f12(x17291,f7(x17291,x17292),f7(x17291,x17293)))
% 3.00/2.89 [1730]~P28(x17301)+P2(x17301,f7(x17301,f10(x17301,x17302,x17303)),f12(x17301,f7(x17301,x17302),f7(x17301,x17303)))
% 3.00/2.89 [1731]~P28(x17311)+P2(x17311,f10(x17311,f7(x17311,x17312),f7(x17311,x17313)),f7(x17311,f10(x17311,x17313,x17312)))
% 3.00/2.89 [1732]~P28(x17321)+P2(x17321,f10(x17321,f7(x17321,x17322),f7(x17321,x17323)),f7(x17321,f10(x17321,x17322,x17323)))
% 3.00/2.89 [936]~E(x9362,f2(a109))+E(f25(f25(f11(a109),x9361),x9362),f25(f25(f11(a109),x9363),x9362))
% 3.00/2.89 [938]~E(x9381,f2(a109))+E(f25(f25(f11(a109),x9381),x9382),f25(f25(f11(a109),x9381),x9383))
% 3.00/2.89 [959]~P39(x9591)+E(f25(f25(f11(x9591),x9592),x9593),f25(f25(f11(x9591),x9593),x9592))
% 3.00/2.89 [1139]P2(a1,x11391,x11392)+~E(x11392,f12(a1,x11391,f25(f17(a1),x11393)))
% 3.00/2.89 [1313]~P49(x13131)+E(f12(x13131,f25(f17(x13131),x13132),f25(f17(x13131),x13133)),f25(f17(x13131),f12(a109,x13132,x13133)))
% 3.00/2.89 [1335]~P51(x13351)+P2(x13351,f2(x13351),f25(f25(f22(x13351),f7(x13351,x13352)),x13353))
% 3.00/2.89 [1353]P3(a109,f2(a109),x13531)+P2(a109,f25(f25(f11(a109),x13532),x13531),f25(f25(f11(a109),x13533),x13531))
% 3.00/2.89 [1354]P3(a109,f2(a109),x13541)+P2(a109,f25(f25(f11(a109),x13541),x13542),f25(f25(f11(a109),x13541),x13543))
% 3.00/2.89 [1398]~P2(a109,x13982,x13983)+P2(a109,f25(f25(f11(a109),x13981),x13982),f25(f25(f11(a109),x13981),x13983))
% 3.00/2.89 [1400]~P2(a109,x14001,x14003)+P2(a109,f25(f25(f11(a109),x14001),x14002),f25(f25(f11(a109),x14003),x14002))
% 3.00/2.89 [1459]~P28(x14591)+E(f7(x14591,f12(x14591,f7(x14591,x14592),f7(x14591,x14593))),f12(x14591,f7(x14591,x14592),f7(x14591,x14593)))
% 3.00/2.89 [1469]~P4(f18(a1,x14691))+E(f12(a109,f18(a109,x14691),f12(a109,f18(a109,x14692),x14693)),f12(a109,f18(a109,x14692),x14693))
% 3.00/2.89 [1606]P3(a109,x16061,x16062)+~P3(a109,f25(f25(f11(a109),x16063),x16061),f25(f25(f11(a109),x16063),x16062))
% 3.00/2.89 [1607]P3(a109,x16071,x16072)+~P3(a109,f25(f25(f11(a109),x16071),x16073),f25(f25(f11(a109),x16072),x16073))
% 3.00/2.89 [1611]P3(a109,f2(a109),x16111)+~P3(a109,f25(f25(f11(a109),x16112),x16111),f25(f25(f11(a109),x16113),x16111))
% 3.00/2.89 [1612]P3(a109,f2(a109),x16121)+~P3(a109,f25(f25(f11(a109),x16121),x16122),f25(f25(f11(a109),x16121),x16123))
% 3.00/2.89 [1882]~P2(a109,x18822,x18823)+E(f10(a109,f12(a109,x18821,x18822),f12(a109,x18823,f3(a109))),f10(a109,x18821,f12(a109,f10(a109,x18823,x18822),f3(a109))))
% 3.00/2.89 [1883]~P2(a109,x18832,x18831)+E(f10(a109,f12(a109,f10(a109,x18831,x18832),f3(a109)),x18833),f10(a109,f12(a109,x18831,f3(a109)),f12(a109,x18832,x18833)))
% 3.00/2.89 [1889]~P40(x18891)+P2(a110,f7(a110,f10(a110,f26(x18891,x18892),f26(x18891,x18893))),f26(x18891,f10(x18891,x18892,x18893)))
% 3.00/2.89 [1892]~P28(x18921)+P2(x18921,f7(x18921,f10(x18921,f7(x18921,x18922),f7(x18921,x18923))),f7(x18921,f10(x18921,x18922,x18923)))
% 3.00/2.89 [1198]~P44(x11981)+E(f26(x11981,f25(f25(f22(x11981),x11982),x11983)),f25(f25(f22(a110),f26(x11981,x11982)),x11983))
% 3.00/2.89 [1208]~P51(x12081)+E(f25(f25(f22(x12081),f7(x12081,x12082)),x12083),f7(x12081,f25(f25(f22(x12081),x12082),x12083)))
% 3.00/2.89 [1261]~P34(x12611)+E(f25(f25(f11(x12611),f18(x12611,x12612)),f18(x12611,x12613)),f18(x12611,f25(f25(f11(a1),x12612),x12613)))
% 3.00/2.89 [1262]~E(x12621,f2(a109))+E(f8(a109,f25(f25(f11(a109),x12621),x12622),f25(f25(f11(a109),x12621),x12623)),f2(a109))
% 3.00/2.89 [1272]~P49(x12721)+E(f25(f25(f22(x12721),f25(f17(x12721),x12722)),x12723),f25(f17(x12721),f25(f25(f22(a109),x12722),x12723)))
% 3.00/2.89 [1288]~P44(x12881)+E(f25(f25(f11(a110),f26(x12881,x12882)),f26(x12881,x12883)),f26(x12881,f25(f25(f11(x12881),x12882),x12883)))
% 3.00/2.89 [1299]~P51(x12991)+E(f25(f25(f11(x12991),f7(x12991,x12992)),f7(x12991,x12993)),f7(x12991,f25(f25(f11(x12991),x12992),x12993)))
% 3.00/2.89 [1348]~P49(x13481)+E(f25(f25(f11(x13481),f25(f17(x13481),x13482)),f25(f17(x13481),x13483)),f25(f17(x13481),f25(f25(f11(a109),x13482),x13483)))
% 3.00/2.89 [1352]E(x13521,f2(a109))+E(f8(a109,f25(f25(f11(a109),x13521),x13522),f25(f25(f11(a109),x13521),x13523)),f8(a109,x13522,x13523))
% 3.00/2.89 [1416]~P39(x14161)+E(f25(f25(f11(x14161),x14162),f25(f25(f22(x14161),x14162),x14163)),f25(f25(f22(x14161),x14162),f12(a109,x14163,f3(a109))))
% 3.00/2.89 [1417]~P43(x14171)+E(f25(f25(f11(x14171),x14172),f25(f25(f22(x14171),x14172),x14173)),f25(f25(f22(x14171),x14172),f12(a109,x14173,f3(a109))))
% 3.00/2.89 [1501]~P3(a1,x15011,a13)+E(f25(f25(f11(a109),f18(a109,x15011)),f25(f25(f11(a109),f18(a109,x15012)),x15013)),f2(a109))
% 3.00/2.89 [1547]~P3(a109,f2(a109),x15471)+E(f8(a109,f25(f25(f11(a109),x15471),x15472),f25(f25(f11(a109),x15471),x15473)),f8(a109,x15472,x15473))
% 3.00/2.89 [1562]~P3(a1,f2(a1),x15623)+E(f8(a1,x15621,f25(f25(f11(a1),x15622),x15623)),f8(a1,f8(a1,x15621,x15622),x15623))
% 3.00/2.89 [1676]~P39(x16761)+E(f12(x16761,x16762,f25(f25(f11(x16761),x16763),x16762)),f25(f25(f11(x16761),f12(x16761,x16763,f3(x16761))),x16762))
% 3.00/2.89 [1677]~P39(x16771)+E(f12(x16771,f25(f25(f11(x16771),x16772),x16773),x16773),f25(f25(f11(x16771),f12(x16771,x16772,f3(x16771))),x16773))
% 3.00/2.89 [1704]~P41(x17041)+P2(a110,f26(x17041,f25(f25(f22(x17041),x17042),x17043)),f25(f25(f22(a110),f26(x17041,x17042)),x17043))
% 3.00/2.89 [1760]P3(a1,x17601,x17602)+~E(x17602,f12(a1,x17601,f25(f17(a1),f12(a109,x17603,f3(a109)))))
% 3.00/2.89 [1763]~P42(x17631)+P2(a110,f26(x17631,f25(f25(f11(x17631),x17632),x17633)),f25(f25(f11(a110),f26(x17631,x17633)),f87(x17632,x17631)))
% 3.00/2.89 [1764]~P42(x17641)+P2(a110,f26(x17641,f25(f25(f11(x17641),x17642),x17643)),f25(f25(f11(a110),f26(x17641,x17643)),f92(x17642,x17641)))
% 3.00/2.89 [1765]~P42(x17651)+P2(a110,f26(x17651,f25(f25(f11(x17651),x17652),x17653)),f25(f25(f11(a110),f26(x17651,x17652)),f26(x17651,x17653)))
% 3.00/2.89 [1766]~P42(x17661)+P2(a110,f26(x17661,f25(f25(f11(x17661),x17662),x17663)),f25(f25(f11(a110),f26(x17661,x17662)),f50(x17663,x17661)))
% 3.00/2.89 [1767]~P42(x17671)+P2(a110,f26(x17671,f25(f25(f11(x17671),x17672),x17673)),f25(f25(f11(a110),f26(x17671,x17672)),f91(x17673,x17671)))
% 3.00/2.89 [1815]~P54(x18151)+P2(x18151,f2(x18151),f12(x18151,f25(f25(f11(x18151),x18152),x18152),f25(f25(f11(x18151),x18153),x18153)))
% 3.00/2.89 [1912]E(x19121,x19122)+~E(f25(f25(f11(a109),f12(a109,x19123,f3(a109))),x19121),f25(f25(f11(a109),f12(a109,x19123,f3(a109))),x19122))
% 3.00/2.89 [1917]~P54(x19171)+~P3(x19171,f12(x19171,f25(f25(f11(x19171),x19172),x19172),f25(f25(f11(x19171),x19173),x19173)),f2(x19171))
% 3.00/2.89 [1946]~P3(a109,x19462,x19463)+P3(a109,f25(f25(f11(a109),f12(a109,x19461,f3(a109))),x19462),f25(f25(f11(a109),f12(a109,x19461,f3(a109))),x19463))
% 3.00/2.89 [1962]~P42(x19621)+P2(a110,f26(x19621,f25(f25(f11(x19621),x19622),x19623)),f25(f25(f11(a110),f25(f25(f11(a110),f26(x19621,x19622)),f26(x19621,x19623))),f29(x19621)))
% 3.00/2.89 [1963]~P42(x19631)+P2(a110,f26(x19631,f25(f25(f11(x19631),x19632),x19633)),f25(f25(f11(a110),f25(f25(f11(a110),f26(x19631,x19632)),f26(x19631,x19633))),f28(x19631)))
% 3.00/2.89 [1972]P2(a109,x19721,x19722)+~P2(a109,f25(f25(f11(a109),f12(a109,x19723,f3(a109))),x19721),f25(f25(f11(a109),f12(a109,x19723,f3(a109))),x19722))
% 3.00/2.89 [1978]~P46(x19781)+E(f10(x19781,f25(f25(f22(x19781),x19782),f12(a109,f12(a109,f2(a109),f3(a109)),f3(a109))),f25(f25(f22(x19781),x19783),f12(a109,f12(a109,f2(a109),f3(a109)),f3(a109)))),f25(f25(f11(x19781),f10(x19781,x19782,x19783)),f12(x19781,x19782,x19783)))
% 3.00/2.89 [1605]~P26(x16051)+E(f25(f25(f11(x16051),f25(f25(f22(x16051),x16052),x16053)),x16052),f25(f25(f11(x16051),x16052),f25(f25(f22(x16051),x16052),x16053)))
% 3.00/2.89 [1619]~P26(x16191)+E(f25(f25(f11(x16191),f25(f25(f22(x16191),x16192),x16193)),x16192),f25(f25(f22(x16191),x16192),f12(a109,x16193,f3(a109))))
% 3.00/2.89 [1620]~P39(x16201)+E(f25(f25(f11(x16201),f25(f25(f22(x16201),x16202),x16203)),x16202),f25(f25(f22(x16201),x16202),f12(a109,x16203,f3(a109))))
% 3.00/2.89 [2000]~P3(a1,f2(a1),x20003)+P3(a1,x20001,f12(a1,x20002,f25(f25(f11(a1),f12(a1,f7(a1,f10(a1,x20002,x20001)),f3(a1))),x20003)))
% 3.00/2.89 [2001]~P3(a1,f2(a1),x20013)+P3(a1,f10(a1,x20011,f25(f25(f11(a1),f12(a1,f7(a1,f10(a1,x20011,x20012)),f3(a1))),x20013)),x20012)
% 3.00/2.89 [1897]P3(a1,x18971,a13)+E(f25(f25(f11(a109),f18(a109,x18971)),f25(f25(f11(a109),f18(a109,x18972)),x18973)),f25(f25(f11(a109),f18(a109,f25(f25(f11(a1),x18971),x18972))),x18973))
% 3.00/2.89 [1429]~P39(x14291)+E(f12(x14291,x14292,f12(x14291,x14293,x14294)),f12(x14291,x14293,f12(x14291,x14292,x14294)))
% 3.00/2.89 [1431]~P14(x14311)+E(f12(x14311,f12(x14311,x14312,x14313),x14314),f12(x14311,x14312,f12(x14311,x14313,x14314)))
% 3.00/2.89 [1432]~P39(x14321)+E(f12(x14321,f12(x14321,x14322,x14323),x14324),f12(x14321,x14322,f12(x14321,x14323,x14324)))
% 3.00/2.89 [1433]~P39(x14331)+E(f12(x14331,f12(x14331,x14332,x14333),x14334),f12(x14331,f12(x14331,x14332,x14334),x14333))
% 3.00/2.89 [1761]~P34(x17611)+E(f12(x17611,f18(x17611,x17612),f12(x17611,f18(x17611,x17613),x17614)),f12(x17611,f18(x17611,f12(a1,x17612,x17613)),x17614))
% 3.00/2.89 [1762]~P34(x17621)+E(f12(x17621,f18(x17621,x17622),f10(x17621,f18(x17621,x17623),x17624)),f10(x17621,f18(x17621,f12(a1,x17622,x17623)),x17624))
% 3.00/2.89 [1848]~P49(x18481)+E(f21(x18481,x18482,f12(a109,x18483,f3(a109)),x18484),f21(x18481,x18482,x18483,f25(x18482,x18484)))
% 3.00/2.89 [1395]~P39(x13951)+E(f25(f25(f11(x13951),x13952),f25(f25(f11(x13951),x13953),x13954)),f25(f25(f11(x13951),x13953),f25(f25(f11(x13951),x13952),x13954)))
% 3.00/2.89 [1613]~P39(x16131)+E(f12(x16131,f25(f25(f11(x16131),x16132),x16133),f25(f25(f11(x16131),x16132),x16134)),f25(f25(f11(x16131),x16132),f12(x16131,x16133,x16134)))
% 3.00/2.89 [1615]~P42(x16151)+E(f12(x16151,f25(f25(f11(x16151),x16152),x16153),f25(f25(f11(x16151),x16152),x16154)),f25(f25(f11(x16151),x16152),f12(x16151,x16153,x16154)))
% 3.00/2.89 [1617]~P42(x16171)+E(f10(x16171,f25(f25(f11(x16171),x16172),x16173),f25(f25(f11(x16171),x16172),x16174)),f25(f25(f11(x16171),x16172),f10(x16171,x16173,x16174)))
% 3.00/2.89 [1739]~P26(x17391)+E(f25(f25(f11(x17391),f25(f25(f22(x17391),x17392),x17393)),f25(f25(f22(x17391),x17392),x17394)),f25(f25(f22(x17391),x17392),f12(a109,x17393,x17394)))
% 3.00/2.89 [1740]~P39(x17401)+E(f25(f25(f11(x17401),f25(f25(f22(x17401),x17402),x17403)),f25(f25(f22(x17401),x17402),x17404)),f25(f25(f22(x17401),x17402),f12(a109,x17403,x17404)))
% 3.00/2.89 [1755]~P42(x17551)+E(f12(x17551,f25(f25(f11(x17551),x17552),x17553),f25(f25(f11(x17551),x17554),x17553)),f25(f25(f11(x17551),f12(x17551,x17552,x17554)),x17553))
% 3.00/2.89 [1756]~P45(x17561)+E(f12(x17561,f25(f25(f11(x17561),x17562),x17563),f25(f25(f11(x17561),x17564),x17563)),f25(f25(f11(x17561),f12(x17561,x17562,x17564)),x17563))
% 3.00/2.89 [1758]~P42(x17581)+E(f10(x17581,f25(f25(f11(x17581),x17582),x17583),f25(f25(f11(x17581),x17584),x17583)),f25(f25(f11(x17581),f10(x17581,x17582,x17584)),x17583))
% 3.00/2.89 [1759]~P39(x17591)+E(f12(x17591,f25(f25(f11(x17591),x17592),x17593),f25(f25(f11(x17591),x17594),x17593)),f25(f25(f11(x17591),f12(x17591,x17592,x17594)),x17593))
% 3.00/2.89 [1594]~P39(x15941)+E(f25(f25(f22(x15941),f25(f25(f22(x15941),x15942),x15943)),x15944),f25(f25(f22(x15941),x15942),f25(f25(f11(a109),x15943),x15944)))
% 3.00/2.89 [1595]~P26(x15951)+E(f25(f25(f22(x15951),f25(f25(f22(x15951),x15952),x15953)),x15954),f25(f25(f22(x15951),x15952),f25(f25(f11(a109),x15953),x15954)))
% 3.00/2.89 [1603]~P39(x16031)+E(f25(f25(f11(x16031),f25(f25(f11(x16031),x16032),x16033)),x16034),f25(f25(f11(x16031),x16032),f25(f25(f11(x16031),x16033),x16034)))
% 3.00/2.89 [1604]~P18(x16041)+E(f25(f25(f11(x16041),f25(f25(f11(x16041),x16042),x16043)),x16044),f25(f25(f11(x16041),x16042),f25(f25(f11(x16041),x16043),x16044)))
% 3.00/2.89 [1738]~P39(x17381)+E(f25(f25(f11(x17381),f25(f25(f11(x17381),x17382),x17383)),x17384),f25(f25(f11(x17381),f25(f25(f11(x17381),x17382),x17384)),x17383))
% 3.00/2.89 [1830]~P39(x18301)+E(f25(f25(f11(x18301),f25(f25(f22(x18301),x18302),x18303)),f25(f25(f22(x18301),x18304),x18303)),f25(f25(f22(x18301),f25(f25(f11(x18301),x18302),x18304)),x18303))
% 3.00/2.89 [1831]~P23(x18311)+E(f25(f25(f11(x18311),f25(f25(f22(x18311),x18312),x18313)),f25(f25(f22(x18311),x18314),x18313)),f25(f25(f22(x18311),f25(f25(f11(x18311),x18312),x18314)),x18313))
% 3.00/2.89 [1903]~P34(x19031)+E(f25(f25(f11(x19031),f18(x19031,x19032)),f25(f25(f11(x19031),f18(x19031,x19033)),x19034)),f25(f25(f11(x19031),f18(x19031,f25(f25(f11(a1),x19032),x19033))),x19034))
% 3.00/2.89 [1777]~P39(x17771)+E(f12(x17771,f12(x17771,x17772,x17773),f12(x17771,x17774,x17775)),f12(x17771,f12(x17771,x17772,x17774),f12(x17771,x17773,x17775)))
% 3.00/2.89 [1778]~P15(x17781)+E(f10(x17781,f12(x17781,x17782,x17783),f12(x17781,x17784,x17785)),f12(x17781,f10(x17781,x17782,x17784),f10(x17781,x17783,x17785)))
% 3.00/2.89 [1979]~P40(x19791)+P2(a110,f26(x19791,f10(x19791,f12(x19791,x19792,x19793),f12(x19791,x19794,x19795))),f12(a110,f26(x19791,f10(x19791,x19792,x19794)),f26(x19791,f10(x19791,x19793,x19795))))
% 3.00/2.89 [1981]~P28(x19811)+P2(x19811,f7(x19811,f10(x19811,f12(x19811,x19812,x19813),f12(x19811,x19814,x19815))),f12(x19811,f7(x19811,f10(x19811,x19812,x19814)),f7(x19811,f10(x19811,x19813,x19815))))
% 3.00/2.89 [1885]~P39(x18851)+E(f25(f25(f11(x18851),f25(f25(f11(x18851),x18852),x18853)),f25(f25(f11(x18851),x18854),x18855)),f25(f25(f11(x18851),f25(f25(f11(x18851),x18852),x18854)),f25(f25(f11(x18851),x18853),x18855)))
% 3.00/2.89 [1942]~P68(x19421)+E(f12(x19421,f25(f25(f11(x19421),x19422),f10(x19421,x19423,x19424)),f25(f25(f11(x19421),f10(x19421,x19422,x19425)),x19424)),f10(x19421,f25(f25(f11(x19421),x19422),x19423),f25(f25(f11(x19421),x19425),x19424)))
% 3.00/2.89 [1998]~P42(x19981)+E(f12(x19981,f12(x19981,f25(f25(f11(x19981),f10(x19981,x19982,x19983)),f10(x19981,x19984,x19985)),f25(f25(f11(x19981),f10(x19981,x19982,x19983)),x19985)),f25(f25(f11(x19981),x19983),f10(x19981,x19984,x19985))),f10(x19981,f25(f25(f11(x19981),x19982),x19984),f25(f25(f11(x19981),x19983),x19985)))
% 3.00/2.89 [1933]~P71(x19331)+E(f12(x19331,f25(f25(f11(x19331),x19332),x19333),f12(x19331,f25(f25(f11(x19331),x19334),x19333),x19335)),f12(x19331,f25(f25(f11(x19331),f12(x19331,x19332,x19334)),x19333),x19335))
% 3.00/2.89 [1976]~P2(a109,x19761,x19764)+E(f10(a109,f12(a109,f25(f25(f11(a109),x19761),x19762),x19763),f12(a109,f25(f25(f11(a109),x19764),x19762),x19765)),f10(a109,x19763,f12(a109,f25(f25(f11(a109),f10(a109,x19764,x19761)),x19762),x19765)))
% 3.00/2.89 [1977]~P2(a109,x19774,x19771)+E(f10(a109,f12(a109,f25(f25(f11(a109),x19771),x19772),x19773),f12(a109,f25(f25(f11(a109),x19774),x19772),x19775)),f10(a109,f12(a109,f25(f25(f11(a109),f10(a109,x19771,x19774)),x19772),x19773),x19775))
% 3.00/2.89 [1873]E(x18731,f2(a109))+E(x18731,f12(a109,f2(a109),f3(a109)))+~P3(a109,x18731,f12(a109,f12(a109,f2(a109),f3(a109)),f3(a109)))
% 3.00/2.89 [792]~P38(x7921)+~P6(x7921,x7922)+P5(x7921,x7922)
% 3.00/2.89 [793]~P38(x7931)+~P8(x7931,x7932)+P5(x7931,x7932)
% 3.00/2.89 [956]E(x9561,x9562)+P3(a109,x9562,x9561)+P3(a109,x9561,x9562)
% 3.00/2.89 [957]E(x9571,x9572)+P3(a1,x9572,x9571)+P3(a1,x9571,x9572)
% 3.00/2.89 [1017]E(x10171,x10172)+P3(a109,x10171,x10172)+~P2(a109,x10171,x10172)
% 3.00/2.89 [1019]E(x10191,x10192)+P3(a110,x10191,x10192)+~P2(a110,x10191,x10192)
% 3.00/2.89 [1020]E(x10201,x10202)+P3(a1,x10201,x10202)+~P2(a1,x10201,x10202)
% 3.00/2.89 [1085]E(x10851,x10852)+~P2(a109,x10852,x10851)+~P2(a109,x10851,x10852)
% 3.00/2.89 [1086]E(x10861,x10862)+~P2(a110,x10862,x10861)+~P2(a110,x10861,x10862)
% 3.00/2.89 [1087]E(x10871,x10872)+~P2(a1,x10872,x10871)+~P2(a1,x10871,x10872)
% 3.00/2.89 [780]~P40(x7801)+~E(x7802,f2(x7801))+E(f26(x7801,x7802),f2(a110))
% 3.00/2.89 [781]~P28(x7811)+~E(x7812,f2(x7811))+E(f7(x7811,x7812),f2(x7811))
% 3.00/2.89 [789]~P40(x7892)+E(x7891,f2(x7892))+~E(f26(x7892,x7891),f2(a110))
% 3.00/2.89 [790]~P28(x7902)+~E(f7(x7902,x7901),f2(x7902))+E(x7901,f2(x7902))
% 3.00/2.89 [833]~E(x8332,f2(a109))+~E(x8331,f2(a109))+E(f12(a109,x8331,x8332),f2(a109))
% 3.00/2.89 [853]~P16(x8532)+E(f8(x8532,x8531,x8531),f3(x8532))+E(x8531,f2(x8532))
% 3.00/2.89 [866]~P24(x8661)+~E(x8662,f2(x8661))+E(f12(x8661,x8662,x8662),f2(x8661))
% 3.00/2.89 [919]~P40(x9192)+E(x9191,f2(x9192))+P3(a110,f2(a110),f26(x9192,x9191))
% 3.00/2.89 [935]~P40(x9351)+~E(x9352,f2(x9351))+P2(a110,f26(x9351,x9352),f2(a110))
% 3.00/2.89 [939]~P28(x9392)+P3(x9392,f2(x9392),f7(x9392,x9391))+E(x9391,f2(x9392))
% 3.00/2.89 [944]~P28(x9441)+P2(x9441,f7(x9441,x9442),f2(x9441))+~E(x9442,f2(x9441))
% 3.00/2.89 [946]~P24(x9462)+~E(f12(x9462,x9461,x9461),f2(x9462))+E(x9461,f2(x9462))
% 3.00/2.89 [960]~P40(x9602)+~P7(x9602,x9601)+P3(a110,f2(a110),f51(x9601,x9602))
% 3.00/2.89 [961]~P40(x9612)+~P7(x9612,x9611)+P3(a110,f2(a110),f77(x9611,x9612))
% 3.00/2.89 [973]~P28(x9731)+~P2(x9731,f2(x9731),x9732)+E(f7(x9731,x9732),x9732)
% 3.00/2.89 [974]~P28(x9741)+~P3(x9741,f2(x9741),x9742)+E(f7(x9741,x9742),x9742)
% 3.00/2.89 [989]~P38(x9891)+P6(x9891,x9892)+P2(a109,f93(x9892,x9891),f94(x9892,x9891))
% 3.00/2.89 [990]~P38(x9901)+P8(x9901,x9902)+P2(a109,f105(x9902,x9901),f107(x9902,x9901))
% 3.00/2.89 [991]~P38(x9911)+P5(x9911,x9912)+P2(a109,f31(x9912,x9911),f32(x9912,x9911))
% 3.00/2.89 [992]~P38(x9921)+P5(x9921,x9922)+P2(a109,f33(x9922,x9921),f34(x9922,x9921))
% 3.00/2.89 [993]~P38(x9931)+P5(x9931,x9932)+P2(a109,f35(x9932,x9931),f39(x9932,x9931))
% 3.00/2.89 [994]~P38(x9941)+P5(x9941,x9942)+P2(a109,f40(x9942,x9941),f41(x9942,x9941))
% 3.00/2.89 [1022]~P40(x10222)+E(x10221,f2(x10222))+~P2(a110,f26(x10222,x10221),f2(a110))
% 3.00/2.89 [1026]~P40(x10262)+~E(x10261,f2(x10262))+~P3(a110,f2(a110),f26(x10262,x10261))
% 3.00/2.89 [1034]~P28(x10342)+~P2(x10342,f7(x10342,x10341),f2(x10342))+E(x10341,f2(x10342))
% 3.00/2.89 [1059]~P28(x10592)+~P3(x10592,f2(x10592),f7(x10592,x10591))+~E(x10591,f2(x10592))
% 3.00/2.89 [1068]~E(f18(a109,x10682),f18(a109,x10681))+P2(a1,f18(a1,x10681),f2(a1))+~P4(f18(a1,x10682))
% 3.00/2.89 [1096]E(x10961,x10962)+~E(f10(a109,x10962,x10961),f2(a109))+~E(f10(a109,x10961,x10962),f2(a109))
% 3.00/2.89 [1148]E(f18(a109,x11481),f18(a109,x11482))+~P2(a1,f18(a1,x11482),f2(a1))+~P4(f18(a1,x11481))
% 3.00/2.89 [1211]~P3(a1,x12112,x12111)+~P2(a1,x12111,f2(a1))+E(f8(a1,x12111,x12112),f2(a1))
% 3.00/2.89 [1214]~P3(a1,x12141,x12142)+~P2(a1,f2(a1),x12141)+E(f8(a1,x12141,x12142),f2(a1))
% 3.00/2.89 [1306]~P2(a1,f2(a1),x13062)+~P2(a1,f2(a1),x13061)+P2(a1,f2(a1),f20(x13061,x13062))
% 3.00/2.89 [1307]~P3(a109,f2(a109),x13072)+~P3(a110,f2(a110),x13071)+P3(a110,f2(a110),f95(x13071,x13072))
% 3.00/2.89 [1308]~P3(a109,f2(a109),x13082)+~P3(a110,f2(a110),x13081)+P3(a110,f2(a110),f98(x13081,x13082))
% 3.00/2.89 [1309]P2(a1,x13091,x13092)+P2(a1,x13091,a13)+~P2(a109,f18(a109,x13091),f18(a109,x13092))
% 3.00/2.89 [1315]~P3(a1,x13151,x13152)+~P3(a1,a13,x13152)+P3(a109,f18(a109,x13151),f18(a109,x13152))
% 3.00/2.89 [1329]~P24(x13291)+~P2(x13291,f2(x13291),x13292)+P2(x13291,f2(x13291),f12(x13291,x13292,x13292))
% 3.00/2.89 [1330]~P24(x13301)+~P3(x13301,f2(x13301),x13302)+P3(x13301,f2(x13301),f12(x13301,x13302,x13302))
% 3.00/2.89 [1331]~P24(x13311)+~P2(x13311,x13312,f2(x13311))+P2(x13311,f12(x13311,x13312,x13312),f2(x13311))
% 3.00/2.89 [1332]~P24(x13321)+~P3(x13321,x13322,f2(x13321))+P3(x13321,f12(x13321,x13322,x13322),f2(x13321))
% 3.00/2.89 [1333]~P51(x13331)+~P3(x13331,x13332,f2(x13331))+P3(x13331,f12(x13331,x13332,x13332),f2(x13331))
% 3.00/2.89 [1357]~P3(a1,x13572,x13571)+P3(a1,a13,x13571)+~P3(a109,f18(a109,x13572),f18(a109,x13571))
% 3.00/2.89 [1436]~P24(x14361)+~P2(x14361,f12(x14361,x14362,x14362),f2(x14361))+P2(x14361,x14362,f2(x14361))
% 3.00/2.89 [1437]~P24(x14371)+~P3(x14371,f12(x14371,x14372,x14372),f2(x14371))+P3(x14371,x14372,f2(x14371))
% 3.00/2.89 [1438]~P51(x14381)+~P3(x14381,f12(x14381,x14382,x14382),f2(x14381))+P3(x14381,x14382,f2(x14381))
% 3.00/2.89 [1439]~P24(x14391)+~P2(x14391,f2(x14391),f12(x14391,x14392,x14392))+P2(x14391,f2(x14391),x14392)
% 3.00/2.89 [1440]~P24(x14401)+~P3(x14401,f2(x14401),f12(x14401,x14402,x14402))+P3(x14401,f2(x14401),x14402)
% 3.00/2.89 [1444]~P2(a1,x14442,x14441)+~P3(a1,f2(a1),x14442)+P3(a1,f2(a1),f8(a1,x14441,x14442))
% 3.00/2.89 [1445]P3(a109,f10(a109,x14451,x14452),x14451)+~P3(a109,f2(a109),x14451)+~P3(a109,f2(a109),x14452)
% 3.00/2.89 [1446]P3(a109,f8(a109,x14461,x14462),x14461)+~P3(a109,f3(a109),x14462)+~P3(a109,f2(a109),x14461)
% 3.00/2.89 [1447]P3(a1,f8(a1,x14471,x14472),x14471)+~P3(a1,f3(a1),x14472)+~P3(a1,f2(a1),x14471)
% 3.00/2.89 [1450]~P2(a1,x14501,f2(a1))+~P3(a1,x14502,f2(a1))+P2(a1,f2(a1),f8(a1,x14501,x14502))
% 3.00/2.89 [1451]~P2(a1,f2(a1),x14512)+~P2(a1,f2(a1),x14511)+P2(a1,f2(a1),f12(a1,x14511,x14512))
% 3.00/2.89 [1452]~P2(a1,f2(a1),x14522)+~P2(a1,f2(a1),x14521)+P2(a1,f2(a1),f8(a1,x14521,x14522))
% 3.00/2.89 [1453]~P2(a1,f2(a1),x14531)+~P3(a1,f2(a1),x14532)+P2(a1,f2(a1),f8(a1,x14531,x14532))
% 3.00/2.89 [1454]~P2(a1,x14541,f2(a1))+~P3(a1,f2(a1),x14542)+P2(a1,f8(a1,x14541,x14542),f2(a1))
% 3.00/2.89 [1455]~P3(a1,x14552,f2(a1))+~P2(a1,f2(a1),x14551)+P2(a1,f8(a1,x14551,x14552),f2(a1))
% 3.00/2.89 [1456]~P3(a1,x14562,f2(a1))+~P3(a1,f2(a1),x14561)+P3(a1,f8(a1,x14561,x14562),f2(a1))
% 3.00/2.89 [1458]~P3(a1,x14581,f2(a1))+~P3(a1,f2(a1),x14582)+P3(a1,f8(a1,x14581,x14582),f2(a1))
% 3.00/2.89 [1530]P3(a109,f2(a109),x15301)+P3(a109,f2(a109),x15302)+~P3(a109,f2(a109),f12(a109,x15302,x15301))
% 3.00/2.89 [1563]P2(a1,x15631,x15632)+~P3(a1,f2(a1),x15631)+~P3(a1,f2(a1),f8(a1,x15632,x15631))
% 3.00/2.89 [1564]P2(a1,x15641,x15642)+~P2(a1,f2(a1),x15642)+~P3(a1,f2(a1),f8(a1,x15642,x15641))
% 3.00/2.89 [1565]P2(a1,x15651,f2(a1))+~P3(a1,x15652,f2(a1))+~P2(a1,f2(a1),f8(a1,x15651,x15652))
% 3.00/2.89 [1566]P3(a1,x15661,f2(a1))+~P3(a1,f2(a1),x15662)+~P3(a1,f8(a1,x15661,x15662),f2(a1))
% 3.00/2.89 [1567]P3(a1,f2(a1),x15671)+~P3(a1,x15672,f2(a1))+~P3(a1,f8(a1,x15671,x15672),f2(a1))
% 3.00/2.89 [1568]P2(a1,f2(a1),x15681)+~P3(a1,f2(a1),x15682)+~P2(a1,f2(a1),f8(a1,x15681,x15682))
% 3.00/2.89 [1569]P3(a1,f2(a1),x15691)+~P2(a1,f2(a1),x15692)+~P3(a1,f2(a1),f8(a1,x15692,x15691))
% 3.00/2.89 [791]~P30(x7911)+E(f9(x7911,x7912),f2(a109))+~E(x7912,f2(f111(x7911)))
% 3.00/2.89 [794]~P30(x7942)+~E(f9(x7942,x7941),f2(a109))+E(x7941,f2(f111(x7942)))
% 3.00/2.89 [907]~P34(x9071)+~P41(x9071)+E(f26(x9071,f18(x9071,x9072)),f7(a110,f18(a110,x9072)))
% 3.00/2.89 [911]~P34(x9111)+E(f25(f17(x9111),f18(a109,x9112)),f18(x9111,x9112))+P4(f18(a1,x9112))
% 3.00/2.89 [934]~P34(x9341)+E(f25(f17(x9341),f18(a109,x9342)),f2(x9341))+~P4(f18(a1,x9342))
% 3.00/2.89 [1000]~P34(x10001)+P2(a1,f2(a1),f18(a1,x10002))+E(f25(f17(x10001),f18(a109,x10002)),f2(x10001))
% 3.00/2.89 [1073]P3(a109,f52(x10732,x10731),x10732)+~P75(f25(x10731,x10732))+P75(f25(x10731,f2(a109)))
% 3.00/2.89 [1130]E(x11301,f2(a109))+E(x11302,f2(a109))+~E(f12(a109,x11302,x11301),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1131]E(x11311,f2(a109))+E(x11312,f2(a109))+~E(f12(a109,f2(a109),f3(a109)),f12(a109,x11312,x11311))
% 3.00/2.89 [1140]~P34(x11401)+~P2(a1,f2(a1),f18(a1,x11402))+E(f25(f17(x11401),f18(a109,x11402)),f18(x11401,x11402))
% 3.00/2.89 [1151]~P50(x11511)+P3(x11511,f2(x11511),f25(f17(x11511),x11512))+~P3(a109,f2(a109),x11512)
% 3.00/2.89 [1181]~E(x11812,f2(a109))+~E(x11811,f12(a109,f2(a109),f3(a109)))+E(f12(a109,x11811,x11812),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1182]~E(x11821,f2(a109))+~E(x11822,f12(a109,f2(a109),f3(a109)))+E(f12(a109,x11821,x11822),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1183]~E(x11832,f2(a109))+~E(x11831,f12(a109,f2(a109),f3(a109)))+E(f12(a109,f2(a109),f3(a109)),f12(a109,x11831,x11832))
% 3.00/2.89 [1184]~E(x11841,f2(a109))+~E(x11842,f12(a109,f2(a109),f3(a109)))+E(f12(a109,f2(a109),f3(a109)),f12(a109,x11841,x11842))
% 3.00/2.89 [1191]~P50(x11912)+~P3(x11912,f2(x11912),f25(f17(x11912),x11911))+P3(a109,f2(a109),x11911)
% 3.00/2.89 [1244]E(x12441,f2(a109))+E(x12441,f12(a109,f2(a109),f3(a109)))+~E(f12(a109,x12442,x12441),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1245]E(x12451,f2(a109))+E(x12451,f12(a109,f2(a109),f3(a109)))+~E(f12(a109,x12451,x12452),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1246]E(x12461,f2(a109))+E(x12461,f12(a109,f2(a109),f3(a109)))+~E(f12(a109,f2(a109),f3(a109)),f12(a109,x12462,x12461))
% 3.00/2.89 [1247]E(x12471,f2(a109))+E(x12471,f12(a109,f2(a109),f3(a109)))+~E(f12(a109,f2(a109),f3(a109)),f12(a109,x12471,x12472))
% 3.00/2.89 [1271]P3(a1,x12711,a13)+~P3(a1,x12712,a13)+E(f12(a109,f18(a109,x12711),f18(a109,x12712)),f18(a109,x12711))
% 3.00/2.89 [1324]~P2(a109,f19(x13241),x13242)+~P2(a110,f2(a110),x13241)+P2(a110,x13241,f25(f16(a109),x13242))
% 3.00/2.89 [1325]~P2(a109,x13251,f24(x13252))+~P2(a110,f2(a110),x13252)+P2(a110,f25(f16(a109),x13251),x13252)
% 3.00/2.89 [1347]P3(a109,f24(x13471),x13472)+~P2(a110,f2(a110),x13471)+~P3(a110,x13471,f25(f16(a109),x13472))
% 3.00/2.89 [1363]E(x13631,f12(a109,f2(a109),f3(a109)))+E(x13632,f12(a109,f2(a109),f3(a109)))+~E(f12(a109,x13631,x13632),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1364]E(x13641,f12(a109,f2(a109),f3(a109)))+E(x13642,f12(a109,f2(a109),f3(a109)))+~E(f12(a109,f2(a109),f3(a109)),f12(a109,x13641,x13642))
% 3.00/2.89 [1373]~P3(a109,x13731,x13732)+P3(a109,f12(a109,x13731,f3(a109)),x13732)+E(f12(a109,x13731,f3(a109)),x13732)
% 3.00/2.89 [1393]E(x13931,x13932)+P3(a109,x13931,x13932)+~P3(a109,x13931,f12(a109,x13932,f3(a109)))
% 3.00/2.89 [1394]E(x13941,x13942)+P3(a1,x13941,x13942)+~P3(a1,x13941,f12(a1,x13942,f3(a1)))
% 3.00/2.89 [1403]P3(a1,x14031,a13)+P3(a1,x14032,a13)+E(f12(a109,f18(a109,x14031),f18(a109,x14032)),f18(a109,f12(a1,x14031,x14032)))
% 3.00/2.89 [1460]P3(a109,f46(x14602,x14601),x14602)+E(x14601,f2(a109))+~P3(a109,x14601,f12(a109,x14602,f3(a109)))
% 3.00/2.89 [1465]E(x14651,x14652)+~P2(a109,x14652,x14651)+~P3(a109,x14651,f12(a109,x14652,f3(a109)))
% 3.00/2.89 [1468]E(x14681,f2(a109))+~P3(a109,x14681,f12(a109,x14682,f3(a109)))+E(f12(a109,f46(x14682,x14681),f3(a109)),x14681)
% 3.00/2.89 [1490]~P38(x14901)+P6(x14901,x14902)+~P2(x14901,f25(x14902,f94(x14902,x14901)),f25(x14902,f93(x14902,x14901)))
% 3.00/2.89 [1491]~P38(x14911)+P8(x14911,x14912)+~P2(x14911,f25(x14912,f105(x14912,x14911)),f25(x14912,f107(x14912,x14911)))
% 3.00/2.89 [1492]~P38(x14921)+P5(x14921,x14922)+~P2(x14921,f25(x14922,f31(x14922,x14921)),f25(x14922,f32(x14922,x14921)))
% 3.00/2.89 [1493]~P38(x14931)+P5(x14931,x14932)+~P2(x14931,f25(x14932,f34(x14932,x14931)),f25(x14932,f33(x14932,x14931)))
% 3.00/2.89 [1494]~P38(x14941)+P5(x14941,x14942)+~P2(x14941,f25(x14942,f39(x14942,x14941)),f25(x14942,f35(x14942,x14941)))
% 3.00/2.89 [1495]~P38(x14951)+P5(x14951,x14952)+~P2(x14951,f25(x14952,f40(x14952,x14951)),f25(x14952,f41(x14952,x14951)))
% 3.00/2.89 [1542]P2(a109,x15421,x15422)+~P2(a109,x15421,f12(a109,x15422,f3(a109)))+E(x15421,f12(a109,x15422,f3(a109)))
% 3.00/2.89 [1713]E(f24(x17131),x17132)+~P2(a110,f25(f16(a109),x17132),x17131)+~P3(a110,x17131,f12(a110,f25(f16(a109),x17132),f3(a110)))
% 3.00/2.89 [1781]~P3(a110,f25(f16(a109),x17812),x17811)+~P2(a110,x17811,f12(a110,f25(f16(a109),x17812),f3(a110)))+E(f19(x17811),f12(a109,x17812,f3(a109)))
% 3.00/2.89 [1785]P3(a109,x17851,x17852)+~P3(a109,f2(a109),x17852)+E(f12(a109,f8(a109,f10(a109,x17851,x17852),x17852),f3(a109)),f8(a109,x17851,x17852))
% 3.00/2.89 [1818]~P2(a109,x18182,x18181)+~P3(a109,f2(a109),x18182)+E(f12(a109,f8(a109,f10(a109,x18181,x18182),x18182),f3(a109)),f8(a109,x18181,x18182))
% 3.00/2.89 [813]~E(x8132,f3(a109))+~E(x8131,f3(a109))+E(f25(f25(f11(a109),x8131),x8132),f3(a109))
% 3.00/2.89 [883]E(x8831,f3(a109))+E(x8832,f2(a109))+~E(f25(f25(f11(a109),x8832),x8831),x8832)
% 3.00/2.89 [884]E(x8841,f2(a109))+E(x8842,f2(a109))+~E(f25(f25(f11(a109),x8842),x8841),f2(a109))
% 3.00/2.89 [1081]E(x10811,f3(a1))+~P3(a1,f2(a1),x10812)+~E(f25(f25(f11(a1),x10812),x10811),f3(a1))
% 3.00/2.89 [1082]E(x10821,f3(a1))+~P3(a1,f2(a1),x10821)+~E(f25(f25(f11(a1),x10821),x10822),f3(a1))
% 3.00/2.89 [1147]~P43(x11471)+~P72(x11471)+E(f25(f25(f22(x11471),f2(x11471)),f12(a109,x11472,f3(a109))),f2(x11471))
% 3.00/2.89 [1216]E(x12161,f2(a109))+E(x12162,f12(a109,f2(a109),f3(a109)))+~E(f25(f25(f22(a109),x12162),x12161),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1301]~P2(a1,f2(a1),x13012)+~P75(f25(x13011,x13012))+P75(f25(x13011,f25(f17(a1),f82(x13011))))
% 3.00/2.89 [1339]~P3(a109,f2(a109),x13392)+~P3(a110,f2(a110),x13391)+E(f25(f25(f22(a110),f95(x13391,x13392)),x13392),x13391)
% 3.00/2.89 [1340]~P3(a109,f2(a109),x13402)+~P3(a110,f2(a110),x13401)+E(f25(f25(f22(a110),f98(x13401,x13402)),x13402),x13401)
% 3.00/2.89 [1356]E(x13561,f2(a109))+P3(a109,f2(a109),x13562)+~P3(a109,f2(a109),f25(f25(f22(a109),x13562),x13561))
% 3.00/2.89 [1358]~E(x13582,f12(a109,f2(a109),f3(a109)))+~E(x13581,f12(a109,f2(a109),f3(a109)))+E(f25(f25(f11(a109),x13581),x13582),f12(a109,f2(a109),f3(a109)))
% 3.00/2.89 [1378]~P2(a1,f2(a1),x13782)+P75(f25(x13781,x13782))+~P75(f25(x13781,f25(f17(a1),f83(x13781))))
% 3.00/2.89 [1418]~P2(a1,f2(a1),x14182)+~P2(a1,f2(a1),x14181)+P2(a1,f2(a1),f25(f25(f11(a1),x14181),x14182))
% 3.00/2.89 [1419]~P3(a109,f2(a109),x14192)+~P3(a109,f2(a109),x14191)+P3(a109,f2(a109),f25(f25(f11(a109),x14191),x14192))
% 3.00/2.89 [1420]~P3(a110,f2(a110),x14202)+~P3(a110,f2(a110),x14201)+P3(a110,f2(a110),f25(f25(f11(a110),x14201),x14202))
% 3.00/2.89 [1488]~P2(a110,f2(a110),x14881)+P4(f18(a1,x14882))+E(f19(f12(a110,x14881,f18(a110,x14882))),f12(a109,f19(x14881),f18(a109,x14882)))
% 3.00/2.89 [1489]~P2(a110,f2(a110),x14891)+P4(f18(a1,x14892))+E(f24(f12(a110,x14891,f18(a110,x14892))),f12(a109,f24(x14891),f18(a109,x14892)))
% 3.00/2.89 [1552]E(x15521,f2(a109))+~E(x15522,f2(a1))+~P3(a1,f2(a1),f25(f25(f22(a1),f7(a1,x15522)),x15521))
% 3.00/2.89 [1637]~P75(f25(x16371,x16372))+P75(f25(x16371,f2(a109)))+P75(f25(x16371,f12(a109,f52(x16372,x16371),f3(a109))))
% 3.00/2.89 [1864]~P3(a109,f12(a109,f2(a109),f3(a109)),x18642)+~P3(a109,f12(a109,f2(a109),f3(a109)),x18641)+P3(a109,x18641,f25(f25(f11(a109),x18642),x18641))
% 3.00/2.89 [1865]~P3(a109,f12(a109,f2(a109),f3(a109)),x18652)+~P3(a109,f12(a109,f2(a109),f3(a109)),x18651)+P3(a109,x18651,f25(f25(f11(a109),x18651),x18652))
% 3.00/2.89 [1898]~P38(x18981)+P8(x18981,x18982)+~P2(x18981,f25(x18982,f36(x18982,x18981)),f25(x18982,f12(a109,f36(x18982,x18981),f3(a109))))
% 3.00/2.89 [1899]~P38(x18991)+P5(x18991,x18992)+~P2(x18991,f25(x18992,f37(x18992,x18991)),f25(x18992,f12(a109,f37(x18992,x18991),f3(a109))))
% 3.00/2.89 [1900]~P38(x19001)+P5(x19001,x19002)+~P2(x19001,f25(x19002,f44(x19002,x19001)),f25(x19002,f12(a109,f44(x19002,x19001),f3(a109))))
% 3.00/2.89 [1901]~P38(x19011)+P5(x19011,x19012)+~P2(x19011,f25(x19012,f12(a109,f38(x19012,x19011),f3(a109))),f25(x19012,f38(x19012,x19011)))
% 3.00/2.89 [1902]~P38(x19021)+P5(x19021,x19022)+~P2(x19021,f25(x19022,f12(a109,f45(x19022,x19021),f3(a109))),f25(x19022,f45(x19022,x19021)))
% 3.00/2.89 [1904]~P2(a109,f12(a109,f2(a109),f3(a109)),x19042)+~P2(a109,f12(a109,f2(a109),f3(a109)),x19041)+P2(a109,f12(a109,f2(a109),f3(a109)),f25(f25(f11(a109),x19041),x19042))
% 3.00/2.89 [1905]~P3(a109,f12(a109,f2(a109),f3(a109)),x19051)+~P3(a109,f12(a109,f2(a109),f3(a109)),x19052)+P3(a109,f12(a109,f2(a109),f3(a109)),f25(f25(f11(a109),x19051),x19052))
% 3.00/2.89 [1289]~E(x12892,f2(a110))+~E(x12891,f2(a110))+E(f12(a110,f25(f25(f11(a110),x12891),x12891),f25(f25(f11(a110),x12892),x12892)),f2(a110))
% 3.00/2.89 [1597]~P2(a110,f3(a110),x15971)+~P3(a109,f2(a109),x15972)+E(f24(f27(a110,x15971,f25(f16(a109),x15972))),f8(a109,f24(x15971),x15972))
% 3.00/2.89 [1779]~P2(a110,f2(a110),x17792)+~P2(a110,f2(a110),x17791)+P2(a109,f25(f25(f11(a109),f24(x17791)),f24(x17792)),f24(f25(f25(f11(a110),x17791),x17792)))
% 3.00/2.89 [1854]~P2(a110,f2(a110),x18541)+~P3(a110,f2(a110),x18542)+P2(a110,f25(f25(f11(a110),f25(f16(a109),f96(x18541,x18542))),x18542),x18541)
% 3.00/2.89 [1859]~P2(a109,f63(x18592),x18591)+~P3(a110,f2(a110),x18592)+P3(a110,f26(a15,f10(a15,f117(f25(a108,x18591)),a119)),x18592)
% 3.00/2.89 [1878]~P3(a109,f2(a109),x18782)+~P3(a1,f2(a1),x18781)+E(f8(a1,f25(f25(f22(a1),x18781),x18782),x18781),f25(f25(f22(a1),x18781),f10(a109,x18782,f12(a109,f2(a109),f3(a109)))))
% 3.00/2.89 [1971]~P2(a110,f2(a110),x19711)+~P3(a110,f2(a110),x19712)+P3(a110,x19711,f25(f25(f11(a110),f25(f16(a109),f12(a109,f96(x19711,x19712),f3(a109)))),x19712))
% 3.00/2.89 [1980]E(x19801,f2(a109))+E(x19802,f2(a15))+P3(a110,f26(a15,f12(a15,f3(a15),f25(f25(f11(a15),x19802),f25(f25(f22(a15),f97(x19801,x19802)),x19801)))),f3(a110))
% 3.00/2.89 [824]~E(x8242,x8243)+~P9(x8241)+P2(x8241,x8242,x8243)
% 3.00/2.89 [826]~E(x8262,x8263)+~P38(x8261)+P2(x8261,x8262,x8263)
% 3.00/2.89 [931]~P3(x9313,x9311,x9312)+~E(x9311,x9312)+~P29(x9313)
% 3.00/2.89 [932]~P3(x9323,x9321,x9322)+~E(x9321,x9322)+~P38(x9323)
% 3.00/2.89 [967]P2(x9671,x9673,x9672)+~P29(x9671)+P2(x9671,x9672,x9673)
% 3.00/2.89 [972]P3(x9721,x9723,x9722)+~P29(x9721)+P2(x9721,x9722,x9723)
% 3.00/2.89 [1031]~P9(x10311)+~P3(x10311,x10312,x10313)+P2(x10311,x10312,x10313)
% 3.00/2.89 [1033]~P38(x10331)+~P3(x10331,x10332,x10333)+P2(x10331,x10332,x10333)
% 3.00/2.89 [1100]~P3(x11001,x11003,x11002)+~P9(x11001)+~P2(x11001,x11002,x11003)
% 3.00/2.89 [1104]~P3(x11041,x11043,x11042)+~P9(x11041)+~P3(x11041,x11042,x11043)
% 3.00/2.89 [1107]~P3(x11071,x11073,x11072)+~P29(x11071)+~P2(x11071,x11072,x11073)
% 3.00/2.89 [1108]~P3(x11081,x11083,x11082)+~P29(x11081)+~P3(x11081,x11082,x11083)
% 3.00/2.89 [1109]~P3(x11091,x11093,x11092)+~P38(x11091)+~P3(x11091,x11092,x11093)
% 3.00/2.89 [1195]~P2(a109,x11951,x11953)+P2(a109,x11951,x11952)+~P2(a109,x11953,x11952)
% 3.00/2.89 [1196]~P2(a110,x11961,x11963)+P2(a110,x11961,x11962)+~P2(a110,x11963,x11962)
% 3.00/2.89 [1197]~P2(a1,x11971,x11973)+P2(a1,x11971,x11972)+~P2(a1,x11973,x11972)
% 3.00/2.89 [842]~E(x8422,x8423)+~P21(x8421)+E(f10(x8421,x8422,x8423),f2(x8421))
% 3.00/2.89 [843]~E(x8432,x8433)+~P15(x8431)+E(f10(x8431,x8432,x8433),f2(x8431))
% 3.00/2.89 [854]~P73(x8541)+~E(x8543,f2(x8541))+E(f12(x8541,x8542,x8543),x8542)
% 3.00/2.89 [940]~P73(x9402)+~E(f12(x9402,x9403,x9401),x9403)+E(x9401,f2(x9402))
% 3.00/2.89 [942]~P21(x9423)+E(x9421,x9422)+~E(f10(x9423,x9421,x9422),f2(x9423))
% 3.00/2.89 [943]~P15(x9433)+E(x9431,x9432)+~E(f10(x9433,x9431,x9432),f2(x9433))
% 3.00/2.89 [1141]~P28(x11411)+P2(x11411,x11412,x11413)+~P2(x11411,f7(x11411,x11412),x11413)
% 3.00/2.89 [1154]~P1(x11541)+~P3(a109,x11542,x11543)+P3(a109,f25(x11541,x11542),f25(x11541,x11543))
% 3.00/2.89 [1203]~P2(a109,x12033,x12031)+~E(f10(a109,x12031,x12033),x12032)+E(x12031,f12(a109,x12032,x12033))
% 3.00/2.89 [1204]~P2(a109,x12042,x12041)+~E(x12041,f12(a109,x12043,x12042))+E(f10(a109,x12041,x12042),x12043)
% 3.00/2.89 [1310]~P27(x13101)+~P2(x13101,x13102,x13103)+P2(x13101,f10(x13101,x13102,x13103),f2(x13101))
% 3.00/2.89 [1311]~P27(x13111)+~P3(x13111,x13112,x13113)+P3(x13111,f10(x13111,x13112,x13113),f2(x13111))
% 3.00/2.89 [1422]~P27(x14221)+P2(x14221,x14222,x14223)+~P2(x14221,f10(x14221,x14222,x14223),f2(x14221))
% 3.00/2.89 [1423]~P27(x14231)+P3(x14231,x14232,x14233)+~P3(x14231,f10(x14231,x14232,x14233),f2(x14231))
% 3.00/2.89 [1434]~P3(a110,x14343,x14342)+~P3(a110,x14342,x14341)+P3(a110,f2(a110),f59(x14341,x14342,x14343))
% 3.00/2.89 [1625]~P3(a109,x16253,x16251)+~P3(a109,x16253,x16252)+P3(a109,f10(a109,x16251,x16252),f10(a109,x16251,x16253))
% 3.00/2.89 [1626]~P2(a109,x16262,x16261)+~P3(a109,x16261,x16263)+P3(a109,f10(a109,x16261,x16262),f10(a109,x16263,x16262))
% 3.00/2.89 [1630]~P2(a1,x16303,x16301)+P2(a1,f8(a1,x16301,x16302),f8(a1,x16303,x16302))+~P3(a1,x16302,f2(a1))
% 3.00/2.89 [1631]~P2(a109,x16313,x16312)+P2(a109,f8(a109,x16311,x16312),f8(a109,x16311,x16313))+~P3(a109,f2(a109),x16313)
% 3.00/2.89 [1632]~P2(a1,x16321,x16323)+P2(a1,f8(a1,x16321,x16322),f8(a1,x16323,x16322))+~P3(a1,f2(a1),x16322)
% 3.00/2.89 [1706]~P2(a109,x17063,x17062)+~P2(a109,f12(a109,x17061,x17063),x17062)+P2(a109,x17061,f10(a109,x17062,x17063))
% 3.00/2.89 [1707]~P2(a109,x17072,x17073)+~P2(a109,x17071,f10(a109,x17073,x17072))+P2(a109,f12(a109,x17071,x17072),x17073)
% 3.00/2.89 [862]~P36(x8623)+E(x8621,x8622)+~E(f25(f17(x8623),x8621),f25(f17(x8623),x8622))
% 3.00/2.89 [997]~P76(x9971,x9972,x9973)+~E(x9972,f2(a1))+P75(f25(x9971,f2(a1)))
% 3.00/2.89 [1137]~P40(x11371)+~P7(x11371,x11372)+P2(a110,f26(x11371,f25(x11372,x11373)),f51(x11372,x11371))
% 3.00/2.89 [1138]~P40(x11381)+~P7(x11381,x11382)+P2(a110,f26(x11381,f25(x11382,x11383)),f77(x11382,x11381))
% 3.00/2.89 [1200]~P50(x12001)+~P2(a109,x12002,x12003)+P2(x12001,f25(f17(x12001),x12002),f25(f17(x12001),x12003))
% 3.00/2.89 [1202]~P50(x12021)+~P3(a109,x12022,x12023)+P3(x12021,f25(f17(x12021),x12022),f25(f17(x12021),x12023))
% 3.00/2.89 [1321]~P50(x13213)+P2(a109,x13211,x13212)+~P2(x13213,f25(f17(x13213),x13211),f25(f17(x13213),x13212))
% 3.00/2.89 [1323]~P50(x13233)+P3(a109,x13231,x13232)+~P3(x13233,f25(f17(x13233),x13231),f25(f17(x13233),x13232))
% 3.00/2.89 [1371]~E(x13713,f2(a109))+P75(f25(x13711,f8(a109,x13712,x13713)))+~P75(f25(x13711,f2(a109)))
% 3.00/2.89 [1435]~P3(a109,x14351,x14353)+~P3(a109,x14353,x14352)+P3(a109,f12(a109,x14351,f3(a109)),x14352)
% 3.00/2.89 [1449]~P3(a109,x14493,x14492)+P3(a109,x14491,f12(a109,x14492,f3(a109)))+~E(x14491,f12(a109,x14493,f3(a109)))
% 3.00/2.89 [1463]~P16(x14632)+E(x14631,f2(x14632))+E(f8(x14632,f12(x14632,x14633,x14631),x14631),f12(x14632,f8(x14632,x14633,x14631),f3(x14632)))
% 3.00/2.89 [1464]~P16(x14642)+E(x14641,f2(x14642))+E(f8(x14642,f12(x14642,x14641,x14643),x14641),f12(x14642,f8(x14642,x14643,x14641),f3(x14642)))
% 3.00/2.89 [1576]P3(a109,f99(x15761,x15762,x15763),x15761)+E(x15761,f2(a109))+P75(f25(x15763,f8(a109,x15762,x15761)))
% 3.00/2.89 [1599]~E(x15992,f2(a109))+~P75(f25(x15991,f8(a109,x15993,x15992)))+P75(f25(x15991,f2(a109)))
% 3.00/2.89 [1618]E(x16181,f2(a110))+~P2(a110,x16182,f2(a110))+~P2(a110,f7(a110,x16181),f25(f25(f11(a110),x16182),f7(a110,x16183)))
% 3.00/2.89 [1674]P3(a109,x16742,x16741)+E(f12(a109,x16741,f47(x16741,x16742,x16743)),x16742)+P75(f25(x16743,f10(a109,x16742,x16741)))
% 3.00/2.89 [1675]P3(a109,x16752,x16751)+E(f12(a109,x16751,f48(x16751,x16752,x16753)),x16752)+P75(f25(x16753,f10(a109,x16752,x16751)))
% 3.00/2.89 [1680]P3(a109,f99(x16801,x16802,x16803),x16801)+P75(f25(x16803,f8(a109,x16802,x16801)))+~P75(f25(x16803,f2(a109)))
% 3.00/2.89 [1681]E(f12(a109,x16811,f47(x16811,x16812,x16813)),x16812)+P75(f25(x16813,f10(a109,x16812,x16811)))+~P75(f25(x16813,f2(a109)))
% 3.00/2.89 [1682]E(f12(a109,x16821,f48(x16821,x16822,x16823)),x16822)+P75(f25(x16823,f10(a109,x16822,x16821)))+~P75(f25(x16823,f2(a109)))
% 3.00/2.89 [1691]~P2(a109,x16912,x16913)+~P2(a109,x16912,x16911)+E(f10(a109,f10(a109,x16911,x16912),f10(a109,x16913,x16912)),f10(a109,x16911,x16913))
% 3.00/2.89 [1712]~P3(a109,x17122,x17123)+~P75(f25(x17121,f10(a109,x17122,x17123)))+P75(f25(x17121,f2(a109)))
% 3.00/2.89 [1826]~P2(a110,x18262,x18261)+~P3(a110,x18261,f12(a110,x18262,x18263))+P3(a110,f7(a110,f10(a110,x18261,x18262)),x18263)
% 3.00/2.89 [1829]E(x18291,f2(a109))+P75(f25(x18292,f101(x18291,x18293,x18292)))+~P75(f25(x18292,f8(a109,x18293,x18291)))
% 3.00/2.89 [1832]E(x18321,f2(a109))+~P75(f25(x18322,f100(x18321,x18323,x18322)))+P75(f25(x18322,f8(a109,x18323,x18321)))
% 3.00/2.89 [1851]P75(f25(x18511,f101(x18512,x18513,x18511)))+~P75(f25(x18511,f8(a109,x18513,x18512)))+P75(f25(x18511,f2(a109)))
% 3.00/2.89 [1862]P3(a109,x18621,x18622)+~P75(f25(x18623,f47(x18622,x18621,x18623)))+P75(f25(x18623,f10(a109,x18621,x18622)))
% 3.00/2.89 [1863]P3(a109,x18631,x18632)+~P75(f25(x18633,f48(x18632,x18631,x18633)))+P75(f25(x18633,f10(a109,x18631,x18632)))
% 3.00/2.89 [1867]~P75(f25(x18671,f47(x18673,x18672,x18671)))+P75(f25(x18671,f10(a109,x18672,x18673)))+~P75(f25(x18671,f2(a109)))
% 3.00/2.89 [1868]~P75(f25(x18681,f48(x18683,x18682,x18681)))+P75(f25(x18681,f10(a109,x18682,x18683)))+~P75(f25(x18681,f2(a109)))
% 3.00/2.89 [1869]~P75(f25(x18691,f100(x18693,x18692,x18691)))+P75(f25(x18691,f8(a109,x18692,x18693)))+~P75(f25(x18691,f2(a109)))
% 3.00/2.89 [1879]E(x18791,f2(a109))+E(f12(a109,f25(f25(f11(a109),x18791),f100(x18791,x18792,x18793)),f99(x18791,x18792,x18793)),x18792)+P75(f25(x18793,f8(a109,x18792,x18791)))
% 3.00/2.89 [1886]E(x18861,f2(a109))+P2(a109,f25(f25(f11(a109),x18861),f101(x18861,x18862,x18863)),x18862)+~P75(f25(x18863,f8(a109,x18862,x18861)))
% 3.00/2.89 [1893]E(f12(a109,f25(f25(f11(a109),x18931),f100(x18931,x18932,x18933)),f99(x18931,x18932,x18933)),x18932)+P75(f25(x18933,f8(a109,x18932,x18931)))+~P75(f25(x18933,f2(a109)))
% 3.00/2.89 [1895]P2(a109,f25(f25(f11(a109),x18952),f101(x18952,x18953,x18951)),x18953)+~P75(f25(x18951,f8(a109,x18953,x18952)))+P75(f25(x18951,f2(a109)))
% 3.00/2.89 [844]~P43(x8441)+~E(x8443,f2(a109))+E(f25(f25(f22(x8441),x8442),x8443),f3(x8441))
% 3.00/2.89 [857]~P61(x8571)+~E(x8573,f2(x8571))+E(f25(f25(f11(x8571),x8572),x8573),f2(x8571))
% 3.00/2.89 [858]~P61(x8581)+~E(x8582,f2(x8581))+E(f25(f25(f11(x8581),x8582),x8583),f2(x8581))
% 3.00/2.89 [941]~P70(x9412)+E(x9411,f2(x9412))+~E(f25(f25(f22(x9412),x9411),x9413),f2(x9412))
% 3.00/2.89 [1051]E(x10511,x10512)+E(x10513,f2(a109))+~E(f25(f25(f11(a109),x10513),x10511),f25(f25(f11(a109),x10513),x10512))
% 3.00/2.89 [1052]E(x10521,x10522)+E(x10523,f2(a110))+~E(f25(f25(f11(a110),x10523),x10521),f25(f25(f11(a110),x10523),x10522))
% 3.00/2.89 [1053]E(x10531,x10532)+E(x10533,f2(a109))+~E(f25(f25(f11(a109),x10531),x10533),f25(f25(f11(a109),x10532),x10533))
% 3.00/2.89 [1054]E(x10541,x10542)+E(x10543,f2(a110))+~E(f25(f25(f11(a110),x10541),x10543),f25(f25(f11(a110),x10542),x10543))
% 3.00/2.89 [1236]E(x12361,x12362)+~P3(a109,f2(a109),x12363)+~E(f25(f25(f11(a109),x12363),x12361),f25(f25(f11(a109),x12363),x12362))
% 3.00/2.89 [1318]~P50(x13181)+~P2(x13181,f3(x13181),x13182)+P2(x13181,f3(x13181),f25(f25(f22(x13181),x13182),x13183))
% 3.00/2.89 [1319]~P50(x13191)+~P2(x13191,f2(x13191),x13192)+P2(x13191,f2(x13191),f25(f25(f22(x13191),x13192),x13193))
% 3.00/2.89 [1320]~P50(x13201)+~P3(x13201,f2(x13201),x13202)+P3(x13201,f2(x13201),f25(f25(f22(x13201),x13202),x13203))
% 3.00/2.89 [1396]~E(x13962,f8(a109,x13963,x13961))+~P3(a109,f2(a109),x13961)+P2(a109,f25(f25(f11(a109),x13961),x13962),x13963)
% 3.00/2.89 [1480]~P69(x14801)+~P2(a109,x14803,x14802)+E(f10(x14801,f25(f17(x14801),x14802),f25(f17(x14801),x14803)),f25(f17(x14801),f10(a109,x14802,x14803)))
% 3.00/2.89 [1543]P4(f18(a1,x15431))+~P4(f18(a1,x15432))+E(f12(a109,f18(a109,x15431),f12(a109,f18(a109,x15432),x15433)),f12(a109,f18(a109,x15431),x15433))
% 3.00/2.89 [1584]~P2(a110,x15842,x15843)+~P3(a110,f2(a110),x15841)+P2(a110,f25(f25(f11(a110),x15841),x15842),f25(f25(f11(a110),x15841),x15843))
% 3.00/2.89 [1585]~P2(a110,x15851,x15853)+~P3(a110,f2(a110),x15852)+P2(a110,f25(f25(f11(a110),x15851),x15852),f25(f25(f11(a110),x15853),x15852))
% 3.00/2.89 [1589]~P3(a109,x15891,x15893)+~P3(a109,f2(a109),x15892)+P3(a109,f25(f25(f11(a109),x15891),x15892),f25(f25(f11(a109),x15893),x15892))
% 3.00/2.89 [1590]~P3(a109,x15902,x15903)+~P3(a109,f2(a109),x15901)+P3(a109,f25(f25(f11(a109),x15901),x15902),f25(f25(f11(a109),x15901),x15903))
% 3.00/2.89 [1591]~P3(a110,x15911,x15913)+~P3(a110,f2(a110),x15912)+P3(a110,f25(f25(f11(a110),x15911),x15912),f25(f25(f11(a110),x15913),x15912))
% 3.00/2.89 [1592]~P3(a110,x15922,x15923)+~P3(a110,f2(a110),x15921)+P3(a110,f25(f25(f11(a110),x15921),x15922),f25(f25(f11(a110),x15921),x15923))
% 3.00/2.89 [1593]~P3(a1,x15932,x15933)+~P3(a1,f2(a1),x15931)+P3(a1,f25(f25(f11(a1),x15931),x15932),f25(f25(f11(a1),x15931),x15933))
% 3.00/2.89 [1705]~P50(x17051)+~P3(x17051,f3(x17051),x17052)+P3(x17051,f3(x17051),f25(f25(f22(x17051),x17052),f12(a109,x17053,f3(a109))))
% 3.00/2.89 [1721]P2(a109,x17211,x17212)+~P3(a109,f2(a109),x17213)+~P2(a109,f25(f25(f11(a109),x17213),x17211),f25(f25(f11(a109),x17213),x17212))
% 3.00/2.89 [1722]P2(a109,x17221,x17222)+~P3(a109,f2(a109),x17223)+~P2(a109,f25(f25(f11(a109),x17221),x17223),f25(f25(f11(a109),x17222),x17223))
% 3.00/2.89 [1723]P2(a110,x17231,x17232)+~P3(a110,f2(a110),x17233)+~P2(a110,f25(f25(f11(a110),x17233),x17231),f25(f25(f11(a110),x17233),x17232))
% 3.00/2.89 [1724]P2(a110,x17241,x17242)+~P3(a110,f2(a110),x17243)+~P2(a110,f25(f25(f11(a110),x17241),x17243),f25(f25(f11(a110),x17242),x17243))
% 3.00/2.89 [1726]P3(a109,x17261,x17262)+~P3(a109,f2(a109),x17263)+~P3(a109,f25(f25(f22(a109),x17263),x17261),f25(f25(f22(a109),x17263),x17262))
% 3.00/2.89 [1727]P3(a110,x17271,x17272)+~P3(a110,f2(a110),x17273)+~P3(a110,f25(f25(f11(a110),x17271),x17273),f25(f25(f11(a110),x17272),x17273))
% 3.00/2.89 [1736]~P40(x17361)+~P7(x17361,x17362)+P2(a110,f26(x17361,f25(x17362,x17363)),f25(f16(a109),f12(a109,f60(x17362,x17361),f3(a109))))
% 3.00/2.89 [1737]~P40(x17371)+~P7(x17371,x17372)+P3(a110,f26(x17371,f25(x17372,x17373)),f25(f16(a109),f12(a109,f61(x17372,x17371),f3(a109))))
% 3.00/2.89 [1770]~E(x17703,f8(a109,x17701,x17702))+~P3(a109,f2(a109),x17702)+P3(a109,x17701,f25(f25(f11(a109),x17702),f12(a109,x17703,f3(a109))))
% 3.00/2.89 [1787]P4(f18(a1,x17871))+P4(f18(a1,x17872))+E(f12(a109,f18(a109,x17871),f12(a109,f18(a109,x17872),x17873)),f12(a109,f18(a109,f12(a1,x17871,x17872)),x17873))
% 3.00/2.89 [1827]P3(a109,x18272,x18271)+P2(a109,x18271,x18272)+P75(f25(x18273,f25(f17(a1),f10(a109,x18272,x18271))))
% 3.00/2.89 [1828]P2(a109,x18281,x18282)+~P75(f25(x18283,f2(a1)))+P75(f25(x18283,f25(f17(a1),f10(a109,x18282,x18281))))
% 3.00/2.89 [1920]~P3(a109,x19202,x19203)+P75(f25(x19201,f2(a1)))+~P75(f25(x19201,f25(f17(a1),f10(a109,x19202,x19203))))
% 3.00/2.89 [1943]E(x19431,f2(a109))+P3(a109,x19432,f25(f25(f11(a109),x19431),f12(a109,f101(x19431,x19432,x19433),f3(a109))))+~P75(f25(x19433,f8(a109,x19432,x19431)))
% 3.00/2.89 [1947]P3(a109,x19472,f25(f25(f11(a109),x19473),f12(a109,f101(x19473,x19472,x19471),f3(a109))))+~P75(f25(x19471,f8(a109,x19472,x19473)))+P75(f25(x19471,f2(a109)))
% 3.00/2.89 [1956]~P40(x19561)+P7(x19561,x19562)+~P2(a110,f26(x19561,f25(x19562,f76(x19562,x19561,x19563))),f25(f16(a109),f12(a109,x19563,f3(a109))))
% 3.00/2.89 [1957]~P40(x19571)+P7(x19571,x19572)+~P3(a110,f26(x19571,f25(x19572,f75(x19572,x19571,x19573))),f25(f16(a109),f12(a109,x19573,f3(a109))))
% 3.00/2.89 [1960]~P40(x19602)+P3(a110,f2(a110),f64(x19601,x19602))+~P2(a110,f26(x19602,f25(x19601,f65(x19601,x19602,x19603))),f25(f16(a109),f12(a109,x19603,f3(a109))))
% 3.00/2.89 [1961]~P40(x19612)+P3(a110,f2(a110),f68(x19611,x19612))+~P3(a110,f26(x19612,f25(x19611,f69(x19611,x19612,x19613))),f25(f16(a109),f12(a109,x19613,f3(a109))))
% 3.00/2.89 [1089]~P16(x10892)+E(x10891,f2(x10892))+E(f8(x10892,f25(f25(f11(x10892),x10893),x10891),x10891),x10893)
% 3.00/2.89 [1090]~P16(x10902)+E(x10901,f2(x10902))+E(f8(x10902,f25(f25(f11(x10902),x10901),x10903),x10901),x10903)
% 3.00/2.89 [1414]~P51(x14141)+~P2(x14141,f2(x14141),x14143)+E(f25(f25(f11(x14141),f7(x14141,x14142)),x14143),f7(x14141,f25(f25(f11(x14141),x14142),x14143)))
% 3.00/2.89 [1621]~P55(x16212)+E(x16211,f2(x16212))+~E(f12(x16212,f25(f25(f11(x16212),x16213),x16213),f25(f25(f11(x16212),x16211),x16211)),f2(x16212))
% 3.00/2.89 [1622]~P55(x16222)+E(x16221,f2(x16222))+~E(f12(x16222,f25(f25(f11(x16222),x16221),x16221),f25(f25(f11(x16222),x16223),x16223)),f2(x16222))
% 3.00/2.89 [1636]~P43(x16362)+E(x16361,f2(a109))+E(f25(f25(f11(x16362),x16363),f25(f25(f22(x16362),x16363),f10(a109,x16361,f3(a109)))),f25(f25(f22(x16362),x16363),x16361))
% 3.00/2.89 [1690]~P50(x16901)+~P3(x16901,f3(x16901),x16902)+P3(x16901,f3(x16901),f25(f25(f11(x16901),x16902),f25(f25(f22(x16901),x16902),x16903)))
% 3.00/2.89 [1806]~P50(x18061)+~P3(x18061,f3(x18061),x18062)+P3(x18061,f25(f25(f22(x18061),x18062),x18063),f25(f25(f11(x18061),x18062),f25(f25(f22(x18061),x18062),x18063)))
% 3.00/2.89 [1816]~P55(x18162)+E(x18161,f2(x18162))+P3(x18162,f2(x18162),f12(x18162,f25(f25(f11(x18162),x18163),x18163),f25(f25(f11(x18162),x18161),x18161)))
% 3.00/2.89 [1817]~P55(x18172)+E(x18171,f2(x18172))+P3(x18172,f2(x18172),f12(x18172,f25(f25(f11(x18172),x18171),x18171),f25(f25(f11(x18172),x18173),x18173)))
% 3.00/2.89 [1857]~P3(a1,x18572,x18573)+~P3(a109,f2(a109),x18571)+P3(a1,f25(f25(f11(a1),f25(f17(a1),x18571)),x18572),f25(f25(f11(a1),f25(f17(a1),x18571)),x18573))
% 3.00/2.89 [1918]~P55(x19182)+E(x19181,f2(x19182))+~P2(x19182,f12(x19182,f25(f25(f11(x19182),x19183),x19183),f25(f25(f11(x19182),x19181),x19181)),f2(x19182))
% 3.00/2.89 [1919]~P55(x19192)+E(x19191,f2(x19192))+~P2(x19192,f12(x19192,f25(f25(f11(x19192),x19191),x19191),f25(f25(f11(x19192),x19193),x19193)),f2(x19192))
% 3.00/2.89 [1958]P3(a109,x19581,x19582)+P75(f25(x19583,f25(f17(a1),f10(a109,x19581,x19582))))+~P75(f25(x19583,f10(a1,f25(f17(a1),x19581),f25(f17(a1),x19582))))
% 3.00/2.89 [1959]~P75(f25(x19591,f2(a1)))+P75(f25(x19591,f25(f17(a1),f10(a109,x19592,x19593))))+~P75(f25(x19591,f10(a1,f25(f17(a1),x19592),f25(f17(a1),x19593))))
% 3.00/2.89 [1964]~P2(a109,x19643,x19642)+~P75(f25(x19641,f25(f17(a1),f10(a109,x19642,x19643))))+P75(f25(x19641,f10(a1,f25(f17(a1),x19642),f25(f17(a1),x19643))))
% 3.00/2.89 [1913]~P26(x19131)+~P3(a109,f2(a109),x19133)+E(f25(f25(f11(x19131),f25(f25(f22(x19131),x19132),f10(a109,x19133,f3(a109)))),x19132),f25(f25(f22(x19131),x19132),x19133))
% 3.00/2.89 [1113]~P12(x11133)+E(x11131,x11132)+~E(f12(x11133,x11134,x11131),f12(x11133,x11134,x11132))
% 3.00/2.89 [1114]~P13(x11143)+E(x11141,x11142)+~E(f12(x11143,x11144,x11141),f12(x11143,x11144,x11142))
% 3.00/2.89 [1116]~P12(x11163)+E(x11161,x11162)+~E(f12(x11163,x11161,x11164),f12(x11163,x11162,x11164))
% 3.00/2.89 [1185]~P37(x11852)+~P3(f114(x11851,x11852),x11853,x11854)+P2(f114(x11851,x11852),x11853,x11854)
% 3.00/2.89 [1312]~P37(x13121)+~P3(f114(x13122,x13121),x13124,x13123)+~P2(f114(x13122,x13121),x13123,x13124)
% 3.00/2.89 [1372]~P3(a109,x13723,x13724)+P3(a109,x13721,x13722)+~E(f12(a109,x13723,x13722),f12(a109,x13721,x13724))
% 3.00/2.89 [1503]~P10(x15031)+~P2(x15031,x15033,x15034)+P2(x15031,f12(x15031,x15032,x15033),f12(x15031,x15032,x15034))
% 3.00/2.89 [1504]~P11(x15041)+~P2(x15041,x15043,x15044)+P2(x15041,f12(x15041,x15042,x15043),f12(x15041,x15042,x15044))
% 3.00/2.89 [1505]~P10(x15051)+~P2(x15051,x15052,x15054)+P2(x15051,f12(x15051,x15052,x15053),f12(x15051,x15054,x15053))
% 3.00/2.89 [1506]~P11(x15061)+~P2(x15061,x15062,x15064)+P2(x15061,f12(x15061,x15062,x15063),f12(x15061,x15064,x15063))
% 3.00/2.89 [1507]~P10(x15071)+~P3(x15071,x15073,x15074)+P3(x15071,f12(x15071,x15072,x15073),f12(x15071,x15072,x15074))
% 3.00/2.89 [1508]~P32(x15081)+~P3(x15081,x15083,x15084)+P3(x15081,f12(x15081,x15082,x15083),f12(x15081,x15082,x15084))
% 3.00/2.89 [1509]~P10(x15091)+~P3(x15091,x15092,x15094)+P3(x15091,f12(x15091,x15092,x15093),f12(x15091,x15094,x15093))
% 3.00/2.89 [1510]~P32(x15101)+~P3(x15101,x15102,x15104)+P3(x15101,f12(x15101,x15102,x15103),f12(x15101,x15104,x15103))
% 3.00/2.89 [1623]~P2(a109,x16232,x16234)+~P2(a109,x16231,x16233)+P2(a109,f12(a109,x16231,x16232),f12(a109,x16233,x16234))
% 3.00/2.89 [1624]~P3(a109,x16242,x16244)+~P3(a109,x16241,x16243)+P3(a109,f12(a109,x16241,x16242),f12(a109,x16243,x16244))
% 3.00/2.89 [1627]~P2(a1,x16272,x16274)+~P3(a1,x16271,x16273)+P3(a1,f12(a1,x16271,x16272),f12(a1,x16273,x16274))
% 3.00/2.89 [1697]~P10(x16971)+P2(x16971,x16972,x16973)+~P2(x16971,f12(x16971,x16974,x16972),f12(x16971,x16974,x16973))
% 3.00/2.89 [1699]~P10(x16991)+P2(x16991,x16992,x16993)+~P2(x16991,f12(x16991,x16992,x16994),f12(x16991,x16993,x16994))
% 3.00/2.89 [1701]~P10(x17011)+P3(x17011,x17012,x17013)+~P3(x17011,f12(x17011,x17014,x17012),f12(x17011,x17014,x17013))
% 3.00/2.89 [1703]~P10(x17031)+P3(x17031,x17032,x17033)+~P3(x17031,f12(x17031,x17032,x17034),f12(x17031,x17033,x17034))
% 3.00/2.89 [1709]~E(x17093,f12(a109,x17094,x17092))+P75(f25(x17091,x17092))+~P75(f25(x17091,f10(a109,x17093,x17094)))
% 3.00/2.89 [1843]~P51(x18431)+P3(x18431,x18432,f12(x18431,x18433,x18434))+~P3(x18431,f7(x18431,f10(x18431,x18432,x18433)),x18434)
% 3.00/2.89 [1844]~P51(x18441)+P3(x18441,f10(x18441,x18442,x18443),x18444)+~P3(x18441,f7(x18441,f10(x18441,x18444,x18442)),x18443)
% 3.00/2.89 [1999]~P37(x19992)+P2(f114(x19991,x19992),x19993,x19994)+~P2(x19992,f25(x19993,f72(x19994,x19993,x19991,x19992)),f25(x19994,f72(x19994,x19993,x19991,x19992)))
% 3.00/2.89 [1575]~P2(a109,x15752,x15754)+~P2(a109,x15751,x15753)+P2(a109,f25(f25(f11(a109),x15751),x15752),f25(f25(f11(a109),x15753),x15754))
% 3.00/2.89 [1860]~P33(x18601)+~P71(x18601)+E(f12(x18601,f25(f25(f11(x18601),x18602),f18(x18601,x18603)),f25(f25(f11(x18601),x18604),f18(x18601,x18603))),f25(f25(f11(x18601),f12(x18601,x18602,x18604)),f18(x18601,x18603)))
% 3.00/2.89 [1861]~P33(x18611)+~P68(x18611)+E(f10(x18611,f25(f25(f11(x18611),x18612),f18(x18611,x18613)),f25(f25(f11(x18611),x18614),f18(x18611,x18613))),f25(f25(f11(x18611),f10(x18611,x18612,x18614)),f18(x18611,x18613)))
% 3.00/2.89 [1967]~P40(x19671)+P2(a110,f26(x19671,f25(x19672,x19673)),f64(x19672,x19671))+~P2(a110,f26(x19671,f25(x19672,f65(x19672,x19671,x19674))),f25(f16(a109),f12(a109,x19674,f3(a109))))
% 3.00/2.89 [1968]~P40(x19681)+P2(a110,f26(x19681,f25(x19682,x19683)),f68(x19682,x19681))+~P3(a110,f26(x19681,f25(x19682,f69(x19682,x19681,x19684))),f25(f16(a109),f12(a109,x19684,f3(a109))))
% 3.00/2.89 [1343]~P16(x13431)+~E(x13432,f2(x13431))+E(f8(x13431,f25(f25(f11(x13431),x13432),x13433),f25(f25(f11(x13431),x13432),x13434)),f2(x13431))
% 3.00/2.89 [1424]~P16(x14242)+E(x14241,f2(x14242))+E(f8(x14242,f25(f25(f11(x14242),x14243),x14241),f25(f25(f11(x14242),x14244),x14241)),f8(x14242,x14243,x14244))
% 3.00/2.89 [1426]~P16(x14262)+E(x14261,f2(x14262))+E(f8(x14262,f25(f25(f11(x14262),x14261),x14263),f25(f25(f11(x14262),x14261),x14264)),f8(x14262,x14263,x14264))
% 3.00/2.89 [1771]~P17(x17712)+E(x17711,f2(x17712))+E(f27(x17712,f25(f25(f22(x17712),x17713),x17714),f25(f25(f22(x17712),x17711),x17714)),f25(f25(f22(x17712),f27(x17712,x17713,x17711)),x17714))
% 3.00/2.89 [1876]~P33(x18761)+~P71(x18761)+E(f12(x18761,f25(f25(f11(x18761),f18(x18761,x18762)),x18763),f25(f25(f11(x18761),f18(x18761,x18762)),x18764)),f25(f25(f11(x18761),f18(x18761,x18762)),f12(x18761,x18763,x18764)))
% 3.00/2.89 [1877]~P33(x18771)+~P68(x18771)+E(f10(x18771,f25(f25(f11(x18771),f18(x18771,x18772)),x18773),f25(f25(f11(x18771),f18(x18771,x18772)),x18774)),f25(f25(f11(x18771),f18(x18771,x18772)),f10(x18771,x18773,x18774)))
% 3.00/2.89 [1941]~P26(x19411)+~P2(a109,x19414,x19413)+E(f25(f25(f11(x19411),f25(f25(f22(x19411),x19412),f10(a109,x19413,x19414))),x19412),f25(f25(f22(x19411),x19412),f10(a109,f12(a109,x19413,f3(a109)),x19414)))
% 3.00/2.89 [1773]~P16(x17732)+E(x17731,f2(x17732))+E(f8(x17732,f12(x17732,x17733,f25(f25(f11(x17732),x17734),x17731)),x17731),f12(x17732,x17734,f8(x17732,x17733,x17731)))
% 3.00/2.89 [1774]~P16(x17742)+E(x17741,f2(x17742))+E(f8(x17742,f12(x17742,x17743,f25(f25(f11(x17742),x17741),x17744)),x17741),f12(x17742,x17744,f8(x17742,x17743,x17741)))
% 3.00/2.89 [1259]~P37(x12591)+P2(x12591,f25(x12592,x12593),f25(x12594,x12593))+~P2(f114(x12595,x12591),x12592,x12594)
% 3.00/2.89 [1748]~E(x17482,x17484)+~P73(x17481)+E(f12(x17481,f25(f25(f11(x17481),x17482),x17483),f25(f25(f11(x17481),x17484),x17485)),f12(x17481,f25(f25(f11(x17481),x17482),x17485),f25(f25(f11(x17481),x17484),x17483)))
% 3.00/2.89 [1939]~P2(a109,x19393,x19392)+E(x19391,f12(a109,f25(f25(f11(a109),f10(a109,x19392,x19393)),x19394),x19395))+~E(f12(a109,f25(f25(f11(a109),x19393),x19394),x19391),f12(a109,f25(f25(f11(a109),x19392),x19394),x19395))
% 3.00/2.89 [1940]~P2(a109,x19402,x19401)+E(f12(a109,f25(f25(f11(a109),f10(a109,x19401,x19402)),x19403),x19404),x19405)+~E(f12(a109,f25(f25(f11(a109),x19401),x19403),x19404),f12(a109,f25(f25(f11(a109),x19402),x19403),x19405))
% 3.00/2.89 [1951]~P2(a109,x19514,x19511)+~E(x19515,f12(a109,f25(f25(f11(a109),f10(a109,x19511,x19514)),x19512),x19513))+E(f12(a109,f25(f25(f11(a109),x19511),x19512),x19513),f12(a109,f25(f25(f11(a109),x19514),x19512),x19515))
% 3.00/2.89 [1952]~P2(a109,x19524,x19521)+~E(f12(a109,f25(f25(f11(a109),f10(a109,x19521,x19524)),x19522),x19523),x19525)+E(f12(a109,f25(f25(f11(a109),x19521),x19522),x19523),f12(a109,f25(f25(f11(a109),x19524),x19522),x19525))
% 3.00/2.89 [1982]~P2(a109,x19823,x19822)+P2(a109,x19821,f12(a109,f25(f25(f11(a109),f10(a109,x19822,x19823)),x19824),x19825))+~P2(a109,f12(a109,f25(f25(f11(a109),x19823),x19824),x19821),f12(a109,f25(f25(f11(a109),x19822),x19824),x19825))
% 3.00/2.89 [1983]~P2(a109,x19833,x19832)+P3(a109,x19831,f12(a109,f25(f25(f11(a109),f10(a109,x19832,x19833)),x19834),x19835))+~P3(a109,f12(a109,f25(f25(f11(a109),x19833),x19834),x19831),f12(a109,f25(f25(f11(a109),x19832),x19834),x19835))
% 3.00/2.89 [1984]~P2(a109,x19842,x19841)+P2(a109,f12(a109,f25(f25(f11(a109),f10(a109,x19841,x19842)),x19843),x19844),x19845)+~P2(a109,f12(a109,f25(f25(f11(a109),x19841),x19843),x19844),f12(a109,f25(f25(f11(a109),x19842),x19843),x19845))
% 3.00/2.89 [1985]~P2(a109,x19852,x19851)+P3(a109,f12(a109,f25(f25(f11(a109),f10(a109,x19851,x19852)),x19853),x19854),x19855)+~P3(a109,f12(a109,f25(f25(f11(a109),x19851),x19853),x19854),f12(a109,f25(f25(f11(a109),x19852),x19853),x19855))
% 3.00/2.89 [1990]~P2(a109,x19901,x19904)+~P2(a109,x19903,f12(a109,f25(f25(f11(a109),f10(a109,x19904,x19901)),x19902),x19905))+P2(a109,f12(a109,f25(f25(f11(a109),x19901),x19902),x19903),f12(a109,f25(f25(f11(a109),x19904),x19902),x19905))
% 3.00/2.89 [1991]~P2(a109,x19911,x19914)+~P3(a109,x19913,f12(a109,f25(f25(f11(a109),f10(a109,x19914,x19911)),x19912),x19915))+P3(a109,f12(a109,f25(f25(f11(a109),x19911),x19912),x19913),f12(a109,f25(f25(f11(a109),x19914),x19912),x19915))
% 3.00/2.89 [1992]~P2(a109,x19924,x19921)+~P2(a109,f12(a109,f25(f25(f11(a109),f10(a109,x19921,x19924)),x19922),x19923),x19925)+P2(a109,f12(a109,f25(f25(f11(a109),x19921),x19922),x19923),f12(a109,f25(f25(f11(a109),x19924),x19922),x19925))
% 3.00/2.89 [1993]~P2(a109,x19934,x19931)+~P3(a109,f12(a109,f25(f25(f11(a109),f10(a109,x19931,x19934)),x19932),x19933),x19935)+P3(a109,f12(a109,f25(f25(f11(a109),x19931),x19932),x19933),f12(a109,f25(f25(f11(a109),x19934),x19932),x19935))
% 3.00/2.89 [1937]~P68(x19372)+~E(f12(x19372,f25(f25(f11(x19372),x19374),x19375),x19371),f12(x19372,f25(f25(f11(x19372),x19373),x19375),x19376))+E(x19371,f12(x19372,f25(f25(f11(x19372),f10(x19372,x19373,x19374)),x19375),x19376))
% 3.00/2.89 [1938]~P68(x19381)+~E(f12(x19381,f25(f25(f11(x19381),x19382),x19384),x19385),f12(x19381,f25(f25(f11(x19381),x19383),x19384),x19386))+E(f12(x19381,f25(f25(f11(x19381),f10(x19381,x19382,x19383)),x19384),x19385),x19386)
% 3.00/2.89 [1949]~P68(x19491)+~E(x19496,f12(x19491,f25(f25(f11(x19491),f10(x19491,x19492,x19495)),x19493),x19494))+E(f12(x19491,f25(f25(f11(x19491),x19492),x19493),x19494),f12(x19491,f25(f25(f11(x19491),x19495),x19493),x19496))
% 3.00/2.89 [1950]~P68(x19501)+~E(f12(x19501,f25(f25(f11(x19501),f10(x19501,x19502,x19505)),x19503),x19504),x19506)+E(f12(x19501,f25(f25(f11(x19501),x19502),x19503),x19504),f12(x19501,f25(f25(f11(x19501),x19505),x19503),x19506))
% 3.00/2.89 [1986]~P64(x19861)+~P2(x19861,f12(x19861,f25(f25(f11(x19861),x19864),x19865),x19862),f12(x19861,f25(f25(f11(x19861),x19863),x19865),x19866))+P2(x19861,x19862,f12(x19861,f25(f25(f11(x19861),f10(x19861,x19863,x19864)),x19865),x19866))
% 3.00/2.89 [1987]~P64(x19871)+~P3(x19871,f12(x19871,f25(f25(f11(x19871),x19874),x19875),x19872),f12(x19871,f25(f25(f11(x19871),x19873),x19875),x19876))+P3(x19871,x19872,f12(x19871,f25(f25(f11(x19871),f10(x19871,x19873,x19874)),x19875),x19876))
% 3.00/2.89 [1988]~P64(x19881)+~P2(x19881,f12(x19881,f25(f25(f11(x19881),x19882),x19884),x19885),f12(x19881,f25(f25(f11(x19881),x19883),x19884),x19886))+P2(x19881,f12(x19881,f25(f25(f11(x19881),f10(x19881,x19882,x19883)),x19884),x19885),x19886)
% 3.00/2.89 [1989]~P64(x19891)+~P3(x19891,f12(x19891,f25(f25(f11(x19891),x19892),x19894),x19895),f12(x19891,f25(f25(f11(x19891),x19893),x19894),x19896))+P3(x19891,f12(x19891,f25(f25(f11(x19891),f10(x19891,x19892,x19893)),x19894),x19895),x19896)
% 3.00/2.89 [1994]~P64(x19941)+~P2(x19941,x19944,f12(x19941,f25(f25(f11(x19941),f10(x19941,x19945,x19942)),x19943),x19946))+P2(x19941,f12(x19941,f25(f25(f11(x19941),x19942),x19943),x19944),f12(x19941,f25(f25(f11(x19941),x19945),x19943),x19946))
% 3.00/2.89 [1995]~P64(x19951)+~P3(x19951,x19954,f12(x19951,f25(f25(f11(x19951),f10(x19951,x19955,x19952)),x19953),x19956))+P3(x19951,f12(x19951,f25(f25(f11(x19951),x19952),x19953),x19954),f12(x19951,f25(f25(f11(x19951),x19955),x19953),x19956))
% 3.00/2.89 [1996]~P64(x19961)+~P2(x19961,f12(x19961,f25(f25(f11(x19961),f10(x19961,x19962,x19965)),x19963),x19964),x19966)+P2(x19961,f12(x19961,f25(f25(f11(x19961),x19962),x19963),x19964),f12(x19961,f25(f25(f11(x19961),x19965),x19963),x19966))
% 3.00/2.89 [1997]~P64(x19971)+~P3(x19971,f12(x19971,f25(f25(f11(x19971),f10(x19971,x19972,x19975)),x19973),x19974),x19976)+P3(x19971,f12(x19971,f25(f25(f11(x19971),x19972),x19973),x19974),f12(x19971,f25(f25(f11(x19971),x19975),x19973),x19976))
% 3.00/2.89 [925]E(x9251,x9252)+~E(f18(a109,x9251),f18(a109,x9252))+P4(f18(a1,x9252))+P4(f18(a1,x9251))
% 3.00/2.89 [982]E(f18(a109,x9821),f18(a109,x9822))+~E(f18(a1,x9822),f2(a1))+P4(f18(a1,x9822))+~P4(f18(a1,x9821))
% 3.00/2.89 [988]~E(f18(a109,x9882),f18(a109,x9881))+E(f18(a1,x9881),f2(a1))+P4(f18(a1,x9881))+~P4(f18(a1,x9882))
% 3.00/2.89 [1122]~P51(x11221)+~P34(x11221)+P2(x11221,f2(x11221),f18(x11221,x11222))+~P2(a1,a13,x11222)
% 3.00/2.89 [1123]~P51(x11231)+~P34(x11231)+P3(x11231,f2(x11231),f18(x11231,x11232))+~P3(a1,a13,x11232)
% 3.00/2.89 [1124]~P51(x11241)+~P34(x11241)+P2(x11241,f18(x11241,x11242),f2(x11241))+~P2(a1,x11242,a13)
% 3.00/2.89 [1125]~P51(x11251)+~P34(x11251)+P3(x11251,f18(x11251,x11252),f2(x11251))+~P3(a1,x11252,a13)
% 3.00/2.89 [1155]P3(a1,x11551,x11552)+P3(a1,x11552,x11551)+E(x11551,f2(a1))+~E(f8(a1,x11552,x11551),f2(a1))
% 3.00/2.89 [1159]P3(a1,x11592,x11591)+E(x11591,f2(a1))+P2(a1,x11592,f2(a1))+~E(f8(a1,x11592,x11591),f2(a1))
% 3.00/2.89 [1160]P3(a1,x11601,x11602)+E(x11601,f2(a1))+P2(a1,f2(a1),x11602)+~E(f8(a1,x11602,x11601),f2(a1))
% 3.00/2.89 [1167]~P34(x11672)+~P51(x11672)+~P2(x11672,f18(x11672,x11671),f2(x11672))+P2(a1,x11671,a13)
% 3.00/2.89 [1168]~P34(x11682)+~P51(x11682)+~P3(x11682,f18(x11682,x11681),f2(x11682))+P3(a1,x11681,a13)
% 3.00/2.89 [1169]~P34(x11692)+~P51(x11692)+~P2(x11692,f2(x11692),f18(x11692,x11691))+P2(a1,a13,x11691)
% 3.00/2.89 [1170]~P34(x11702)+~P51(x11702)+~P3(x11702,f2(x11702),f18(x11702,x11701))+P3(a1,a13,x11701)
% 3.00/2.89 [1189]E(f18(a109,x11891),f18(a109,x11892))+~E(f18(a1,x11892),f2(a1))+~P2(a1,f18(a1,x11891),f2(a1))+~P4(f18(a1,x11891))
% 3.00/2.89 [1401]~P2(a110,x14012,f18(a110,x14011))+P2(a109,f19(x14012),f18(a109,x14011))+~P2(a110,f2(a110),x14012)+P4(f18(a1,x14011))
% 3.00/2.89 [1402]~P2(a110,f18(a110,x14021),x14022)+P2(a109,f18(a109,x14021),f24(x14022))+~P2(a110,f2(a110),x14022)+P4(f18(a1,x14021))
% 3.00/2.89 [1412]~P2(a109,f19(x14122),f18(a109,x14121))+P2(a110,x14122,f18(a110,x14121))+~P2(a110,f2(a110),x14122)+P4(f18(a1,x14121))
% 3.00/2.89 [1413]~P2(a109,f18(a109,x14131),f24(x14132))+P2(a110,f18(a110,x14131),x14132)+~P2(a110,f2(a110),x14132)+P4(f18(a1,x14131))
% 3.00/2.89 [891]~P43(x8912)+~P72(x8912)+E(x8911,f2(a109))+E(f25(f25(f22(x8912),f2(x8912)),x8911),f2(x8912))
% 3.00/2.89 [1037]~E(x10372,f3(a1))+~E(x10371,f3(a1))+~P3(a1,f2(a1),x10371)+E(f25(f25(f11(a1),x10371),x10372),f3(a1))
% 3.00/2.89 [980]P3(x9803,x9801,x9802)+~P51(x9803)+E(x9801,x9802)+P3(x9803,x9802,x9801)
% 3.00/2.89 [981]P3(x9813,x9811,x9812)+~P29(x9813)+E(x9811,x9812)+P3(x9813,x9812,x9811)
% 3.00/2.89 [983]P3(x9831,x9832,x9833)+~E(x9832,x9833)+~P29(x9831)+P2(x9831,x9832,x9833)
% 3.00/2.89 [1039]~P38(x10393)+~P2(x10393,x10392,x10391)+E(x10391,x10392)+P3(x10393,x10392,x10391)
% 3.00/2.89 [1041]~P29(x10413)+~P2(x10413,x10411,x10412)+E(x10411,x10412)+P3(x10413,x10411,x10412)
% 3.00/2.89 [1047]~P38(x10473)+~P2(x10473,x10471,x10472)+E(x10471,x10472)+P3(x10473,x10471,x10472)
% 3.00/2.89 [1121]~P2(x11213,x11212,x11211)+~P2(x11213,x11211,x11212)+E(x11211,x11212)+~P38(x11213)
% 3.00/2.89 [1171]P3(x11711,x11713,x11712)+~P9(x11711)+~P2(x11711,x11713,x11712)+P2(x11711,x11712,x11713)
% 3.00/2.89 [815]~P34(x8153)+~P35(x8153)+E(x8151,x8152)+~E(f18(x8153,x8151),f18(x8153,x8152))
% 3.00/2.89 [1173]~P51(x11731)+~P34(x11731)+~P2(a1,x11732,x11733)+P2(x11731,f18(x11731,x11732),f18(x11731,x11733))
% 3.00/2.89 [1174]~P51(x11741)+~P34(x11741)+~P3(a1,x11742,x11743)+P3(x11741,f18(x11741,x11742),f18(x11741,x11743))
% 3.00/2.89 [1233]~P34(x12333)+~P51(x12333)+~P2(x12333,f18(x12333,x12331),f18(x12333,x12332))+P2(a1,x12331,x12332)
% 3.00/2.89 [1234]~P34(x12343)+~P51(x12343)+~P3(x12343,f18(x12343,x12341),f18(x12343,x12342))+P3(a1,x12341,x12342)
% 3.00/2.89 [1337]P76(x13372,x13371,x13373)+P3(a1,f102(x13373,x13371,x13372),x13371)+E(x13371,f2(a1))+P3(a1,x13371,f2(a1))
% 3.00/2.89 [1338]P76(x13382,x13381,x13383)+P3(a1,x13381,f106(x13383,x13381,x13382))+E(x13381,f2(a1))+P3(a1,f2(a1),x13381)
% 3.00/2.89 [1341]P76(x13412,x13411,x13413)+E(x13411,f2(a1))+P3(a1,x13411,f2(a1))+P2(a1,f2(a1),f102(x13413,x13411,x13412))
% 3.00/2.89 [1342]P76(x13422,x13421,x13423)+E(x13421,f2(a1))+P3(a1,f2(a1),x13421)+P2(a1,f106(x13423,x13421,x13422),f2(a1))
% 3.00/2.89 [1448]E(x14481,x14482)+~P2(a109,x14483,x14482)+~P2(a109,x14483,x14481)+~E(f10(a109,x14481,x14483),f10(a109,x14482,x14483))
% 3.00/2.89 [1536]~P31(x15361)+~P3(x15361,f2(x15361),x15363)+~P3(x15361,f2(x15361),x15362)+P3(x15361,f2(x15361),f12(x15361,x15362,x15363))
% 3.00/2.89 [1537]~P31(x15371)+~P2(x15371,x15373,f2(x15371))+~P2(x15371,x15372,f2(x15371))+P2(x15371,f12(x15371,x15372,x15373),f2(x15371))
% 3.00/2.89 [1538]~P31(x15381)+~P2(x15381,x15383,f2(x15381))+~P3(x15381,x15382,f2(x15381))+P3(x15381,f12(x15381,x15382,x15383),f2(x15381))
% 3.00/2.89 [1539]~P31(x15391)+~P2(x15391,x15392,f2(x15391))+~P3(x15391,x15393,f2(x15391))+P3(x15391,f12(x15391,x15392,x15393),f2(x15391))
% 3.00/2.89 [1540]~P31(x15401)+~P3(x15401,x15403,f2(x15401))+~P3(x15401,x15402,f2(x15401))+P3(x15401,f12(x15401,x15402,x15403),f2(x15401))
% 3.00/2.89 [1549]P76(x15492,x15491,x15493)+P3(a1,x15491,f106(x15493,x15491,x15492))+P3(a1,f102(x15493,x15491,x15492),x15491)+E(x15491,f2(a1))
% 3.00/2.89 [1550]P76(x15502,x15501,x15503)+P3(a1,x15501,f106(x15503,x15501,x15502))+E(x15501,f2(a1))+P2(a1,f2(a1),f102(x15503,x15501,x15502))
% 3.00/2.89 [1551]P76(x15512,x15511,x15513)+P3(a1,f102(x15513,x15511,x15512),x15511)+E(x15511,f2(a1))+P2(a1,f106(x15513,x15511,x15512),f2(a1))
% 3.00/2.89 [1553]P76(x15532,x15531,x15533)+E(x15531,f2(a1))+P2(a1,f2(a1),f102(x15533,x15531,x15532))+P2(a1,f106(x15533,x15531,x15532),f2(a1))
% 3.00/2.89 [1741]~P2(a1,x17412,x17413)+P2(a1,f8(a1,x17411,x17412),f8(a1,x17411,x17413))+~P3(a1,x17411,f2(a1))+~P3(a1,f2(a1),x17412)
% 3.00/2.89 [1742]~P2(a1,x17423,x17422)+P2(a1,f8(a1,x17421,x17422),f8(a1,x17421,x17423))+~P2(a1,f2(a1),x17421)+~P3(a1,f2(a1),x17423)
% 3.00/2.89 [1841]~P2(a109,x18413,x18411)+P2(a109,x18411,x18412)+~P2(a109,x18413,x18412)+~P2(a109,f10(a109,x18411,x18413),f10(a109,x18412,x18413))
% 3.00/2.89 [1842]~P2(a109,x18423,x18421)+P3(a109,x18421,x18422)+~P2(a109,x18423,x18422)+~P3(a109,f10(a109,x18421,x18423),f10(a109,x18422,x18423))
% 3.00/2.89 [1205]P76(x12051,x12052,x12053)+P3(a1,x12052,f2(a1))+P3(a1,f2(a1),x12052)+~P75(f25(x12051,f2(a1)))
% 3.00/2.89 [1304]~P2(a109,x13043,f52(x13042,x13041))+~P75(f25(x13041,x13042))+~P75(f25(x13041,x13043))+P75(f25(x13041,f2(a109)))
% 3.00/2.89 [1427]P76(x14271,x14272,x14273)+P3(a1,f102(x14273,x14272,x14271),x14272)+P3(a1,x14272,f2(a1))+~P75(f25(x14271,f2(a1)))
% 3.00/2.89 [1428]P76(x14281,x14282,x14283)+P3(a1,x14282,f106(x14283,x14282,x14281))+P3(a1,f2(a1),x14282)+~P75(f25(x14281,f2(a1)))
% 3.00/2.89 [1442]P76(x14421,x14422,x14423)+P3(a1,x14422,f2(a1))+P2(a1,f2(a1),f102(x14423,x14422,x14421))+~P75(f25(x14421,f2(a1)))
% 3.00/2.89 [1443]P76(x14431,x14432,x14433)+P3(a1,f2(a1),x14432)+P2(a1,f106(x14433,x14432,x14431),f2(a1))+~P75(f25(x14431,f2(a1)))
% 3.00/2.89 [1629]P76(x16291,x16292,x16293)+P3(a1,x16292,f106(x16293,x16292,x16291))+P3(a1,f102(x16293,x16292,x16291),x16292)+~P75(f25(x16291,f2(a1)))
% 3.00/2.89 [1633]P76(x16331,x16332,x16333)+P3(a1,x16332,f106(x16333,x16332,x16331))+P2(a1,f2(a1),f102(x16333,x16332,x16331))+~P75(f25(x16331,f2(a1)))
% 3.00/2.89 [1634]P76(x16341,x16342,x16343)+P3(a1,f102(x16343,x16342,x16341),x16342)+P2(a1,f106(x16343,x16342,x16341),f2(a1))+~P75(f25(x16341,f2(a1)))
% 3.00/2.89 [1638]P76(x16381,x16382,x16383)+P2(a1,f2(a1),f102(x16383,x16382,x16381))+P2(a1,f106(x16383,x16382,x16381),f2(a1))+~P75(f25(x16381,f2(a1)))
% 3.00/2.89 [1714]P76(x17142,x17141,x17143)+E(x17141,f2(a1))+P3(a1,x17141,f2(a1))+~P75(f25(x17142,f103(x17143,x17141,x17142)))
% 3.00/2.89 [1715]P76(x17152,x17151,x17153)+E(x17151,f2(a1))+P3(a1,f2(a1),x17151)+~P75(f25(x17152,f104(x17153,x17151,x17152)))
% 3.00/2.89 [1782]P76(x17821,x17822,x17823)+P3(a1,x17822,f2(a1))+~P75(f25(x17821,f103(x17823,x17822,x17821)))+~P75(f25(x17821,f2(a1)))
% 3.00/2.89 [1783]P76(x17831,x17832,x17833)+P3(a1,f2(a1),x17832)+~P75(f25(x17831,f104(x17833,x17832,x17831)))+~P75(f25(x17831,f2(a1)))
% 3.00/2.89 [1812]P76(x18123,x18121,x18122)+E(x18121,f2(a1))+P3(a1,x18121,f2(a1))+E(f12(a1,f25(f25(f11(a1),x18121),f103(x18122,x18121,x18123)),f102(x18122,x18121,x18123)),x18122)
% 3.00/2.89 [1813]P76(x18133,x18131,x18132)+E(x18131,f2(a1))+P3(a1,f2(a1),x18131)+E(f12(a1,f25(f25(f11(a1),x18131),f104(x18132,x18131,x18133)),f106(x18132,x18131,x18133)),x18132)
% 3.00/2.89 [1820]P76(x18202,x18201,x18203)+P3(a1,x18201,f106(x18203,x18201,x18202))+E(x18201,f2(a1))+~P75(f25(x18202,f103(x18203,x18201,x18202)))
% 3.00/2.89 [1821]P76(x18212,x18211,x18213)+P3(a1,f102(x18213,x18211,x18212),x18211)+E(x18211,f2(a1))+~P75(f25(x18212,f104(x18213,x18211,x18212)))
% 3.00/2.89 [1824]P76(x18242,x18241,x18243)+E(x18241,f2(a1))+P2(a1,f2(a1),f102(x18243,x18241,x18242))+~P75(f25(x18242,f104(x18243,x18241,x18242)))
% 3.00/2.89 [1825]P76(x18252,x18251,x18253)+E(x18251,f2(a1))+P2(a1,f106(x18253,x18251,x18252),f2(a1))+~P75(f25(x18252,f103(x18253,x18251,x18252)))
% 3.00/2.89 [1846]P76(x18463,x18461,x18462)+P3(a1,x18461,f2(a1))+E(f12(a1,f25(f25(f11(a1),x18461),f103(x18462,x18461,x18463)),f102(x18462,x18461,x18463)),x18462)+~P75(f25(x18463,f2(a1)))
% 3.00/2.89 [1847]P76(x18473,x18471,x18472)+P3(a1,f2(a1),x18471)+E(f12(a1,f25(f25(f11(a1),x18471),f104(x18472,x18471,x18473)),f106(x18472,x18471,x18473)),x18472)+~P75(f25(x18473,f2(a1)))
% 3.00/2.89 [1852]P76(x18521,x18522,x18523)+P3(a1,x18522,f106(x18523,x18522,x18521))+~P75(f25(x18521,f103(x18523,x18522,x18521)))+~P75(f25(x18521,f2(a1)))
% 3.00/2.89 [1853]P76(x18531,x18532,x18533)+P3(a1,f102(x18533,x18532,x18531),x18532)+~P75(f25(x18531,f104(x18533,x18532,x18531)))+~P75(f25(x18531,f2(a1)))
% 3.00/2.89 [1855]P76(x18551,x18552,x18553)+P2(a1,f2(a1),f102(x18553,x18552,x18551))+~P75(f25(x18551,f104(x18553,x18552,x18551)))+~P75(f25(x18551,f2(a1)))
% 3.00/2.89 [1856]P76(x18561,x18562,x18563)+P2(a1,f106(x18563,x18562,x18561),f2(a1))+~P75(f25(x18561,f103(x18563,x18562,x18561)))+~P75(f25(x18561,f2(a1)))
% 3.00/2.89 [1871]P76(x18713,x18711,x18712)+P3(a1,x18711,f106(x18712,x18711,x18713))+E(x18711,f2(a1))+E(f12(a1,f25(f25(f11(a1),x18711),f103(x18712,x18711,x18713)),f102(x18712,x18711,x18713)),x18712)
% 3.00/2.89 [1872]P76(x18723,x18721,x18722)+P3(a1,f102(x18722,x18721,x18723),x18721)+E(x18721,f2(a1))+E(f12(a1,f25(f25(f11(a1),x18721),f104(x18722,x18721,x18723)),f106(x18722,x18721,x18723)),x18722)
% 3.00/2.89 [1874]P76(x18743,x18741,x18742)+E(x18741,f2(a1))+P2(a1,f2(a1),f102(x18742,x18741,x18743))+E(f12(a1,f25(f25(f11(a1),x18741),f104(x18742,x18741,x18743)),f106(x18742,x18741,x18743)),x18742)
% 3.00/2.89 [1875]P76(x18753,x18751,x18752)+E(x18751,f2(a1))+P2(a1,f106(x18752,x18751,x18753),f2(a1))+E(f12(a1,f25(f25(f11(a1),x18751),f103(x18752,x18751,x18753)),f102(x18752,x18751,x18753)),x18752)
% 3.00/2.89 [1887]P76(x18873,x18871,x18872)+P3(a1,x18871,f106(x18872,x18871,x18873))+E(f12(a1,f25(f25(f11(a1),x18871),f103(x18872,x18871,x18873)),f102(x18872,x18871,x18873)),x18872)+~P75(f25(x18873,f2(a1)))
% 3.00/2.89 [1888]P76(x18883,x18881,x18882)+P3(a1,f102(x18882,x18881,x18883),x18881)+E(f12(a1,f25(f25(f11(a1),x18881),f104(x18882,x18881,x18883)),f106(x18882,x18881,x18883)),x18882)+~P75(f25(x18883,f2(a1)))
% 3.00/2.89 [1890]P76(x18903,x18901,x18902)+P2(a1,f2(a1),f102(x18902,x18901,x18903))+E(f12(a1,f25(f25(f11(a1),x18901),f104(x18902,x18901,x18903)),f106(x18902,x18901,x18903)),x18902)+~P75(f25(x18903,f2(a1)))
% 3.00/2.89 [1891]P76(x18913,x18911,x18912)+P2(a1,f106(x18912,x18911,x18913),f2(a1))+E(f12(a1,f25(f25(f11(a1),x18911),f103(x18912,x18911,x18913)),f102(x18912,x18911,x18913)),x18912)+~P75(f25(x18913,f2(a1)))
% 3.00/2.89 [1909]P76(x19092,x19091,x19093)+E(x19091,f2(a1))+~P75(f25(x19092,f103(x19093,x19091,x19092)))+~P75(f25(x19092,f104(x19093,x19091,x19092)))
% 3.00/2.89 [1914]P76(x19141,x19142,x19143)+~P75(f25(x19141,f103(x19143,x19142,x19141)))+~P75(f25(x19141,f104(x19143,x19142,x19141)))+~P75(f25(x19141,f2(a1)))
% 3.00/2.89 [1915]P76(x19153,x19151,x19152)+E(x19151,f2(a1))+E(f12(a1,f25(f25(f11(a1),x19151),f103(x19152,x19151,x19153)),f102(x19152,x19151,x19153)),x19152)+~P75(f25(x19153,f104(x19152,x19151,x19153)))
% 3.00/2.89 [1916]P76(x19163,x19161,x19162)+E(x19161,f2(a1))+E(f12(a1,f25(f25(f11(a1),x19161),f104(x19162,x19161,x19163)),f106(x19162,x19161,x19163)),x19162)+~P75(f25(x19163,f103(x19162,x19161,x19163)))
% 3.00/2.89 [1924]P76(x19243,x19241,x19242)+E(f12(a1,f25(f25(f11(a1),x19241),f103(x19242,x19241,x19243)),f102(x19242,x19241,x19243)),x19242)+~P75(f25(x19243,f104(x19242,x19241,x19243)))+~P75(f25(x19243,f2(a1)))
% 3.00/2.89 [1925]P76(x19253,x19251,x19252)+E(f12(a1,f25(f25(f11(a1),x19251),f104(x19252,x19251,x19253)),f106(x19252,x19251,x19253)),x19252)+~P75(f25(x19253,f103(x19252,x19251,x19253)))+~P75(f25(x19253,f2(a1)))
% 3.00/2.89 [1926]P76(x19263,x19261,x19262)+E(x19261,f2(a1))+E(f12(a1,f25(f25(f11(a1),x19261),f104(x19262,x19261,x19263)),f106(x19262,x19261,x19263)),x19262)+E(f12(a1,f25(f25(f11(a1),x19261),f103(x19262,x19261,x19263)),f102(x19262,x19261,x19263)),x19262)
% 3.00/2.89 [1931]P76(x19313,x19311,x19312)+E(f12(a1,f25(f25(f11(a1),x19311),f104(x19312,x19311,x19313)),f106(x19312,x19311,x19313)),x19312)+E(f12(a1,f25(f25(f11(a1),x19311),f103(x19312,x19311,x19313)),f102(x19312,x19311,x19313)),x19312)+~P75(f25(x19313,f2(a1)))
% 3.00/2.89 [949]~P61(x9492)+E(x9491,f2(x9492))+E(x9493,f2(x9492))+~E(f25(f25(f11(x9492),x9493),x9491),f2(x9492))
% 3.00/2.89 [951]~P62(x9512)+E(x9511,f2(x9512))+E(x9513,f2(x9512))+~E(f25(f25(f11(x9512),x9513),x9511),f2(x9512))
% 3.00/2.89 [1496]~P50(x14961)+~P3(x14961,f3(x14961),x14962)+~P3(a109,f2(a109),x14963)+P3(x14961,f3(x14961),f25(f25(f22(x14961),x14962),x14963))
% 3.00/2.89 [1511]~P55(x15111)+~P2(x15111,x15113,f2(x15111))+~P2(x15111,x15112,f2(x15111))+P2(x15111,f2(x15111),f25(f25(f11(x15111),x15112),x15113))
% 3.00/2.89 [1513]~P64(x15131)+~P2(x15131,x15133,f2(x15131))+~P2(x15131,x15132,f2(x15131))+P2(x15131,f2(x15131),f25(f25(f11(x15131),x15132),x15133))
% 3.00/2.89 [1514]~P55(x15141)+~P3(x15141,x15143,f2(x15141))+~P3(x15141,x15142,f2(x15141))+P3(x15141,f2(x15141),f25(f25(f11(x15141),x15142),x15143))
% 3.00/2.89 [1515]~P55(x15151)+~P2(x15151,f2(x15151),x15153)+~P2(x15151,f2(x15151),x15152)+P2(x15151,f2(x15151),f25(f25(f11(x15151),x15152),x15153))
% 3.00/2.89 [1516]~P63(x15161)+~P2(x15161,f2(x15161),x15163)+~P2(x15161,f2(x15161),x15162)+P2(x15161,f2(x15161),f25(f25(f11(x15161),x15162),x15163))
% 3.00/2.89 [1517]~P64(x15171)+~P2(x15171,f2(x15171),x15173)+~P2(x15171,f2(x15171),x15172)+P2(x15171,f2(x15171),f25(f25(f11(x15171),x15172),x15173))
% 3.00/2.89 [1518]~P50(x15181)+~P3(x15181,f3(x15181),x15183)+~P3(x15181,f3(x15181),x15182)+P3(x15181,f3(x15181),f25(f25(f11(x15181),x15182),x15183))
% 3.00/2.89 [1519]~P57(x15191)+~P3(x15191,f2(x15191),x15193)+~P3(x15191,f2(x15191),x15192)+P3(x15191,f2(x15191),f25(f25(f11(x15191),x15192),x15193))
% 3.00/2.89 [1521]~P55(x15211)+~P2(x15211,x15213,f2(x15211))+~P2(x15211,f2(x15211),x15212)+P2(x15211,f25(f25(f11(x15211),x15212),x15213),f2(x15211))
% 3.00/2.89 [1522]~P55(x15221)+~P2(x15221,x15222,f2(x15221))+~P2(x15221,f2(x15221),x15223)+P2(x15221,f25(f25(f11(x15221),x15222),x15223),f2(x15221))
% 3.00/2.89 [1524]~P63(x15241)+~P2(x15241,x15243,f2(x15241))+~P2(x15241,f2(x15241),x15242)+P2(x15241,f25(f25(f11(x15241),x15242),x15243),f2(x15241))
% 3.00/2.89 [1526]~P63(x15261)+~P2(x15261,x15262,f2(x15261))+~P2(x15261,f2(x15261),x15263)+P2(x15261,f25(f25(f11(x15261),x15262),x15263),f2(x15261))
% 3.00/2.89 [1528]~P57(x15281)+~P3(x15281,x15283,f2(x15281))+~P3(x15281,f2(x15281),x15282)+P3(x15281,f25(f25(f11(x15281),x15282),x15283),f2(x15281))
% 3.00/2.89 [1529]~P57(x15291)+~P3(x15291,x15292,f2(x15291))+~P3(x15291,f2(x15291),x15293)+P3(x15291,f25(f25(f11(x15291),x15292),x15293),f2(x15291))
% 3.00/2.89 [1554]~P55(x15541)+P2(x15541,x15542,f2(x15541))+P2(x15541,x15543,f2(x15541))+~P2(x15541,f25(f25(f11(x15541),x15543),x15542),f2(x15541))
% 3.00/2.89 [1555]~P55(x15551)+P2(x15551,x15552,f2(x15551))+P2(x15551,f2(x15551),x15553)+~P2(x15551,f2(x15551),f25(f25(f11(x15551),x15553),x15552))
% 3.00/2.89 [1556]~P55(x15561)+P2(x15561,x15562,f2(x15561))+P2(x15561,f2(x15561),x15563)+~P2(x15561,f2(x15561),f25(f25(f11(x15561),x15562),x15563))
% 3.00/2.89 [1557]~P55(x15571)+P2(x15571,f2(x15571),x15572)+P2(x15571,x15572,f2(x15571))+~P2(x15571,f2(x15571),f25(f25(f11(x15571),x15573),x15572))
% 3.00/2.89 [1558]~P55(x15581)+P2(x15581,f2(x15581),x15582)+P2(x15581,x15582,f2(x15581))+~P2(x15581,f2(x15581),f25(f25(f11(x15581),x15582),x15583))
% 3.00/2.89 [1559]~P55(x15591)+P2(x15591,f2(x15591),x15592)+P2(x15591,x15592,f2(x15591))+~P2(x15591,f25(f25(f11(x15591),x15593),x15592),f2(x15591))
% 3.00/2.89 [1560]~P55(x15601)+P2(x15601,f2(x15601),x15602)+P2(x15601,x15602,f2(x15601))+~P2(x15601,f25(f25(f11(x15601),x15602),x15603),f2(x15601))
% 3.00/2.89 [1561]~P55(x15611)+P2(x15611,f2(x15611),x15612)+P2(x15611,f2(x15611),x15613)+~P2(x15611,f25(f25(f11(x15611),x15612),x15613),f2(x15611))
% 3.00/2.89 [1608]~P57(x16081)+P3(x16081,f2(x16081),x16082)+~P3(x16081,f2(x16081),x16083)+~P3(x16081,f2(x16081),f25(f25(f11(x16081),x16083),x16082))
% 3.00/2.89 [1609]~P57(x16091)+P3(x16091,f2(x16091),x16092)+~P3(x16091,f2(x16091),x16093)+~P3(x16091,f2(x16091),f25(f25(f11(x16091),x16092),x16093))
% 3.00/2.89 [1808]~P50(x18081)+~P2(x18081,x18082,f3(x18081))+~P2(x18081,f2(x18081),x18082)+P2(x18081,f25(f25(f22(x18081),x18082),f12(a109,x18083,f3(a109))),x18082)
% 3.00/2.89 [1814]~P50(x18141)+~P3(x18141,x18142,f3(x18141))+~P3(x18141,f2(x18141),x18142)+P3(x18141,f25(f25(f22(x18141),x18142),f12(a109,x18143,f3(a109))),f3(x18141))
% 3.00/2.89 [1923]E(x19231,f8(a109,x19232,x19233))+~P3(a109,f2(a109),x19233)+~P2(a109,f25(f25(f11(a109),x19233),x19231),x19232)+~P3(a109,x19232,f25(f25(f11(a109),x19233),f12(a109,x19231,f3(a109))))
% 3.00/2.89 [1927]~P40(x19271)+P7(x19271,x19272)+~P3(a110,f2(a110),x19273)+~P2(a110,f26(x19271,f25(x19272,f78(x19272,x19271,x19273))),x19273)
% 3.00/2.89 [1928]~P40(x19281)+P7(x19281,x19282)+~P3(a110,f2(a110),x19283)+~P2(a110,f26(x19281,f25(x19282,f80(x19282,x19283,x19281))),x19283)
% 3.00/2.89 [1351]~P55(x13511)+~E(x13513,f2(x13511))+~E(x13512,f2(x13511))+E(f12(x13511,f25(f25(f11(x13511),x13512),x13512),f25(f25(f11(x13511),x13513),x13513)),f2(x13511))
% 3.00/2.89 [1639]~P67(x16391)+~P2(x16391,x16392,f2(x16391))+~P2(x16391,x16393,f2(x16391))+E(f25(f25(f11(x16391),f7(x16391,x16392)),f7(x16391,x16393)),f7(x16391,f25(f25(f11(x16391),x16392),x16393)))
% 3.00/2.89 [1640]~P67(x16401)+~P2(x16401,x16402,f2(x16401))+~P2(x16401,f2(x16401),x16403)+E(f25(f25(f11(x16401),f7(x16401,x16402)),f7(x16401,x16403)),f7(x16401,f25(f25(f11(x16401),x16402),x16403)))
% 3.00/2.89 [1641]~P67(x16411)+~P2(x16411,x16413,f2(x16411))+~P2(x16411,f2(x16411),x16412)+E(f25(f25(f11(x16411),f7(x16411,x16412)),f7(x16411,x16413)),f7(x16411,f25(f25(f11(x16411),x16412),x16413)))
% 3.00/2.89 [1642]~P67(x16421)+~P2(x16421,f2(x16421),x16422)+~P2(x16421,f2(x16421),x16423)+E(f25(f25(f11(x16421),f7(x16421,x16422)),f7(x16421,x16423)),f7(x16421,f25(f25(f11(x16421),x16422),x16423)))
% 3.00/2.89 [1679]~P3(a1,x16792,x16793)+~P3(a1,f2(a1),x16793)+P2(a1,f3(a1),x16791)+~E(f12(a1,x16792,f25(f25(f11(a1),x16793),x16791)),x16793)
% 3.00/2.89 [1683]~P2(a1,f2(a1),x16832)+~P3(a1,f2(a1),x16833)+P2(a1,x16831,f3(a1))+~E(f12(a1,x16832,f25(f25(f11(a1),x16833),x16831)),x16833)
% 3.00/2.89 [1819]~P55(x18191)+~E(x18193,f2(x18191))+~E(x18192,f2(x18191))+P2(x18191,f12(x18191,f25(f25(f11(x18191),x18192),x18192),f25(f25(f11(x18191),x18193),x18193)),f2(x18191))
% 3.00/2.89 [1858]~P50(x18581)+~P3(x18581,x18582,f3(x18581))+~P3(x18581,f2(x18581),x18582)+P3(x18581,f25(f25(f11(x18581),x18582),f25(f25(f22(x18581),x18582),x18583)),f25(f25(f22(x18581),x18582),x18583))
% 3.00/2.89 [1894]~P3(a1,x18942,x18943)+~P3(a1,f2(a1),x18943)+P2(a1,f2(a1),x18941)+~P2(a1,f2(a1),f12(a1,f25(f25(f11(a1),x18943),x18941),x18942))
% 3.00/2.89 [1896]P2(a1,x18961,f2(a1))+~P2(a1,f2(a1),x18962)+~P3(a1,f2(a1),x18963)+~P3(a1,f12(a1,f25(f25(f11(a1),x18963),x18961),x18962),f2(a1))
% 3.00/2.89 [1922]~P55(x19222)+~E(x19221,f2(x19222))+~E(x19223,f2(x19222))+~P3(x19222,f2(x19222),f12(x19222,f25(f25(f11(x19222),x19223),x19223),f25(f25(f11(x19222),x19221),x19221)))
% 3.00/2.89 [1222]~P38(x12221)+~P2(x12221,x12224,x12223)+P2(x12221,x12222,x12223)+~P2(x12221,x12222,x12224)
% 3.00/2.89 [1223]~P9(x12231)+~P2(x12231,x12232,x12234)+P2(x12231,x12232,x12233)+~P2(x12231,x12234,x12233)
% 3.00/2.89 [1224]~P38(x12241)+~P3(x12241,x12244,x12243)+P3(x12241,x12242,x12243)+~P2(x12241,x12242,x12244)
% 3.00/2.89 [1225]~P38(x12251)+~P3(x12251,x12252,x12254)+P3(x12251,x12252,x12253)+~P2(x12251,x12254,x12253)
% 3.00/2.89 [1226]~P38(x12261)+~P3(x12261,x12264,x12263)+P3(x12261,x12262,x12263)+~P3(x12261,x12262,x12264)
% 3.00/2.89 [1227]~P9(x12271)+~P3(x12271,x12272,x12274)+P3(x12271,x12272,x12273)+~P2(x12271,x12274,x12273)
% 3.00/2.89 [1228]~P9(x12281)+~P3(x12281,x12284,x12283)+P3(x12281,x12282,x12283)+~P2(x12281,x12282,x12284)
% 3.00/2.89 [1229]~P9(x12291)+~P3(x12291,x12292,x12294)+P3(x12291,x12292,x12293)+~P3(x12291,x12294,x12293)
% 3.00/2.89 [1193]~P38(x11931)+~P6(x11931,x11932)+~P2(a109,x11934,x11933)+P2(x11931,f25(x11932,x11933),f25(x11932,x11934))
% 3.00/2.89 [1194]~P38(x11941)+~P8(x11941,x11942)+~P2(a109,x11943,x11944)+P2(x11941,f25(x11942,x11943),f25(x11942,x11944))
% 3.00/2.89 [1359]~P37(x13592)+P3(f114(x13591,x13592),x13594,x13593)+~P2(f114(x13591,x13592),x13594,x13593)+P2(f114(x13591,x13592),x13593,x13594)
% 3.00/2.89 [1483]~P31(x14831)+~P2(x14831,x14832,x14833)+~P2(x14831,f2(x14831),x14834)+P2(x14831,x14832,f12(x14831,x14833,x14834))
% 3.00/2.89 [1484]~P31(x14841)+~P2(x14841,x14842,x14844)+~P2(x14841,f2(x14841),x14843)+P2(x14841,x14842,f12(x14841,x14843,x14844))
% 3.00/2.89 [1485]~P31(x14851)+~P2(x14851,x14852,x14854)+~P3(x14851,f2(x14851),x14853)+P3(x14851,x14852,f12(x14851,x14853,x14854))
% 3.00/2.89 [1486]~P31(x14861)+~P3(x14861,x14862,x14864)+~P2(x14861,f2(x14861),x14863)+P3(x14861,x14862,f12(x14861,x14863,x14864))
% 3.00/2.89 [1487]~P50(x14871)+~P3(x14871,x14872,x14874)+~P3(x14871,f2(x14871),x14873)+P3(x14871,x14872,f12(x14871,x14873,x14874))
% 3.00/2.89 [1671]~P40(x16712)+E(x16711,f2(x16712))+~P2(a110,x16713,f2(a110))+~P2(a110,f26(x16712,x16711),f25(f25(f11(a110),x16713),f26(x16712,x16714)))
% 3.00/2.89 [1906]~P51(x19061)+~P3(x19061,x19062,f12(x19061,x19063,x19064))+~P3(x19061,f10(x19061,x19063,x19064),x19062)+P3(x19061,f7(x19061,f10(x19061,x19062,x19063)),x19064)
% 3.00/2.89 [1910]~P3(a110,x19104,x19102)+P2(a110,x19101,x19102)+~P3(a110,x19103,x19104)+~P3(a110,f7(a110,f10(a110,x19104,x19101)),f59(x19102,x19104,x19103))
% 3.00/2.89 [1911]~P3(a110,x19111,x19113)+P2(a110,x19111,x19112)+~P3(a110,x19113,x19114)+~P3(a110,f7(a110,f10(a110,x19113,x19112)),f59(x19114,x19113,x19111))
% 3.00/2.89 [1327]~P50(x13273)+E(x13271,x13272)+~P3(x13273,f3(x13273),x13274)+~E(f25(f25(f22(x13273),x13274),x13271),f25(f25(f22(x13273),x13274),x13272))
% 3.00/2.89 [1643]~P50(x16431)+~P2(a109,x16433,x16434)+~P3(x16431,f3(x16431),x16432)+P2(x16431,f25(f25(f22(x16431),x16432),x16433),f25(f25(f22(x16431),x16432),x16434))
% 3.00/2.89 [1644]~P50(x16441)+~P2(a109,x16443,x16444)+~P2(x16441,f3(x16441),x16442)+P2(x16441,f25(f25(f22(x16441),x16442),x16443),f25(f25(f22(x16441),x16442),x16444))
% 3.00/2.89 [1646]~P50(x16461)+~P3(a109,x16463,x16464)+~P3(x16461,f3(x16461),x16462)+P3(x16461,f25(f25(f22(x16461),x16462),x16463),f25(f25(f22(x16461),x16462),x16464))
% 3.00/2.89 [1652]~P55(x16521)+~P2(x16521,x16524,x16523)+~P3(x16521,x16522,f2(x16521))+P2(x16521,f25(f25(f11(x16521),x16522),x16523),f25(f25(f11(x16521),x16522),x16524))
% 3.00/2.89 [1653]~P64(x16531)+~P2(x16531,x16534,x16533)+~P2(x16531,x16532,f2(x16531))+P2(x16531,f25(f25(f11(x16531),x16532),x16533),f25(f25(f11(x16531),x16532),x16534))
% 3.00/2.89 [1654]~P64(x16541)+~P2(x16541,x16544,x16542)+~P2(x16541,x16543,f2(x16541))+P2(x16541,f25(f25(f11(x16541),x16542),x16543),f25(f25(f11(x16541),x16544),x16543))
% 3.00/2.89 [1658]~P55(x16581)+~P3(x16581,x16584,x16582)+~P3(x16581,x16583,f2(x16581))+P3(x16581,f25(f25(f11(x16581),x16582),x16583),f25(f25(f11(x16581),x16584),x16583))
% 3.00/2.89 [1659]~P55(x16591)+~P3(x16591,x16594,x16593)+~P3(x16591,x16592,f2(x16591))+P3(x16591,f25(f25(f11(x16591),x16592),x16593),f25(f25(f11(x16591),x16592),x16594))
% 3.00/2.89 [1660]~P55(x16601)+~P2(x16601,x16603,x16604)+~P3(x16601,f2(x16601),x16602)+P2(x16601,f25(f25(f11(x16601),x16602),x16603),f25(f25(f11(x16601),x16602),x16604))
% 3.00/2.89 [1661]~P66(x16611)+~P2(x16611,x16613,x16614)+~P2(x16611,f2(x16611),x16612)+P2(x16611,f25(f25(f11(x16611),x16612),x16613),f25(f25(f11(x16611),x16612),x16614))
% 3.00/2.89 [1662]~P65(x16621)+~P2(x16621,x16623,x16624)+~P2(x16621,f2(x16621),x16622)+P2(x16621,f25(f25(f11(x16621),x16622),x16623),f25(f25(f11(x16621),x16622),x16624))
% 3.00/2.89 [1663]~P66(x16631)+~P2(x16631,x16632,x16634)+~P2(x16631,f2(x16631),x16633)+P2(x16631,f25(f25(f11(x16631),x16632),x16633),f25(f25(f11(x16631),x16634),x16633))
% 3.00/2.89 [1664]~P50(x16641)+~P2(x16641,x16642,x16644)+~P2(x16641,f2(x16641),x16642)+P2(x16641,f25(f25(f22(x16641),x16642),x16643),f25(f25(f22(x16641),x16644),x16643))
% 3.00/2.89 [1666]~P57(x16661)+~P3(x16661,x16663,x16664)+~P3(x16661,f2(x16661),x16662)+P3(x16661,f25(f25(f11(x16661),x16662),x16663),f25(f25(f11(x16661),x16662),x16664))
% 3.00/2.89 [1667]~P52(x16671)+~P3(x16671,x16673,x16674)+~P3(x16671,f2(x16671),x16672)+P3(x16671,f25(f25(f11(x16671),x16672),x16673),f25(f25(f11(x16671),x16672),x16674))
% 3.00/2.89 [1668]~P55(x16681)+~P3(x16681,x16682,x16684)+~P3(x16681,f2(x16681),x16683)+P3(x16681,f25(f25(f11(x16681),x16682),x16683),f25(f25(f11(x16681),x16684),x16683))
% 3.00/2.89 [1669]~P57(x16691)+~P3(x16691,x16692,x16694)+~P3(x16691,f2(x16691),x16693)+P3(x16691,f25(f25(f11(x16691),x16692),x16693),f25(f25(f11(x16691),x16694),x16693))
% 3.00/2.89 [1670]~P55(x16701)+~P3(x16701,x16703,x16704)+~P3(x16701,f2(x16701),x16702)+P3(x16701,f25(f25(f11(x16701),x16702),x16703),f25(f25(f11(x16701),x16702),x16704))
% 3.00/2.89 [1743]P3(x17431,x17433,x17432)+~P55(x17431)+P3(x17431,x17432,x17433)+~P3(x17431,f25(f25(f11(x17431),x17434),x17432),f25(f25(f11(x17431),x17434),x17433))
% 3.00/2.89 [1744]P3(x17441,x17443,x17442)+~P55(x17441)+P3(x17441,x17442,x17443)+~P3(x17441,f25(f25(f11(x17441),x17442),x17444),f25(f25(f11(x17441),x17443),x17444))
% 3.00/2.89 [1749]~P55(x17491)+P3(x17491,x17492,x17493)+P3(x17491,x17494,f2(x17491))+~P3(x17491,f25(f25(f11(x17491),x17492),x17494),f25(f25(f11(x17491),x17493),x17494))
% 3.00/2.89 [1750]~P55(x17501)+P3(x17501,x17502,x17503)+P3(x17501,x17504,f2(x17501))+~P3(x17501,f25(f25(f11(x17501),x17504),x17502),f25(f25(f11(x17501),x17504),x17503))
% 3.00/2.89 [1751]~P55(x17511)+P3(x17511,x17512,x17513)+P3(x17511,f2(x17511),x17514)+~P3(x17511,f25(f25(f11(x17511),x17514),x17513),f25(f25(f11(x17511),x17514),x17512))
% 3.00/2.89 [1752]~P55(x17521)+P3(x17521,x17522,x17523)+P3(x17521,f2(x17521),x17524)+~P3(x17521,f25(f25(f11(x17521),x17523),x17524),f25(f25(f11(x17521),x17522),x17524))
% 3.00/2.89 [1768]~P55(x17681)+P3(x17681,f2(x17681),x17682)+P3(x17681,x17682,f2(x17681))+~P3(x17681,f25(f25(f11(x17681),x17683),x17682),f25(f25(f11(x17681),x17684),x17682))
% 3.00/2.89 [1769]~P55(x17691)+P3(x17691,f2(x17691),x17692)+P3(x17691,x17692,f2(x17691))+~P3(x17691,f25(f25(f11(x17691),x17692),x17693),f25(f25(f11(x17691),x17692),x17694))
% 3.00/2.89 [1789]~P50(x17893)+P2(a109,x17891,x17892)+~P3(x17893,f3(x17893),x17894)+~P2(x17893,f25(f25(f22(x17893),x17894),x17891),f25(f25(f22(x17893),x17894),x17892))
% 3.00/2.89 [1791]~P50(x17913)+P3(a109,x17911,x17912)+~P3(x17913,f3(x17913),x17914)+~P3(x17913,f25(f25(f22(x17913),x17914),x17911),f25(f25(f22(x17913),x17914),x17912))
% 3.00/2.89 [1795]~P55(x17951)+P2(x17951,x17952,x17953)+~P3(x17951,x17954,f2(x17951))+~P2(x17951,f25(f25(f11(x17951),x17954),x17953),f25(f25(f11(x17951),x17954),x17952))
% 3.00/2.89 [1796]~P55(x17961)+P3(x17961,x17962,x17963)+~P3(x17961,x17964,f2(x17961))+~P3(x17961,f25(f25(f11(x17961),x17964),x17963),f25(f25(f11(x17961),x17964),x17962))
% 3.00/2.89 [1797]~P55(x17971)+P2(x17971,x17972,x17973)+~P3(x17971,f2(x17971),x17974)+~P2(x17971,f25(f25(f11(x17971),x17974),x17972),f25(f25(f11(x17971),x17974),x17973))
% 3.00/2.89 [1798]~P57(x17981)+P2(x17981,x17982,x17983)+~P3(x17981,f2(x17981),x17984)+~P2(x17981,f25(f25(f11(x17981),x17984),x17982),f25(f25(f11(x17981),x17984),x17983))
% 3.00/2.89 [1799]~P57(x17991)+P2(x17991,x17992,x17993)+~P3(x17991,f2(x17991),x17994)+~P2(x17991,f25(f25(f11(x17991),x17992),x17994),f25(f25(f11(x17991),x17993),x17994))
% 3.00/2.89 [1800]~P55(x18001)+P3(x18001,x18002,x18003)+~P3(x18001,f2(x18001),x18004)+~P3(x18001,f25(f25(f11(x18001),x18004),x18002),f25(f25(f11(x18001),x18004),x18003))
% 3.00/2.89 [1801]~P57(x18011)+P3(x18011,x18012,x18013)+~P2(x18011,f2(x18011),x18014)+~P3(x18011,f25(f25(f11(x18011),x18014),x18012),f25(f25(f11(x18011),x18014),x18013))
% 3.00/2.89 [1802]~P58(x18021)+P3(x18021,x18022,x18023)+~P2(x18021,f2(x18021),x18024)+~P3(x18021,f25(f25(f11(x18021),x18024),x18022),f25(f25(f11(x18021),x18024),x18023))
% 3.00/2.89 [1803]~P50(x18031)+P3(x18031,x18032,x18033)+~P2(x18031,f2(x18031),x18033)+~P3(x18031,f25(f25(f22(x18031),x18032),x18034),f25(f25(f22(x18031),x18033),x18034))
% 3.00/2.89 [1804]~P57(x18041)+P3(x18041,x18042,x18043)+~P2(x18041,f2(x18041),x18044)+~P3(x18041,f25(f25(f11(x18041),x18042),x18044),f25(f25(f11(x18041),x18043),x18044))
% 3.00/2.89 [1805]~P58(x18051)+P3(x18051,x18052,x18053)+~P2(x18051,f2(x18051),x18054)+~P3(x18051,f25(f25(f11(x18051),x18052),x18054),f25(f25(f11(x18051),x18053),x18054))
% 3.00/2.89 [1870]~P38(x18701)+~P5(x18701,x18702)+P2(x18701,f25(x18702,x18703),f25(x18702,f12(a109,x18703,f3(a109))))+P2(x18701,f25(x18702,f12(a109,x18704,f3(a109))),f25(x18702,x18704))
% 3.00/2.89 [1936]~P75(f25(x19361,x19364))+~P2(a109,f25(f25(f11(a109),x19363),x19364),x19362)+~P3(a109,x19362,f25(f25(f11(a109),x19363),f12(a109,x19364,f3(a109))))+P75(f25(x19361,f8(a109,x19362,x19363)))
% 3.00/2.89 [1953]~P50(x19531)+P2(x19531,x19532,x19533)+~P2(x19531,f2(x19531),x19533)+~P2(x19531,f25(f25(f22(x19531),x19532),f12(a109,x19534,f3(a109))),f25(f25(f22(x19531),x19533),f12(a109,x19534,f3(a109))))
% 3.00/2.89 [1969]~P40(x19691)+~P3(a110,f2(a110),x19694)+~P2(a110,f26(x19691,f25(x19692,f67(x19692,x19691,x19694))),x19694)+P2(a110,f26(x19691,f25(x19692,x19693)),f25(f16(a109),f12(a109,f66(x19692,x19691),f3(a109))))
% 3.00/2.89 [1970]~P40(x19701)+~P3(a110,f2(a110),x19704)+~P2(a110,f26(x19701,f25(x19702,f71(x19702,x19701,x19704))),x19704)+P3(a110,f26(x19701,f25(x19702,x19703)),f25(f16(a109),f12(a109,f70(x19702,x19701),f3(a109))))
% 3.00/2.89 [2002]~P38(x20021)+~P2(a109,x20023,x20024)+P2(x20021,f25(x20022,x20023),f25(x20022,x20024))+~P2(x20021,f25(x20022,f86(x20024,x20023,x20022,x20021)),f25(x20022,f12(a109,f86(x20024,x20023,x20022,x20021),f3(a109))))
% 3.00/2.89 [1133]~P15(x11335)+E(x11331,x11332)+~E(x11333,x11334)+~E(f10(x11335,x11333,x11334),f10(x11335,x11331,x11332))
% 3.00/2.89 [1407]~P27(x14071)+~P2(x14071,x14074,x14075)+P2(x14071,x14072,x14073)+~E(f10(x14071,x14074,x14075),f10(x14071,x14072,x14073))
% 3.00/2.89 [1409]~P27(x14091)+~P3(x14091,x14094,x14095)+P3(x14091,x14092,x14093)+~E(f10(x14091,x14094,x14095),f10(x14091,x14092,x14093))
% 3.00/2.89 [1647]~P11(x16471)+~P2(x16471,x16473,x16475)+~P2(x16471,x16472,x16474)+P2(x16471,f12(x16471,x16472,x16473),f12(x16471,x16474,x16475))
% 3.00/2.89 [1648]~P32(x16481)+~P2(x16481,x16483,x16485)+~P3(x16481,x16482,x16484)+P3(x16481,f12(x16481,x16482,x16483),f12(x16481,x16484,x16485))
% 3.00/2.89 [1649]~P32(x16491)+~P2(x16491,x16492,x16494)+~P3(x16491,x16493,x16495)+P3(x16491,f12(x16491,x16492,x16493),f12(x16491,x16494,x16495))
% 3.00/2.89 [1650]~P32(x16501)+~P3(x16501,x16503,x16505)+~P3(x16501,x16502,x16504)+P3(x16501,f12(x16501,x16502,x16503),f12(x16501,x16504,x16505))
% 3.00/2.89 [1849]~P40(x18491)+~P3(a110,f26(x18491,x18493),x18495)+~P3(a110,f26(x18491,x18492),x18494)+P3(a110,f26(x18491,f12(x18491,x18492,x18493)),f12(a110,x18494,x18495))
% 3.00/2.89 [1866]~P51(x18661)+~P3(x18661,f7(x18661,x18662),x18664)+~P3(x18661,f7(x18661,x18663),x18665)+P3(x18661,f25(f25(f11(x18661),f7(x18661,x18662)),f7(x18661,x18663)),f25(f25(f11(x18661),x18664),x18665))
% 3.00/2.89 [1834]~P42(x18341)+~P3(a110,f26(x18341,x18343),x18345)+~P3(a110,f26(x18341,x18342),x18344)+P3(a110,f26(x18341,f25(f25(f11(x18341),x18342),x18343)),f25(f25(f11(a110),x18344),x18345))
% 3.00/2.89 [1908]~P73(x19085)+E(x19081,x19082)+E(x19083,x19084)+~E(f12(x19085,f25(f25(f11(x19085),x19083),x19081),f25(f25(f11(x19085),x19084),x19082)),f12(x19085,f25(f25(f11(x19085),x19083),x19082),f25(f25(f11(x19085),x19084),x19081)))
% 3.00/2.89 [1944]~E(f26(a15,x19441),f3(a110))+P3(a110,f26(a15,f10(a15,x19441,a6)),f3(a110))+P3(a110,f26(a15,f12(a15,x19441,a6)),f3(a110))+P3(a110,f26(a15,f12(a15,x19441,f3(a15))),f3(a110))+P3(a110,f26(a15,f10(a15,x19441,f3(a15))),f3(a110))
% 3.00/2.89 [1360]~P31(x13602)+~P2(x13602,f2(x13602),x13603)+~P2(x13602,f2(x13602),x13601)+~E(f12(x13602,x13603,x13601),f2(x13602))+E(x13601,f2(x13602))
% 3.00/2.89 [1361]~P31(x13612)+~P2(x13612,f2(x13612),x13613)+~P2(x13612,f2(x13612),x13611)+~E(f12(x13612,x13611,x13613),f2(x13612))+E(x13611,f2(x13612))
% 3.00/2.89 [1497]E(x14971,f95(x14972,x14973))+~P3(a109,f2(a109),x14973)+~P3(a110,f2(a110),x14972)+~P3(a110,f2(a110),x14971)+~E(f25(f25(f22(a110),x14971),x14973),x14972)
% 3.00/2.89 [1672]~P51(x16721)+~P2(x16721,x16722,f3(x16721))+~P2(x16721,f2(x16721),x16722)+~P2(x16721,f2(x16721),x16723)+P2(x16721,f25(f25(f11(x16721),x16722),x16723),x16723)
% 3.00/2.89 [1673]~P51(x16731)+~P2(x16731,x16733,f3(x16731))+~P2(x16731,f2(x16731),x16733)+~P2(x16731,f2(x16731),x16732)+P2(x16731,f25(f25(f11(x16731),x16732),x16733),x16732)
% 3.00/2.89 [1772]~P50(x17721)+~P3(x17721,x17722,x17724)+~P2(x17721,f2(x17721),x17722)+~P3(a109,f2(a109),x17723)+P3(x17721,f25(f25(f22(x17721),x17722),x17723),f25(f25(f22(x17721),x17724),x17723))
% 3.00/2.89 [1775]~P50(x17751)+~P2(a109,x17754,x17753)+~P2(x17751,x17752,f3(x17751))+~P2(x17751,f2(x17751),x17752)+P2(x17751,f25(f25(f22(x17751),x17752),x17753),f25(f25(f22(x17751),x17752),x17754))
% 3.00/2.89 [1776]~P50(x17761)+~P3(a109,x17764,x17763)+~P3(x17761,x17762,f3(x17761))+~P3(x17761,f2(x17761),x17762)+P3(x17761,f25(f25(f22(x17761),x17762),x17763),f25(f25(f22(x17761),x17762),x17764))
% 3.00/2.89 [1880]~P50(x18803)+E(x18801,x18802)+~P2(x18803,f2(x18803),x18802)+~P2(x18803,f2(x18803),x18801)+~E(f25(f25(f22(x18803),x18801),f12(a109,x18804,f3(a109))),f25(f25(f22(x18803),x18802),f12(a109,x18804,f3(a109))))
% 3.00/2.89 [1934]~P2(a1,f2(a1),x19342)+~P3(a1,f2(a1),x19343)+~P75(f25(x19341,x19344))+P75(f25(x19341,f89(x19342,x19341,x19343)))+P75(f25(x19341,f10(a1,x19344,f25(f25(f11(a1),x19342),x19343))))
% 3.00/2.89 [1935]~P2(a1,f2(a1),x19352)+~P3(a1,f2(a1),x19353)+~P75(f25(x19351,x19354))+P75(f25(x19351,f90(x19352,x19351,x19353)))+P75(f25(x19351,f12(a1,x19354,f25(f25(f11(a1),x19352),x19353))))
% 3.00/2.89 [1974]~P2(a1,f2(a1),x19743)+~P3(a1,f2(a1),x19744)+~P75(f25(x19741,x19742))+~P75(f25(x19741,f12(a1,f90(x19743,x19741,x19744),x19744)))+P75(f25(x19741,f12(a1,x19742,f25(f25(f11(a1),x19743),x19744))))
% 3.00/2.89 [1975]~P2(a1,f2(a1),x19753)+~P3(a1,f2(a1),x19754)+~P75(f25(x19751,x19752))+~P75(f25(x19751,f10(a1,f89(x19753,x19751,x19754),x19754)))+P75(f25(x19751,f10(a1,x19752,f25(f25(f11(a1),x19753),x19754))))
% 3.00/2.89 [1932]~P37(x19321)+~P40(x19324)+~P2(x19321,x19322,x19325)+P2(x19321,x19322,f74(x19323,x19322,x19321,x19324))+P3(a110,f26(x19324,f25(x19323,x19325)),f12(a110,f3(a110),f26(x19324,f25(x19323,x19322))))
% 3.00/2.89 [1881]~P3(a109,x18815,x18811)+E(x18811,f2(a109))+P75(f25(x18812,x18813))+~P75(f25(x18812,f8(a109,x18814,x18811)))+~E(x18814,f12(a109,f25(f25(f11(a109),x18811),x18813),x18815))
% 3.00/2.89 [1954]P2(a1,x19541,x19542)+~P3(a1,x19543,x19544)+~P3(a1,x19543,x19545)+~P2(a1,x19544,f2(a1))+~P2(a1,f12(a1,f25(f25(f11(a1),x19543),x19542),x19545),f12(a1,f25(f25(f11(a1),x19543),x19541),x19544))
% 3.00/2.89 [1955]P2(a1,x19551,x19552)+~P3(a1,x19553,x19554)+~P3(a1,x19555,x19554)+~P2(a1,f2(a1),x19555)+~P2(a1,f12(a1,f25(f25(f11(a1),x19554),x19551),x19555),f12(a1,f25(f25(f11(a1),x19554),x19552),x19553))
% 3.00/2.89 [2003]~P40(x20031)+~P2(x20035,x20034,x20033)+~P37(x20035)+P3(a110,f26(x20031,f25(x20032,x20033)),f12(a110,f3(a110),f26(x20031,f25(x20032,x20034))))+~P3(a110,f26(x20031,f10(x20031,f25(x20032,x20034),f25(x20032,f74(x20032,x20034,x20035,x20031)))),f3(a110))
% 3.00/2.89 [1728]~P73(x17284)+E(x17281,x17282)+~E(x17285,x17286)+E(x17283,f2(x17284))+~E(f12(x17284,x17285,f25(f25(f11(x17284),x17283),x17281)),f12(x17284,x17286,f25(f25(f11(x17284),x17283),x17282)))
% 3.00/2.89 [1336]~P31(x13361)+~P2(x13361,f2(x13361),x13363)+~P2(x13361,f2(x13361),x13362)+~E(x13363,f2(x13361))+~E(x13362,f2(x13361))+E(f12(x13361,x13362,x13363),f2(x13361))
% 3.00/2.89 [985]~P74(x9852)+~P56(x9852)+~P62(x9852)+~P43(x9852)+E(x9851,f2(x9852))+~E(f25(f25(f22(x9852),x9851),x9853),f2(x9852))
% 3.00/2.89 [986]~P74(x9862)+~P56(x9862)+~P62(x9862)+~P43(x9862)+~E(x9861,f2(a109))+~E(f25(f25(f22(x9862),x9863),x9861),f2(x9862))
% 3.00/2.89 [1678]~P50(x16783)+E(x16781,x16782)+~P2(x16783,f2(x16783),x16782)+~P2(x16783,f2(x16783),x16781)+~P3(a109,f2(a109),x16784)+~E(f25(f25(f22(x16783),x16781),x16784),f25(f25(f22(x16783),x16782),x16784))
% 3.00/2.89 [1735]~P3(a1,x17351,x17354)+E(f8(a1,x17352,x17351),x17353)+E(x17351,f2(a1))+P3(a1,f2(a1),x17351)+~P2(a1,x17354,f2(a1))+~E(x17352,f12(a1,f25(f25(f11(a1),x17351),x17353),x17354))
% 3.00/2.89 [1780]~P3(a1,x17804,x17801)+E(f8(a1,x17802,x17801),x17803)+E(x17801,f2(a1))+~P2(a1,f2(a1),x17804)+~P3(a1,f2(a1),x17801)+~E(x17802,f12(a1,f25(f25(f11(a1),x17801),x17803),x17804))
% 3.00/2.89 [1835]~P66(x18351)+~P2(x18351,x18353,x18355)+~P2(x18351,x18352,x18354)+~P2(x18351,f2(x18351),x18353)+~P2(x18351,f2(x18351),x18354)+P2(x18351,f25(f25(f11(x18351),x18352),x18353),f25(f25(f11(x18351),x18354),x18355))
% 3.00/2.89 [1836]~P66(x18361)+~P2(x18361,x18363,x18365)+~P2(x18361,x18362,x18364)+~P2(x18361,f2(x18361),x18363)+~P2(x18361,f2(x18361),x18362)+P2(x18361,f25(f25(f11(x18361),x18362),x18363),f25(f25(f11(x18361),x18364),x18365))
% 3.00/2.89 [1837]~P57(x18371)+~P2(x18371,x18373,x18375)+~P3(x18371,x18372,x18374)+~P2(x18371,f2(x18371),x18372)+~P3(x18371,f2(x18371),x18373)+P3(x18371,f25(f25(f11(x18371),x18372),x18373),f25(f25(f11(x18371),x18374),x18375))
% 3.00/2.89 [1838]~P57(x18381)+~P2(x18381,x18382,x18384)+~P3(x18381,x18383,x18385)+~P2(x18381,f2(x18381),x18383)+~P3(x18381,f2(x18381),x18382)+P3(x18381,f25(f25(f11(x18381),x18382),x18383),f25(f25(f11(x18381),x18384),x18385))
% 3.00/2.89 [1839]~P57(x18391)+~P3(x18391,x18393,x18395)+~P3(x18391,x18392,x18394)+~P2(x18391,f2(x18391),x18393)+~P2(x18391,f2(x18391),x18392)+P3(x18391,f25(f25(f11(x18391),x18392),x18393),f25(f25(f11(x18391),x18394),x18395))
% 3.00/2.89 [1840]~P57(x18401)+~P3(x18401,x18403,x18405)+~P3(x18401,x18402,x18404)+~P2(x18401,f2(x18401),x18403)+~P3(x18401,f2(x18401),x18404)+P3(x18401,f25(f25(f11(x18401),x18402),x18403),f25(f25(f11(x18401),x18404),x18405))
% 3.00/2.89 [1822]~P76(x18221,x18224,x18223)+~P3(a1,x18224,x18225)+~P2(a1,x18225,f2(a1))+~P3(a1,x18224,f2(a1))+P75(f25(x18221,x18222))+~E(x18223,f12(a1,f25(f25(f11(a1),x18224),x18222),x18225))
% 3.00/2.89 [1823]~P76(x18231,x18234,x18233)+~P3(a1,x18235,x18234)+~P2(a1,f2(a1),x18235)+~P3(a1,f2(a1),x18234)+P75(f25(x18231,x18232))+~E(x18233,f12(a1,f25(f25(f11(a1),x18234),x18232),x18235))
% 3.00/2.89 [1598]~P38(x15981)+~P5(x15981,x15982)+~P2(a109,x15984,x15983)+~P2(a109,x15985,x15986)+P2(x15981,f25(x15982,x15983),f25(x15982,x15984))+P2(x15981,f25(x15982,x15985),f25(x15982,x15986))
% 3.00/2.89 [933]~P74(x9332)+~P56(x9332)+~P62(x9332)+~P43(x9332)+~E(x9333,f2(x9332))+E(x9331,f2(a109))+E(f25(f25(f22(x9332),x9333),x9331),f2(x9332))
% 3.00/2.89 [1833]~P3(a1,x18334,x18331)+~P3(a1,x18331,x18334)+E(f8(a1,x18332,x18331),x18333)+E(x18331,f2(a1))+~P2(a1,x18334,f2(a1))+~P2(a1,f2(a1),x18334)+~E(x18332,f12(a1,f25(f25(f11(a1),x18331),x18333),x18334))
% 3.00/2.89 [1929]~P59(x19291)+~P2(x19291,x19295,x19296)+~P2(x19291,x19293,x19296)+~P2(x19291,f2(x19291),x19294)+~P2(x19291,f2(x19291),x19292)+~E(f12(x19291,x19292,x19294),f3(x19291))+P2(x19291,f12(x19291,f25(f25(f11(x19291),x19292),x19293),f25(f25(f11(x19291),x19294),x19295)),x19296)
% 3.00/2.89 [1930]~P60(x19301)+~P3(x19301,x19305,x19306)+~P3(x19301,x19303,x19306)+~P2(x19301,f2(x19301),x19304)+~P2(x19301,f2(x19301),x19302)+~E(f12(x19301,x19302,x19304),f3(x19301))+P3(x19301,f12(x19301,f25(f25(f11(x19301),x19302),x19303),f25(f25(f11(x19301),x19304),x19305)),x19306)
% 3.00/2.89 [1965]~P2(a1,x19655,x19653)+~P3(a1,x19656,x19655)+P2(a1,x19651,x19652)+~P2(a1,f2(a1),x19654)+~P3(a1,f2(a1),x19655)+~P2(a1,f2(a1),f12(a1,f25(f25(f11(a1),x19655),x19652),x19656))+~E(f12(a1,f25(f25(f11(a1),x19653),x19651),x19654),f12(a1,f25(f25(f11(a1),x19655),x19652),x19656))
% 3.00/2.89 [1966]~P2(a1,x19665,x19663)+~P3(a1,x19664,x19663)+P2(a1,x19661,x19662)+~P2(a1,f2(a1),x19666)+~P3(a1,f2(a1),x19665)+~P3(a1,f12(a1,f25(f25(f11(a1),x19665),x19661),x19666),f2(a1))+~E(f12(a1,f25(f25(f11(a1),x19663),x19662),x19664),f12(a1,f25(f25(f11(a1),x19665),x19661),x19666))
% 3.00/2.89 %EqnAxiom
% 3.00/2.89 [1]E(x11,x11)
% 3.00/2.89 [2]E(x22,x21)+~E(x21,x22)
% 3.00/2.89 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 3.00/2.89 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 3.00/2.89 [5]~E(x51,x52)+E(f16(x51),f16(x52))
% 3.00/2.89 [6]~E(x61,x62)+E(f17(x61),f17(x62))
% 3.00/2.89 [7]~E(x71,x72)+E(f25(x71,x73),f25(x72,x73))
% 3.00/2.89 [8]~E(x81,x82)+E(f25(x83,x81),f25(x83,x82))
% 3.00/2.89 [9]~E(x91,x92)+E(f106(x91,x93,x94),f106(x92,x93,x94))
% 3.00/2.89 [10]~E(x101,x102)+E(f106(x103,x101,x104),f106(x103,x102,x104))
% 3.00/2.89 [11]~E(x111,x112)+E(f106(x113,x114,x111),f106(x113,x114,x112))
% 3.00/2.89 [12]~E(x121,x122)+E(f3(x121),f3(x122))
% 3.00/2.89 [13]~E(x131,x132)+E(f19(x131),f19(x132))
% 3.00/2.89 [14]~E(x141,x142)+E(f10(x141,x143,x144),f10(x142,x143,x144))
% 3.00/2.89 [15]~E(x151,x152)+E(f10(x153,x151,x154),f10(x153,x152,x154))
% 3.00/2.89 [16]~E(x161,x162)+E(f10(x163,x164,x161),f10(x163,x164,x162))
% 3.00/2.89 [17]~E(x171,x172)+E(f11(x171),f11(x172))
% 3.00/2.89 [18]~E(x181,x182)+E(f18(x181,x183),f18(x182,x183))
% 3.00/2.89 [19]~E(x191,x192)+E(f18(x193,x191),f18(x193,x192))
% 3.00/2.89 [20]~E(x201,x202)+E(f26(x201,x203),f26(x202,x203))
% 3.00/2.89 [21]~E(x211,x212)+E(f26(x213,x211),f26(x213,x212))
% 3.00/2.89 [22]~E(x221,x222)+E(f12(x221,x223,x224),f12(x222,x223,x224))
% 3.00/2.89 [23]~E(x231,x232)+E(f12(x233,x231,x234),f12(x233,x232,x234))
% 3.00/2.89 [24]~E(x241,x242)+E(f12(x243,x244,x241),f12(x243,x244,x242))
% 3.00/2.89 [25]~E(x251,x252)+E(f24(x251),f24(x252))
% 3.00/2.89 [26]~E(x261,x262)+E(f103(x261,x263,x264),f103(x262,x263,x264))
% 3.00/2.89 [27]~E(x271,x272)+E(f103(x273,x271,x274),f103(x273,x272,x274))
% 3.00/2.89 [28]~E(x281,x282)+E(f103(x283,x284,x281),f103(x283,x284,x282))
% 3.00/2.89 [29]~E(x291,x292)+E(f98(x291,x293),f98(x292,x293))
% 3.00/2.89 [30]~E(x301,x302)+E(f98(x303,x301),f98(x303,x302))
% 3.00/2.89 [31]~E(x311,x312)+E(f101(x311,x313,x314),f101(x312,x313,x314))
% 3.00/2.89 [32]~E(x321,x322)+E(f101(x323,x321,x324),f101(x323,x322,x324))
% 3.00/2.89 [33]~E(x331,x332)+E(f101(x333,x334,x331),f101(x333,x334,x332))
% 3.00/2.89 [34]~E(x341,x342)+E(f8(x341,x343,x344),f8(x342,x343,x344))
% 3.00/2.89 [35]~E(x351,x352)+E(f8(x353,x351,x354),f8(x353,x352,x354))
% 3.00/2.89 [36]~E(x361,x362)+E(f8(x363,x364,x361),f8(x363,x364,x362))
% 3.00/2.89 [37]~E(x371,x372)+E(f74(x371,x373,x374,x375),f74(x372,x373,x374,x375))
% 3.00/2.89 [38]~E(x381,x382)+E(f74(x383,x381,x384,x385),f74(x383,x382,x384,x385))
% 3.00/2.89 [39]~E(x391,x392)+E(f74(x393,x394,x391,x395),f74(x393,x394,x392,x395))
% 3.00/2.89 [40]~E(x401,x402)+E(f74(x403,x404,x405,x401),f74(x403,x404,x405,x402))
% 3.00/2.89 [41]~E(x411,x412)+E(f4(x411),f4(x412))
% 3.00/2.89 [42]~E(x421,x422)+E(f22(x421),f22(x422))
% 3.00/2.89 [43]~E(x431,x432)+E(f111(x431),f111(x432))
% 3.00/2.89 [44]~E(x441,x442)+E(f38(x441,x443),f38(x442,x443))
% 3.00/2.89 [45]~E(x451,x452)+E(f38(x453,x451),f38(x453,x452))
% 3.00/2.89 [46]~E(x461,x462)+E(f102(x461,x463,x464),f102(x462,x463,x464))
% 3.00/2.89 [47]~E(x471,x472)+E(f102(x473,x471,x474),f102(x473,x472,x474))
% 3.00/2.89 [48]~E(x481,x482)+E(f102(x483,x484,x481),f102(x483,x484,x482))
% 3.00/2.89 [49]~E(x491,x492)+E(f117(x491),f117(x492))
% 3.00/2.89 [50]~E(x501,x502)+E(f45(x501,x503),f45(x502,x503))
% 3.00/2.89 [51]~E(x511,x512)+E(f45(x513,x511),f45(x513,x512))
% 3.00/2.89 [52]~E(x521,x522)+E(f5(x521,x523),f5(x522,x523))
% 3.00/2.89 [53]~E(x531,x532)+E(f5(x533,x531),f5(x533,x532))
% 3.00/2.89 [54]~E(x541,x542)+E(f95(x541,x543),f95(x542,x543))
% 3.00/2.89 [55]~E(x551,x552)+E(f95(x553,x551),f95(x553,x552))
% 3.00/2.89 [56]~E(x561,x562)+E(f7(x561,x563),f7(x562,x563))
% 3.00/2.89 [57]~E(x571,x572)+E(f7(x573,x571),f7(x573,x572))
% 3.00/2.89 [58]~E(x581,x582)+E(f51(x581,x583),f51(x582,x583))
% 3.00/2.89 [59]~E(x591,x592)+E(f51(x593,x591),f51(x593,x592))
% 3.00/2.89 [60]~E(x601,x602)+E(f92(x601,x603),f92(x602,x603))
% 3.00/2.89 [61]~E(x611,x612)+E(f92(x613,x611),f92(x613,x612))
% 3.00/2.89 [62]~E(x621,x622)+E(f104(x621,x623,x624),f104(x622,x623,x624))
% 3.00/2.89 [63]~E(x631,x632)+E(f104(x633,x631,x634),f104(x633,x632,x634))
% 3.00/2.89 [64]~E(x641,x642)+E(f104(x643,x644,x641),f104(x643,x644,x642))
% 3.00/2.89 [65]~E(x651,x652)+E(f89(x651,x653,x654),f89(x652,x653,x654))
% 3.00/2.89 [66]~E(x661,x662)+E(f89(x663,x661,x664),f89(x663,x662,x664))
% 3.00/2.89 [67]~E(x671,x672)+E(f89(x673,x674,x671),f89(x673,x674,x672))
% 3.00/2.89 [68]~E(x681,x682)+E(f81(x681),f81(x682))
% 3.00/2.89 [69]~E(x691,x692)+E(f56(x691,x693),f56(x692,x693))
% 3.00/2.89 [70]~E(x701,x702)+E(f56(x703,x701),f56(x703,x702))
% 3.00/2.89 [71]~E(x711,x712)+E(f20(x711,x713),f20(x712,x713))
% 3.00/2.89 [72]~E(x721,x722)+E(f20(x723,x721),f20(x723,x722))
% 3.00/2.89 [73]~E(x731,x732)+E(f82(x731),f82(x732))
% 3.00/2.89 [74]~E(x741,x742)+E(f36(x741,x743),f36(x742,x743))
% 3.00/2.89 [75]~E(x751,x752)+E(f36(x753,x751),f36(x753,x752))
% 3.00/2.89 [76]~E(x761,x762)+E(f37(x761,x763),f37(x762,x763))
% 3.00/2.89 [77]~E(x771,x772)+E(f37(x773,x771),f37(x773,x772))
% 3.00/2.89 [78]~E(x781,x782)+E(f79(x781),f79(x782))
% 3.00/2.89 [79]~E(x791,x792)+E(f53(x791,x793),f53(x792,x793))
% 3.00/2.89 [80]~E(x801,x802)+E(f53(x803,x801),f53(x803,x802))
% 3.00/2.89 [81]~E(x811,x812)+E(f87(x811,x813),f87(x812,x813))
% 3.00/2.89 [82]~E(x821,x822)+E(f87(x823,x821),f87(x823,x822))
% 3.00/2.89 [83]~E(x831,x832)+E(f69(x831,x833,x834),f69(x832,x833,x834))
% 3.00/2.89 [84]~E(x841,x842)+E(f69(x843,x841,x844),f69(x843,x842,x844))
% 3.00/2.89 [85]~E(x851,x852)+E(f69(x853,x854,x851),f69(x853,x854,x852))
% 3.00/2.89 [86]~E(x861,x862)+E(f55(x861),f55(x862))
% 3.00/2.89 [87]~E(x871,x872)+E(f52(x871,x873),f52(x872,x873))
% 3.00/2.89 [88]~E(x881,x882)+E(f52(x883,x881),f52(x883,x882))
% 3.00/2.89 [89]~E(x891,x892)+E(f68(x891,x893),f68(x892,x893))
% 3.00/2.89 [90]~E(x901,x902)+E(f68(x903,x901),f68(x903,x902))
% 3.00/2.89 [91]~E(x911,x912)+E(f91(x911,x913),f91(x912,x913))
% 3.00/2.89 [92]~E(x921,x922)+E(f91(x923,x921),f91(x923,x922))
% 3.00/2.89 [93]~E(x931,x932)+E(f114(x931,x933),f114(x932,x933))
% 3.00/2.89 [94]~E(x941,x942)+E(f114(x943,x941),f114(x943,x942))
% 3.00/2.89 [95]~E(x951,x952)+E(f50(x951,x953),f50(x952,x953))
% 3.00/2.89 [96]~E(x961,x962)+E(f50(x963,x961),f50(x963,x962))
% 3.00/2.89 [97]~E(x971,x972)+E(f47(x971,x973,x974),f47(x972,x973,x974))
% 3.00/2.89 [98]~E(x981,x982)+E(f47(x983,x981,x984),f47(x983,x982,x984))
% 3.00/2.89 [99]~E(x991,x992)+E(f47(x993,x994,x991),f47(x993,x994,x992))
% 3.00/2.89 [100]~E(x1001,x1002)+E(f71(x1001,x1003,x1004),f71(x1002,x1003,x1004))
% 3.00/2.89 [101]~E(x1011,x1012)+E(f71(x1013,x1011,x1014),f71(x1013,x1012,x1014))
% 3.00/2.89 [102]~E(x1021,x1022)+E(f71(x1023,x1024,x1021),f71(x1023,x1024,x1022))
% 3.00/2.89 [103]~E(x1031,x1032)+E(f64(x1031,x1033),f64(x1032,x1033))
% 3.00/2.89 [104]~E(x1041,x1042)+E(f64(x1043,x1041),f64(x1043,x1042))
% 3.00/2.89 [105]~E(x1051,x1052)+E(f29(x1051),f29(x1052))
% 3.00/2.89 [106]~E(x1061,x1062)+E(f23(x1061,x1063,x1064),f23(x1062,x1063,x1064))
% 3.00/2.89 [107]~E(x1071,x1072)+E(f23(x1073,x1071,x1074),f23(x1073,x1072,x1074))
% 3.00/2.89 [108]~E(x1081,x1082)+E(f23(x1083,x1084,x1081),f23(x1083,x1084,x1082))
% 3.00/2.89 [109]~E(x1091,x1092)+E(f86(x1091,x1093,x1094,x1095),f86(x1092,x1093,x1094,x1095))
% 3.00/2.89 [110]~E(x1101,x1102)+E(f86(x1103,x1101,x1104,x1105),f86(x1103,x1102,x1104,x1105))
% 3.00/2.89 [111]~E(x1111,x1112)+E(f86(x1113,x1114,x1111,x1115),f86(x1113,x1114,x1112,x1115))
% 3.00/2.89 [112]~E(x1121,x1122)+E(f86(x1123,x1124,x1125,x1121),f86(x1123,x1124,x1125,x1122))
% 3.00/2.89 [113]~E(x1131,x1132)+E(f49(x1131),f49(x1132))
% 3.00/2.89 [114]~E(x1141,x1142)+E(f65(x1141,x1143,x1144),f65(x1142,x1143,x1144))
% 3.00/2.89 [115]~E(x1151,x1152)+E(f65(x1153,x1151,x1154),f65(x1153,x1152,x1154))
% 3.00/2.89 [116]~E(x1161,x1162)+E(f65(x1163,x1164,x1161),f65(x1163,x1164,x1162))
% 3.00/2.89 [117]~E(x1171,x1172)+E(f80(x1171,x1173,x1174),f80(x1172,x1173,x1174))
% 3.00/2.89 [118]~E(x1181,x1182)+E(f80(x1183,x1181,x1184),f80(x1183,x1182,x1184))
% 3.00/2.89 [119]~E(x1191,x1192)+E(f80(x1193,x1194,x1191),f80(x1193,x1194,x1192))
% 3.00/2.89 [120]~E(x1201,x1202)+E(f66(x1201,x1203),f66(x1202,x1203))
% 3.00/2.89 [121]~E(x1211,x1212)+E(f66(x1213,x1211),f66(x1213,x1212))
% 3.00/2.89 [122]~E(x1221,x1222)+E(f34(x1221,x1223),f34(x1222,x1223))
% 3.00/2.89 [123]~E(x1231,x1232)+E(f34(x1233,x1231),f34(x1233,x1232))
% 3.00/2.89 [124]~E(x1241,x1242)+E(f42(x1241,x1243),f42(x1242,x1243))
% 3.00/2.89 [125]~E(x1251,x1252)+E(f42(x1253,x1251),f42(x1253,x1252))
% 3.00/2.89 [126]~E(x1261,x1262)+E(f44(x1261,x1263),f44(x1262,x1263))
% 3.00/2.89 [127]~E(x1271,x1272)+E(f44(x1273,x1271),f44(x1273,x1272))
% 3.00/2.89 [128]~E(x1281,x1282)+E(f107(x1281,x1283),f107(x1282,x1283))
% 3.00/2.89 [129]~E(x1291,x1292)+E(f107(x1293,x1291),f107(x1293,x1292))
% 3.00/2.89 [130]~E(x1301,x1302)+E(f96(x1301,x1303),f96(x1302,x1303))
% 3.00/2.89 [131]~E(x1311,x1312)+E(f96(x1313,x1311),f96(x1313,x1312))
% 3.00/2.89 [132]~E(x1321,x1322)+E(f41(x1321,x1323),f41(x1322,x1323))
% 3.00/2.89 [133]~E(x1331,x1332)+E(f41(x1333,x1331),f41(x1333,x1332))
% 3.00/2.89 [134]~E(x1341,x1342)+E(f40(x1341,x1343),f40(x1342,x1343))
% 3.00/2.89 [135]~E(x1351,x1352)+E(f40(x1353,x1351),f40(x1353,x1352))
% 3.00/2.89 [136]~E(x1361,x1362)+E(f77(x1361,x1363),f77(x1362,x1363))
% 3.00/2.89 [137]~E(x1371,x1372)+E(f77(x1373,x1371),f77(x1373,x1372))
% 3.00/2.89 [138]~E(x1381,x1382)+E(f39(x1381,x1383),f39(x1382,x1383))
% 3.00/2.89 [139]~E(x1391,x1392)+E(f39(x1393,x1391),f39(x1393,x1392))
% 3.00/2.89 [140]~E(x1401,x1402)+E(f35(x1401,x1403),f35(x1402,x1403))
% 3.00/2.89 [141]~E(x1411,x1412)+E(f35(x1413,x1411),f35(x1413,x1412))
% 3.00/2.89 [142]~E(x1421,x1422)+E(f46(x1421,x1423),f46(x1422,x1423))
% 3.00/2.89 [143]~E(x1431,x1432)+E(f46(x1433,x1431),f46(x1433,x1432))
% 3.00/2.89 [144]~E(x1441,x1442)+E(f57(x1441),f57(x1442))
% 3.00/2.89 [145]~E(x1451,x1452)+E(f99(x1451,x1453,x1454),f99(x1452,x1453,x1454))
% 3.00/2.89 [146]~E(x1461,x1462)+E(f99(x1463,x1461,x1464),f99(x1463,x1462,x1464))
% 3.00/2.89 [147]~E(x1471,x1472)+E(f99(x1473,x1474,x1471),f99(x1473,x1474,x1472))
% 3.00/2.89 [148]~E(x1481,x1482)+E(f83(x1481),f83(x1482))
% 3.00/2.89 [149]~E(x1491,x1492)+E(f85(x1491,x1493),f85(x1492,x1493))
% 3.00/2.89 [150]~E(x1501,x1502)+E(f85(x1503,x1501),f85(x1503,x1502))
% 3.00/2.89 [151]~E(x1511,x1512)+E(f33(x1511,x1513),f33(x1512,x1513))
% 3.00/2.89 [152]~E(x1521,x1522)+E(f33(x1523,x1521),f33(x1523,x1522))
% 3.00/2.89 [153]~E(x1531,x1532)+E(f32(x1531,x1533),f32(x1532,x1533))
% 3.00/2.89 [154]~E(x1541,x1542)+E(f32(x1543,x1541),f32(x1543,x1542))
% 3.00/2.89 [155]~E(x1551,x1552)+E(f31(x1551,x1553),f31(x1552,x1553))
% 3.00/2.89 [156]~E(x1561,x1562)+E(f31(x1563,x1561),f31(x1563,x1562))
% 3.00/2.89 [157]~E(x1571,x1572)+E(f48(x1571,x1573,x1574),f48(x1572,x1573,x1574))
% 3.00/2.89 [158]~E(x1581,x1582)+E(f48(x1583,x1581,x1584),f48(x1583,x1582,x1584))
% 3.00/2.89 [159]~E(x1591,x1592)+E(f48(x1593,x1594,x1591),f48(x1593,x1594,x1592))
% 3.00/2.89 [160]~E(x1601,x1602)+E(f58(x1601),f58(x1602))
% 3.00/2.89 [161]~E(x1611,x1612)+E(f105(x1611,x1613),f105(x1612,x1613))
% 3.00/2.89 [162]~E(x1621,x1622)+E(f105(x1623,x1621),f105(x1623,x1622))
% 3.00/2.89 [163]~E(x1631,x1632)+E(f100(x1631,x1633,x1634),f100(x1632,x1633,x1634))
% 3.00/2.89 [164]~E(x1641,x1642)+E(f100(x1643,x1641,x1644),f100(x1643,x1642,x1644))
% 3.00/2.89 [165]~E(x1651,x1652)+E(f100(x1653,x1654,x1651),f100(x1653,x1654,x1652))
% 3.00/2.89 [166]~E(x1661,x1662)+E(f94(x1661,x1663),f94(x1662,x1663))
% 3.00/2.89 [167]~E(x1671,x1672)+E(f94(x1673,x1671),f94(x1673,x1672))
% 3.00/2.89 [168]~E(x1681,x1682)+E(f93(x1681,x1683),f93(x1682,x1683))
% 3.00/2.89 [169]~E(x1691,x1692)+E(f93(x1693,x1691),f93(x1693,x1692))
% 3.00/2.89 [170]~E(x1701,x1702)+E(f88(x1701),f88(x1702))
% 3.00/2.89 [171]~E(x1711,x1712)+E(f27(x1711,x1713,x1714),f27(x1712,x1713,x1714))
% 3.00/2.89 [172]~E(x1721,x1722)+E(f27(x1723,x1721,x1724),f27(x1723,x1722,x1724))
% 3.00/2.89 [173]~E(x1731,x1732)+E(f27(x1733,x1734,x1731),f27(x1733,x1734,x1732))
% 3.00/2.89 [174]~E(x1741,x1742)+E(f59(x1741,x1743,x1744),f59(x1742,x1743,x1744))
% 3.00/2.89 [175]~E(x1751,x1752)+E(f59(x1753,x1751,x1754),f59(x1753,x1752,x1754))
% 3.00/2.89 [176]~E(x1761,x1762)+E(f59(x1763,x1764,x1761),f59(x1763,x1764,x1762))
% 3.00/2.89 [177]~E(x1771,x1772)+E(f67(x1771,x1773,x1774),f67(x1772,x1773,x1774))
% 3.00/2.89 [178]~E(x1781,x1782)+E(f67(x1783,x1781,x1784),f67(x1783,x1782,x1784))
% 3.00/2.89 [179]~E(x1791,x1792)+E(f67(x1793,x1794,x1791),f67(x1793,x1794,x1792))
% 3.00/2.89 [180]~E(x1801,x1802)+E(f28(x1801),f28(x1802))
% 3.00/2.89 [181]~E(x1811,x1812)+E(f90(x1811,x1813,x1814),f90(x1812,x1813,x1814))
% 3.00/2.89 [182]~E(x1821,x1822)+E(f90(x1823,x1821,x1824),f90(x1823,x1822,x1824))
% 3.00/2.89 [183]~E(x1831,x1832)+E(f90(x1833,x1834,x1831),f90(x1833,x1834,x1832))
% 3.00/2.89 [184]~E(x1841,x1842)+E(f9(x1841,x1843),f9(x1842,x1843))
% 3.00/2.89 [185]~E(x1851,x1852)+E(f9(x1853,x1851),f9(x1853,x1852))
% 3.00/2.89 [186]~E(x1861,x1862)+E(f30(x1861),f30(x1862))
% 3.00/2.89 [187]~E(x1871,x1872)+E(f21(x1871,x1873,x1874,x1875),f21(x1872,x1873,x1874,x1875))
% 3.00/2.89 [188]~E(x1881,x1882)+E(f21(x1883,x1881,x1884,x1885),f21(x1883,x1882,x1884,x1885))
% 3.00/2.89 [189]~E(x1891,x1892)+E(f21(x1893,x1894,x1891,x1895),f21(x1893,x1894,x1892,x1895))
% 3.00/2.89 [190]~E(x1901,x1902)+E(f21(x1903,x1904,x1905,x1901),f21(x1903,x1904,x1905,x1902))
% 3.00/2.89 [191]~E(x1911,x1912)+E(f84(x1911,x1913),f84(x1912,x1913))
% 3.00/2.89 [192]~E(x1921,x1922)+E(f84(x1923,x1921),f84(x1923,x1922))
% 3.00/2.89 [193]~E(x1931,x1932)+E(f72(x1931,x1933,x1934,x1935),f72(x1932,x1933,x1934,x1935))
% 3.00/2.89 [194]~E(x1941,x1942)+E(f72(x1943,x1941,x1944,x1945),f72(x1943,x1942,x1944,x1945))
% 3.00/2.89 [195]~E(x1951,x1952)+E(f72(x1953,x1954,x1951,x1955),f72(x1953,x1954,x1952,x1955))
% 3.00/2.89 [196]~E(x1961,x1962)+E(f72(x1963,x1964,x1965,x1961),f72(x1963,x1964,x1965,x1962))
% 3.00/2.89 [197]~E(x1971,x1972)+E(f76(x1971,x1973,x1974),f76(x1972,x1973,x1974))
% 3.00/2.89 [198]~E(x1981,x1982)+E(f76(x1983,x1981,x1984),f76(x1983,x1982,x1984))
% 3.00/2.89 [199]~E(x1991,x1992)+E(f76(x1993,x1994,x1991),f76(x1993,x1994,x1992))
% 3.00/2.89 [200]~E(x2001,x2002)+E(f54(x2001,x2003),f54(x2002,x2003))
% 3.00/2.89 [201]~E(x2011,x2012)+E(f54(x2013,x2011),f54(x2013,x2012))
% 3.00/2.89 [202]~E(x2021,x2022)+E(f78(x2021,x2023,x2024),f78(x2022,x2023,x2024))
% 3.00/2.89 [203]~E(x2031,x2032)+E(f78(x2033,x2031,x2034),f78(x2033,x2032,x2034))
% 3.00/2.89 [204]~E(x2041,x2042)+E(f78(x2043,x2044,x2041),f78(x2043,x2044,x2042))
% 3.00/2.89 [205]~E(x2051,x2052)+E(f70(x2051,x2053),f70(x2052,x2053))
% 3.00/2.89 [206]~E(x2061,x2062)+E(f70(x2063,x2061),f70(x2063,x2062))
% 3.00/2.89 [207]~E(x2071,x2072)+E(f75(x2071,x2073,x2074),f75(x2072,x2073,x2074))
% 3.00/2.89 [208]~E(x2081,x2082)+E(f75(x2083,x2081,x2084),f75(x2083,x2082,x2084))
% 3.00/2.89 [209]~E(x2091,x2092)+E(f75(x2093,x2094,x2091),f75(x2093,x2094,x2092))
% 3.00/2.89 [210]~E(x2101,x2102)+E(f60(x2101,x2103),f60(x2102,x2103))
% 3.00/2.89 [211]~E(x2111,x2112)+E(f60(x2113,x2111),f60(x2113,x2112))
% 3.00/2.89 [212]~E(x2121,x2122)+E(f43(x2121),f43(x2122))
% 3.00/2.89 [213]~E(x2131,x2132)+E(f63(x2131),f63(x2132))
% 3.00/2.89 [214]~E(x2141,x2142)+E(f61(x2141,x2143),f61(x2142,x2143))
% 3.00/2.89 [215]~E(x2151,x2152)+E(f61(x2153,x2151),f61(x2153,x2152))
% 3.00/2.89 [216]~E(x2161,x2162)+E(f97(x2161,x2163),f97(x2162,x2163))
% 3.00/2.89 [217]~E(x2171,x2172)+E(f97(x2173,x2171),f97(x2173,x2172))
% 3.00/2.89 [218]~P1(x2181)+P1(x2182)+~E(x2181,x2182)
% 3.00/2.89 [219]~P9(x2191)+P9(x2192)+~E(x2191,x2192)
% 3.00/2.89 [220]P2(x2202,x2203,x2204)+~E(x2201,x2202)+~P2(x2201,x2203,x2204)
% 3.00/2.89 [221]P2(x2213,x2212,x2214)+~E(x2211,x2212)+~P2(x2213,x2211,x2214)
% 3.00/2.89 [222]P2(x2223,x2224,x2222)+~E(x2221,x2222)+~P2(x2223,x2224,x2221)
% 3.00/2.89 [223]~P38(x2231)+P38(x2232)+~E(x2231,x2232)
% 3.00/2.89 [224]~P64(x2241)+P64(x2242)+~E(x2241,x2242)
% 3.00/2.89 [225]~P10(x2251)+P10(x2252)+~E(x2251,x2252)
% 3.00/2.89 [226]~P67(x2261)+P67(x2262)+~E(x2261,x2262)
% 3.00/2.89 [227]~P57(x2271)+P57(x2272)+~E(x2271,x2272)
% 3.00/2.89 [228]~P11(x2281)+P11(x2282)+~E(x2281,x2282)
% 3.00/2.89 [229]P3(x2292,x2293,x2294)+~E(x2291,x2292)+~P3(x2291,x2293,x2294)
% 3.00/2.89 [230]P3(x2303,x2302,x2304)+~E(x2301,x2302)+~P3(x2303,x2301,x2304)
% 3.00/2.89 [231]P3(x2313,x2314,x2312)+~E(x2311,x2312)+~P3(x2313,x2314,x2311)
% 3.00/2.89 [232]~P50(x2321)+P50(x2322)+~E(x2321,x2322)
% 3.00/2.89 [233]~P29(x2331)+P29(x2332)+~E(x2331,x2332)
% 3.00/2.89 [234]~P51(x2341)+P51(x2342)+~E(x2341,x2342)
% 3.00/2.89 [235]~P37(x2351)+P37(x2352)+~E(x2351,x2352)
% 3.00/2.89 [236]~P40(x2361)+P40(x2362)+~E(x2361,x2362)
% 3.00/2.89 [237]P7(x2372,x2373)+~E(x2371,x2372)+~P7(x2371,x2373)
% 3.00/2.89 [238]P7(x2383,x2382)+~E(x2381,x2382)+~P7(x2383,x2381)
% 3.00/2.89 [239]~P71(x2391)+P71(x2392)+~E(x2391,x2392)
% 3.00/2.89 [240]P76(x2402,x2403,x2404)+~E(x2401,x2402)+~P76(x2401,x2403,x2404)
% 3.00/2.89 [241]P76(x2413,x2412,x2414)+~E(x2411,x2412)+~P76(x2413,x2411,x2414)
% 3.00/2.89 [242]P76(x2423,x2424,x2422)+~E(x2421,x2422)+~P76(x2423,x2424,x2421)
% 3.00/2.89 [243]~P55(x2431)+P55(x2432)+~E(x2431,x2432)
% 3.00/2.89 [244]~P75(x2441)+P75(x2442)+~E(x2441,x2442)
% 3.00/2.89 [245]~P4(x2451)+P4(x2452)+~E(x2451,x2452)
% 3.00/2.89 [246]~P39(x2461)+P39(x2462)+~E(x2461,x2462)
% 3.00/2.89 [247]~P12(x2471)+P12(x2472)+~E(x2471,x2472)
% 3.00/2.89 [248]~P43(x2481)+P43(x2482)+~E(x2481,x2482)
% 3.00/2.89 [249]~P73(x2491)+P73(x2492)+~E(x2491,x2492)
% 3.00/2.89 [250]~P42(x2501)+P42(x2502)+~E(x2501,x2502)
% 3.00/2.89 [251]~P13(x2511)+P13(x2512)+~E(x2511,x2512)
% 3.00/2.89 [252]~P28(x2521)+P28(x2522)+~E(x2521,x2522)
% 3.00/2.89 [253]~P41(x2531)+P41(x2532)+~E(x2531,x2532)
% 3.00/2.89 [254]~P26(x2541)+P26(x2542)+~E(x2541,x2542)
% 3.00/2.89 [255]~P14(x2551)+P14(x2552)+~E(x2551,x2552)
% 3.00/2.89 [256]~P74(x2561)+P74(x2562)+~E(x2561,x2562)
% 3.00/2.89 [257]~P23(x2571)+P23(x2572)+~E(x2571,x2572)
% 3.00/2.89 [258]~P24(x2581)+P24(x2582)+~E(x2581,x2582)
% 3.00/2.89 [259]~P32(x2591)+P32(x2592)+~E(x2591,x2592)
% 3.00/2.89 [260]~P63(x2601)+P63(x2602)+~E(x2601,x2602)
% 3.00/2.89 [261]~P45(x2611)+P45(x2612)+~E(x2611,x2612)
% 3.00/2.89 [262]P5(x2622,x2623)+~E(x2621,x2622)+~P5(x2621,x2623)
% 3.00/2.89 [263]P5(x2633,x2632)+~E(x2631,x2632)+~P5(x2633,x2631)
% 3.00/2.89 [264]~P20(x2641)+P20(x2642)+~E(x2641,x2642)
% 3.00/2.89 [265]~P48(x2651)+P48(x2652)+~E(x2651,x2652)
% 3.00/2.89 [266]~P72(x2661)+P72(x2662)+~E(x2661,x2662)
% 3.00/2.89 [267]~P47(x2671)+P47(x2672)+~E(x2671,x2672)
% 3.00/2.89 [268]~P49(x2681)+P49(x2682)+~E(x2681,x2682)
% 3.00/2.89 [269]~P62(x2691)+P62(x2692)+~E(x2691,x2692)
% 3.00/2.89 [270]~P56(x2701)+P56(x2702)+~E(x2701,x2702)
% 3.00/2.89 [271]~P54(x2711)+P54(x2712)+~E(x2711,x2712)
% 3.00/2.89 [272]~P30(x2721)+P30(x2722)+~E(x2721,x2722)
% 3.00/2.89 [273]~P16(x2731)+P16(x2732)+~E(x2731,x2732)
% 3.00/2.89 [274]~P27(x2741)+P27(x2742)+~E(x2741,x2742)
% 3.00/2.89 [275]~P34(x2751)+P34(x2752)+~E(x2751,x2752)
% 3.00/2.89 [276]~P21(x2761)+P21(x2762)+~E(x2761,x2762)
% 3.00/2.89 [277]~P68(x2771)+P68(x2772)+~E(x2771,x2772)
% 3.00/2.89 [278]~P22(x2781)+P22(x2782)+~E(x2781,x2782)
% 3.00/2.89 [279]~P15(x2791)+P15(x2792)+~E(x2791,x2792)
% 3.00/2.89 [280]~P69(x2801)+P69(x2802)+~E(x2801,x2802)
% 3.00/2.89 [281]~P19(x2811)+P19(x2812)+~E(x2811,x2812)
% 3.00/2.89 [282]~P58(x2821)+P58(x2822)+~E(x2821,x2822)
% 3.00/2.89 [283]~P17(x2831)+P17(x2832)+~E(x2831,x2832)
% 3.00/2.89 [284]P6(x2842,x2843)+~E(x2841,x2842)+~P6(x2841,x2843)
% 3.00/2.89 [285]P6(x2853,x2852)+~E(x2851,x2852)+~P6(x2853,x2851)
% 3.00/2.89 [286]~P46(x2861)+P46(x2862)+~E(x2861,x2862)
% 3.00/2.89 [287]~P31(x2871)+P31(x2872)+~E(x2871,x2872)
% 3.00/2.89 [288]~P65(x2881)+P65(x2882)+~E(x2881,x2882)
% 3.00/2.89 [289]~P53(x2891)+P53(x2892)+~E(x2891,x2892)
% 3.00/2.89 [290]~P66(x2901)+P66(x2902)+~E(x2901,x2902)
% 3.00/2.89 [291]~P61(x2911)+P61(x2912)+~E(x2911,x2912)
% 3.00/2.89 [292]P8(x2922,x2923)+~E(x2921,x2922)+~P8(x2921,x2923)
% 3.00/2.89 [293]P8(x2933,x2932)+~E(x2931,x2932)+~P8(x2933,x2931)
% 3.00/2.89 [294]~P25(x2941)+P25(x2942)+~E(x2941,x2942)
% 3.00/2.89 [295]~P70(x2951)+P70(x2952)+~E(x2951,x2952)
% 3.00/2.89 [296]~P44(x2961)+P44(x2962)+~E(x2961,x2962)
% 3.00/2.89 [297]~P33(x2971)+P33(x2972)+~E(x2971,x2972)
% 3.00/2.89 [298]~P59(x2981)+P59(x2982)+~E(x2981,x2982)
% 3.00/2.90 [299]~P52(x2991)+P52(x2992)+~E(x2991,x2992)
% 3.00/2.90 [300]~P18(x3001)+P18(x3002)+~E(x3001,x3002)
% 3.00/2.90 [301]~P36(x3011)+P36(x3012)+~E(x3011,x3012)
% 3.00/2.90 [302]~P60(x3021)+P60(x3022)+~E(x3021,x3022)
% 3.00/2.90 [303]~P35(x3031)+P35(x3032)+~E(x3031,x3032)
% 3.00/2.90
% 3.00/2.90 %-------------------------------------------
% 3.00/2.90 cnf(2029,plain,
% 3.00/2.90 (~P3(a109,f12(a109,x20291,x20292),x20292)),
% 3.00/2.90 inference(rename_variables,[],[703])).
% 3.00/2.90 cnf(2032,plain,
% 3.00/2.90 (E(f18(a1,x20321),x20321)),
% 3.00/2.90 inference(rename_variables,[],[522])).
% 3.00/2.90 cnf(2035,plain,
% 3.00/2.90 (E(f18(a1,x20351),x20351)),
% 3.00/2.90 inference(rename_variables,[],[522])).
% 3.00/2.90 cnf(2038,plain,
% 3.00/2.90 (P2(a109,x20381,f12(a109,x20382,x20381))),
% 3.00/2.90 inference(rename_variables,[],[591])).
% 3.00/2.90 cnf(2043,plain,
% 3.00/2.90 (P2(a1,x20431,x20431)),
% 3.00/2.90 inference(rename_variables,[],[550])).
% 3.00/2.90 cnf(2051,plain,
% 3.00/2.90 (P2(a1,x20511,x20511)),
% 3.00/2.90 inference(rename_variables,[],[550])).
% 3.00/2.90 cnf(2056,plain,
% 3.00/2.90 (E(f18(a1,x20561),x20561)),
% 3.00/2.90 inference(rename_variables,[],[522])).
% 3.00/2.90 cnf(2059,plain,
% 3.00/2.90 (P3(a109,x20591,f12(a109,f12(a109,x20592,x20591),f3(a109)))),
% 3.00/2.90 inference(rename_variables,[],[655])).
% 3.00/2.90 cnf(2066,plain,
% 3.00/2.90 (~P3(a109,f12(a109,x20661,x20662),x20661)),
% 3.00/2.90 inference(rename_variables,[],[704])).
% 3.00/2.90 cnf(2071,plain,
% 3.00/2.90 (~P3(a109,f12(a109,x20711,x20712),x20712)),
% 3.00/2.90 inference(rename_variables,[],[703])).
% 3.00/2.90 cnf(2074,plain,
% 3.00/2.90 (~P3(a109,f12(a109,x20741,x20742),x20742)),
% 3.00/2.90 inference(rename_variables,[],[703])).
% 3.00/2.90 cnf(2077,plain,
% 3.00/2.90 (~P2(a109,f12(a109,x20771,f3(a109)),x20771)),
% 3.00/2.90 inference(rename_variables,[],[705])).
% 3.00/2.90 cnf(2080,plain,
% 3.00/2.90 (~P2(a109,f12(a109,x20801,f3(a109)),x20801)),
% 3.00/2.90 inference(rename_variables,[],[705])).
% 3.00/2.90 cnf(2086,plain,
% 3.00/2.90 (E(f18(a1,x20861),x20861)),
% 3.00/2.90 inference(rename_variables,[],[522])).
% 3.00/2.90 cnf(2092,plain,
% 3.00/2.90 (E(f18(a1,x20921),x20921)),
% 3.00/2.90 inference(rename_variables,[],[522])).
% 3.00/2.90 cnf(2095,plain,
% 3.00/2.90 (~E(f12(a109,x20951,f3(a109)),x20951)),
% 3.00/2.90 inference(rename_variables,[],[694])).
% 3.00/2.90 cnf(2109,plain,
% 3.00/2.90 (P2(a110,x21091,f25(f16(a109),f19(x21091)))),
% 3.00/2.90 inference(rename_variables,[],[584])).
% 3.00/2.90 cnf(2115,plain,
% 3.00/2.90 (P2(a109,x21151,x21151)),
% 3.00/2.90 inference(rename_variables,[],[548])).
% 3.00/2.90 cnf(2122,plain,
% 3.00/2.90 (P2(a110,x21221,f25(f16(a109),f19(x21221)))),
% 3.00/2.90 inference(rename_variables,[],[584])).
% 3.00/2.90 cnf(2131,plain,
% 3.00/2.90 (P2(a110,x21311,x21311)),
% 3.00/2.90 inference(rename_variables,[],[549])).
% 3.00/2.90 cnf(2137,plain,
% 3.00/2.90 (~E(f12(a109,x21371,f3(a109)),f2(a109))),
% 3.00/2.90 inference(rename_variables,[],[700])).
% 3.00/2.90 cnf(2145,plain,
% 3.00/2.90 (~E(f12(a109,x21451,f3(a109)),f2(a109))),
% 3.00/2.90 inference(rename_variables,[],[700])).
% 3.00/2.90 cnf(2152,plain,
% 3.00/2.90 (~P3(a109,x21521,x21521)),
% 3.00/2.90 inference(rename_variables,[],[688])).
% 3.00/2.90 cnf(2155,plain,
% 3.00/2.90 (~P3(a109,x21551,x21551)),
% 3.00/2.90 inference(rename_variables,[],[688])).
% 3.00/2.90 cnf(2161,plain,
% 3.00/2.90 (E(f18(a1,x21611),x21611)),
% 3.00/2.90 inference(rename_variables,[],[522])).
% 3.00/2.90 cnf(2163,plain,
% 3.00/2.90 (E(f18(a1,x21631),x21631)),
% 3.00/2.90 inference(rename_variables,[],[522])).
% 3.00/2.90 cnf(2168,plain,
% 3.00/2.90 (P2(a1,x21681,x21681)),
% 3.00/2.90 inference(rename_variables,[],[550])).
% 3.00/2.90 cnf(2170,plain,
% 3.00/2.90 (P2(a110,x21701,x21701)),
% 3.00/2.90 inference(rename_variables,[],[549])).
% 3.00/2.90 cnf(2183,plain,
% 3.00/2.90 (P2(a109,f2(a109),x21831)),
% 3.00/2.90 inference(rename_variables,[],[559])).
% 3.00/2.90 cnf(2208,plain,
% 3.00/2.90 (P3(a109,x22081,f12(a109,f12(a109,x22082,x22081),f3(a109)))),
% 3.00/2.90 inference(rename_variables,[],[655])).
% 3.00/2.90 cnf(2216,plain,
% 3.00/2.90 (P3(a109,x22161,f12(a109,x22161,f3(a109)))),
% 3.00/2.90 inference(rename_variables,[],[598])).
% 3.00/2.90 cnf(2220,plain,
% 3.00/2.90 (P3(a109,x22201,f12(a109,x22201,f3(a109)))),
% 3.00/2.90 inference(rename_variables,[],[598])).
% 3.00/2.90 cnf(2226,plain,
% 3.00/2.90 (P3(a109,x22261,f12(a109,x22261,f3(a109)))),
% 3.00/2.90 inference(rename_variables,[],[598])).
% 3.00/2.90 cnf(2227,plain,
% 3.00/2.90 (~P3(a109,x22271,x22271)),
% 3.00/2.90 inference(rename_variables,[],[688])).
% 3.00/2.90 cnf(2230,plain,
% 3.00/2.90 (P2(a110,x22301,x22301)),
% 3.00/2.90 inference(rename_variables,[],[549])).
% 3.00/2.90 cnf(2236,plain,
% 3.00/2.90 (P2(a110,f2(a110),f25(f16(a109),x22361))),
% 3.00/2.90 inference(rename_variables,[],[578])).
% 3.00/2.90 cnf(2245,plain,
% 3.00/2.90 (P3(a109,x22451,f12(a109,x22451,f3(a109)))),
% 3.00/2.90 inference(rename_variables,[],[598])).
% 3.00/2.90 cnf(2249,plain,
% 3.00/2.90 ($false),
% 3.00/2.90 inference(scs_inference,[],[708,548,2115,549,2131,2170,2230,550,2043,2051,2168,688,2152,2155,2227,306,307,316,317,318,323,324,383,402,559,2183,692,684,555,689,304,516,525,567,569,680,654,522,2032,2035,2056,2086,2092,2161,2163,591,2038,593,594,703,2029,2071,2074,704,2066,598,2216,2220,2226,2245,705,2077,2080,595,694,2095,584,2109,2122,655,2059,2208,707,629,578,2236,700,2137,2145,551,626,616,632,2,1008,953,914,898,897,896,805,922,908,820,912,1080,1029,1760,1462,1461,1389,1387,1384,1382,1381,1379,1369,1368,1367,1277,1256,1255,1253,1251,1249,1187,1139,1076,1011,900,809,1207,24,8,1695,1687,1685,1684,1502,1477,1241,1238,1176,1164,1161,1150,1149,1083,1021,1268,1266,878,877,1581,1579,1578,276,245,231,230,222,221,3,1109,1108,1107,1087,1085,1033,1031,1019,1017,972,956,932,931,826,824,1465,1449,1447,1446,1445,833,1530,1141,1347,1325,1324,1191,1151,1624,1623]),
% 3.00/2.90 ['proof']).
% 3.00/2.90 % SZS output end Proof
% 3.00/2.90 % Total time :1.190000s
%------------------------------------------------------------------------------