TSTP Solution File: SWW198+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:05 EDT 2023
% Result : Theorem 1.14s 1.27s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 19:44:35 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.17/0.53 start to proof:theBenchmark
% 0.99/1.20 %-------------------------------------------
% 0.99/1.20 % File :CSE---1.6
% 0.99/1.20 % Problem :theBenchmark
% 0.99/1.20 % Transform :cnf
% 0.99/1.20 % Format :tptp:raw
% 0.99/1.20 % Command :java -jar mcs_scs.jar %d %s
% 0.99/1.20
% 0.99/1.20 % Result :Theorem 0.090000s
% 0.99/1.20 % Output :CNFRefutation 0.090000s
% 0.99/1.20 %-------------------------------------------
% 0.99/1.21 %------------------------------------------------------------------------------
% 0.99/1.21 % File : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% 0.99/1.21 % Domain : Software Verification
% 0.99/1.21 % Problem : Fundamental Theorem of Algebra 436513, 1000 axioms selected
% 0.99/1.21 % Version : Especial.
% 0.99/1.21 % English :
% 0.99/1.21
% 0.99/1.21 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.99/1.21 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.99/1.21 % Source : [Bla11]
% 0.99/1.21 % Names : fta_436513.1000.p [Bla11]
% 0.99/1.21
% 0.99/1.21 % Status : Theorem
% 0.99/1.21 % Rating : 0.28 v7.5.0, 0.31 v7.4.0, 0.30 v7.3.0, 0.28 v7.2.0, 0.24 v7.1.0, 0.17 v7.0.0, 0.20 v6.4.0, 0.23 v6.3.0, 0.25 v6.2.0, 0.32 v6.1.0, 0.43 v6.0.0, 0.39 v5.5.0, 0.52 v5.4.0, 0.54 v5.3.0, 0.56 v5.2.0
% 0.99/1.21 % Syntax : Number of formulae : 1186 ( 374 unt; 0 def)
% 0.99/1.21 % Number of atoms : 2943 ( 731 equ)
% 0.99/1.21 % Maximal formula atoms : 13 ( 2 avg)
% 0.99/1.21 % Number of connectives : 1977 ( 220 ~; 69 |; 176 &)
% 0.99/1.21 % ( 273 <=>;1239 =>; 0 <=; 0 <~>)
% 0.99/1.21 % Maximal formula depth : 13 ( 5 avg)
% 0.99/1.21 % Maximal term depth : 11 ( 1 avg)
% 0.99/1.21 % Number of predicates : 68 ( 67 usr; 0 prp; 1-3 aty)
% 0.99/1.21 % Number of functors : 31 ( 31 usr; 11 con; 0-3 aty)
% 0.99/1.21 % Number of variables : 2495 (2482 !; 13 ?)
% 0.99/1.21 % SPC : FOF_THM_RFO_SEQ
% 0.99/1.21
% 0.99/1.21 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.99/1.21 % 2011-03-01 11:25:37
% 0.99/1.21 %------------------------------------------------------------------------------
% 0.99/1.21 %----Relevant facts (994)
% 0.99/1.21 fof(fact_o,axiom,
% 0.99/1.21 ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_n,axiom,
% 0.99/1.21 v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_assms_I2_J,axiom,
% 0.99/1.21 v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__numeral__1__right,axiom,
% 0.99/1.21 ! [V_a,T_a] :
% 0.99/1.21 ( class_Int_Onumber__ring(T_a)
% 0.99/1.21 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__numeral__1,axiom,
% 0.99/1.21 ! [V_a,T_a] :
% 0.99/1.21 ( class_Int_Onumber__ring(T_a)
% 0.99/1.21 => c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)),V_a) = V_a ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_Suc__mult__cancel1,axiom,
% 0.99/1.21 ! [V_nb_2,V_m_2,V_k_2] :
% 0.99/1.21 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_nb_2)
% 0.99/1.21 <=> V_m_2 = V_nb_2 ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_Bit0__Pls,axiom,
% 0.99/1.21 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 0.99/1.21
% 0.99/1.21 fof(fact_rel__simps_I38_J,axiom,
% 0.99/1.21 ! [V_l_2] :
% 0.99/1.21 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 0.99/1.21 <=> c_Int_OPls = V_l_2 ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_rel__simps_I44_J,axiom,
% 0.99/1.21 ! [V_k_2] :
% 0.99/1.21 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 0.99/1.21 <=> V_k_2 = c_Int_OPls ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_rel__simps_I49_J,axiom,
% 0.99/1.21 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_rel__simps_I50_J,axiom,
% 0.99/1.21 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_rel__simps_I39_J,axiom,
% 0.99/1.21 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_rel__simps_I46_J,axiom,
% 0.99/1.21 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__Pls,axiom,
% 0.99/1.21 ! [V_w] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,V_w) = c_Int_OPls ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__Bit0,axiom,
% 0.99/1.21 ! [V_l,V_k] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k),V_l) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_l)) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_Suc__neq__Zero,axiom,
% 0.99/1.21 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_Zero__neq__Suc,axiom,
% 0.99/1.21 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_nat_Osimps_I3_J,axiom,
% 0.99/1.21 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_Suc__not__Zero,axiom,
% 0.99/1.21 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_nat_Osimps_I2_J,axiom,
% 0.99/1.21 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_Zero__not__Suc,axiom,
% 0.99/1.21 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__cancel2,axiom,
% 0.99/1.21 ! [V_nb_2,V_k_2,V_m_2] :
% 0.99/1.21 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_nb_2,V_k_2)
% 0.99/1.21 <=> ( V_m_2 = V_nb_2
% 0.99/1.21 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__cancel1,axiom,
% 0.99/1.21 ! [V_nb_2,V_m_2,V_k_2] :
% 0.99/1.21 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_nb_2)
% 0.99/1.21 <=> ( V_m_2 = V_nb_2
% 0.99/1.21 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__is__0,axiom,
% 0.99/1.21 ! [V_nb_2,V_m_2] :
% 0.99/1.21 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.99/1.21 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.99/1.21 | V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__0__right,axiom,
% 0.99/1.21 ! [V_m] : 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) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__0,axiom,
% 0.99/1.21 ! [V_n] : 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) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_number__of__Pls,axiom,
% 0.99/1.21 ! [T_a] :
% 0.99/1.21 ( class_Int_Onumber__ring(T_a)
% 0.99/1.21 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_semiring__norm_I112_J,axiom,
% 0.99/1.21 ! [T_a] :
% 0.99/1.21 ( class_Int_Onumber__ring(T_a)
% 0.99/1.21 => c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_nat__number__of__Pls,axiom,
% 0.99/1.21 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_semiring__norm_I113_J,axiom,
% 0.99/1.21 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__eq__1__iff,axiom,
% 0.99/1.21 ! [V_nb_2,V_m_2] :
% 0.99/1.21 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 0.99/1.21 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 0.99/1.21 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_numeral__3__eq__3,axiom,
% 0.99/1.21 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_numeral__1__eq__Suc__0,axiom,
% 0.99/1.21 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_eq__number__of,axiom,
% 0.99/1.21 ! [V_y_2,V_x_2,T_a] :
% 0.99/1.21 ( ( class_Int_Onumber__ring(T_a)
% 0.99/1.21 & class_Int_Oring__char__0(T_a) )
% 0.99/1.21 => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
% 0.99/1.21 <=> V_x_2 = V_y_2 ) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_number__of__reorient,axiom,
% 0.99/1.21 ! [V_x_2,V_w_2,T_a] :
% 0.99/1.21 ( class_Int_Onumber(T_a)
% 0.99/1.21 => ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = V_x_2
% 0.99/1.21 <=> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_w_2) ) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_rel__simps_I51_J,axiom,
% 0.99/1.21 ! [V_l_2,V_k_2] :
% 0.99/1.21 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 0.99/1.21 <=> V_k_2 = V_l_2 ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_Suc__inject,axiom,
% 0.99/1.21 ! [V_y,V_x] :
% 0.99/1.21 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 0.99/1.21 => V_x = V_y ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_nat_Oinject,axiom,
% 0.99/1.21 ! [V_nat_H_2,V_nat_2] :
% 0.99/1.21 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 0.99/1.21 <=> V_nat_2 = V_nat_H_2 ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_Suc__n__not__n,axiom,
% 0.99/1.21 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 0.99/1.21
% 0.99/1.21 fof(fact_n__not__Suc__n,axiom,
% 0.99/1.21 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_rel__simps_I48_J,axiom,
% 0.99/1.21 ! [V_l_2,V_k_2] :
% 0.99/1.21 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 0.99/1.21 <=> V_k_2 = V_l_2 ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_nat__mult__assoc,axiom,
% 0.99/1.21 ! [V_k,V_n,V_m] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_nat__mult__commute,axiom,
% 0.99/1.21 ! [V_n,V_m] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_numeral__2__eq__2,axiom,
% 0.99/1.21 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_semiring__norm_I115_J,axiom,
% 0.99/1.21 c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_mult__number__of__left,axiom,
% 0.99/1.21 ! [V_z,V_w,V_v,T_a] :
% 0.99/1.21 ( class_Int_Onumber__ring(T_a)
% 0.99/1.21 => c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_arith__simps_I32_J,axiom,
% 0.99/1.21 ! [V_w,V_v,T_a] :
% 0.99/1.21 ( class_Int_Onumber__ring(T_a)
% 0.99/1.21 => c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_number__of__mult,axiom,
% 0.99/1.21 ! [V_w,V_v,T_a] :
% 0.99/1.21 ( class_Int_Onumber__ring(T_a)
% 0.99/1.21 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_odd__Suc__mult__two__ex,axiom,
% 0.99/1.21 ! [V_nb_2] :
% 0.99/1.21 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 0.99/1.21 <=> ? [B_m] : V_nb_2 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_even__mult__two__ex,axiom,
% 0.99/1.21 ! [V_nb_2] :
% 0.99/1.21 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 0.99/1.21 <=> ? [B_m] : V_nb_2 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_odd__nat__equiv__def2,axiom,
% 0.99/1.21 ! [V_x_2] :
% 0.99/1.21 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 0.99/1.21 <=> ? [B_y] : V_x_2 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B_y)) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_even__nat__equiv__def2,axiom,
% 0.99/1.21 ! [V_x_2] :
% 0.99/1.21 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 0.99/1.21 <=> ? [B_y] : V_x_2 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B_y) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_even__product__nat,axiom,
% 0.99/1.21 ! [V_y_2,V_x_2] :
% 0.99/1.21 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_x_2,V_y_2))
% 0.99/1.21 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 0.99/1.21 | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_y_2) ) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_even__Suc,axiom,
% 0.99/1.21 ! [V_x_2] :
% 0.99/1.21 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(V_x_2))
% 0.99/1.21 <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_even__zero__nat,axiom,
% 0.99/1.21 c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 0.99/1.21 ! [V_nb_2,V_m_2,V_k_2] :
% 0.99/1.21 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_nb_2)
% 0.99/1.21 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.99/1.21 | V_m_2 = V_nb_2 ) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_power__odd__eq,axiom,
% 0.99/1.21 ! [V_n,V_a,T_a] :
% 0.99/1.21 ( class_Groups_Omonoid__mult(T_a)
% 0.99/1.21 => c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 0.99/1.21
% 0.99/1.21 fof(fact_divisors__zero,axiom,
% 0.99/1.21 ! [V_b,V_a,T_a] :
% 0.99/1.21 ( class_Rings_Ono__zero__divisors(T_a)
% 0.99/1.21 => ( c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.21 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_no__zero__divisors,axiom,
% 0.99/1.22 ! [V_b,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Ono__zero__divisors(T_a)
% 0.99/1.22 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_mult__eq__0__iff,axiom,
% 0.99/1.22 ! [V_ba_2,V_a_2,T_a] :
% 0.99/1.22 ( class_Rings_Oring__no__zero__divisors(T_a)
% 0.99/1.22 => ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ba_2) = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 | V_ba_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_b,axiom,
% 0.99/1.22 v_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_zmult__commute,axiom,
% 0.99/1.22 ! [V_w,V_z] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,V_w) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_times__numeral__code_I5_J,axiom,
% 0.99/1.22 ! [V_w,V_v] : 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_zmult__assoc,axiom,
% 0.99/1.22 ! [V_z3,V_z2,V_z1] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_z3)) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_zpower__zpower,axiom,
% 0.99/1.22 ! [V_z,V_y,V_x] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),V_z) = c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_y,V_z)) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_Pls__def,axiom,
% 0.99/1.22 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_zero__is__num__zero,axiom,
% 0.99/1.22 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__eq__0__iff__number__of,axiom,
% 0.99/1.22 ! [V_w_2,V_a_2,T_a] :
% 0.99/1.22 ( ( class_Power_Opower(T_a)
% 0.99/1.22 & class_Rings_Omult__zero(T_a)
% 0.99/1.22 & class_Rings_Ono__zero__divisors(T_a)
% 0.99/1.22 & class_Rings_Ozero__neq__one(T_a) )
% 0.99/1.22 => ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power3__eq__cube,axiom,
% 0.99/1.22 ! [V_a,T_a] :
% 0.99/1.22 ( class_Groups_Omonoid__mult(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),V_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_zero__power2,axiom,
% 0.99/1.22 ! [T_a] :
% 0.99/1.22 ( class_Rings_Osemiring__1(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_zero__eq__power2,axiom,
% 0.99/1.22 ! [V_a_2,T_a] :
% 0.99/1.22 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 0.99/1.22 => ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power2__eq__square,axiom,
% 0.99/1.22 ! [V_a,T_a] :
% 0.99/1.22 ( class_Groups_Omonoid__mult(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__even__eq,axiom,
% 0.99/1.22 ! [V_n,V_a,T_a] :
% 0.99/1.22 ( class_Groups_Omonoid__mult(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)) = c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power2__eq__square__number__of,axiom,
% 0.99/1.22 ! [V_w,T_b] :
% 0.99/1.22 ( ( class_Groups_Omonoid__mult(T_b)
% 0.99/1.22 & class_Int_Onumber(T_b) )
% 0.99/1.22 => c_Power_Opower__class_Opower(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_mult__zero__left,axiom,
% 0.99/1.22 ! [V_a,T_a] :
% 0.99/1.22 ( class_Rings_Omult__zero(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_mult__zero__right,axiom,
% 0.99/1.22 ! [V_a,T_a] :
% 0.99/1.22 ( class_Rings_Omult__zero(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 0.99/1.22 ! [V_n,V_x,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))) = c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_x,V_n))) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 0.99/1.22 ! [V_n,V_x,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_x,V_n)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 0.99/1.22 ! [V_x,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_x,V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_csqrt,axiom,
% 0.99/1.22 ! [V_z] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z ).
% 0.99/1.22
% 0.99/1.22 fof(fact_four__x__squared,axiom,
% 0.99/1.22 ! [V_x] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__Suc,axiom,
% 0.99/1.22 ! [V_n,V_a,T_a] :
% 0.99/1.22 ( class_Power_Opower(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 0.99/1.22 ! [V_q,V_x,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)) = c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__Suc2,axiom,
% 0.99/1.22 ! [V_n,V_a,T_a] :
% 0.99/1.22 ( class_Groups_Omonoid__mult(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),V_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 0.99/1.22 ! [V_q,V_x,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q)) = c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 0.99/1.22 ! [V_q,V_x,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_number__of__is__id,axiom,
% 0.99/1.22 ! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.99/1.22 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),c_Groups_Otimes__class_Otimes(T_a,V_ly,V_ry)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.99/1.22 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_ry)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.99/1.22 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.99/1.22 ! [V_rx,V_ly,V_lx,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ly) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.99/1.22 ! [V_rx,V_ly,V_lx,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx) = c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,V_rx)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.99/1.22 ! [V_ry,V_rx,V_lx,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ry) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.99/1.22 ! [V_ry,V_rx,V_lx,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)) = c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.99/1.22 ! [V_b,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_b,V_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 0.99/1.22 ! [V_a,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 0.99/1.22 ! [V_a,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_field__power__not__zero,axiom,
% 0.99/1.22 ! [V_n,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 0.99/1.22 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 0.99/1.22 ! [V_q,V_y,V_x,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_q) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),c_Power_Opower__class_Opower(T_a,V_y,V_q)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__mult__distrib,axiom,
% 0.99/1.22 ! [V_n,V_b,V_a,T_a] :
% 0.99/1.22 ( class_Groups_Ocomm__monoid__mult(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_n) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__commutes,axiom,
% 0.99/1.22 ! [V_n,V_a,T_a] :
% 0.99/1.22 ( class_Groups_Omonoid__mult(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),V_a) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__Suc__0,axiom,
% 0.99/1.22 ! [V_n] : 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)) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 0.99/1.22 ! [V_m_2,V_x_2] :
% 0.99/1.22 ( 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))
% 0.99/1.22 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.99/1.22 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 0.99/1.22 ! [V_q,V_p,V_x,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q) = c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_p,V_q)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__mult,axiom,
% 0.99/1.22 ! [V_n,V_m,V_a,T_a] :
% 0.99/1.22 ( class_Groups_Omonoid__mult(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) = c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),V_n) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__eq__0__iff,axiom,
% 0.99/1.22 ! [V_nb_2,V_a_2,T_a] :
% 0.99/1.22 ( ( class_Power_Opower(T_a)
% 0.99/1.22 & class_Rings_Omult__zero(T_a)
% 0.99/1.22 & class_Rings_Ono__zero__divisors(T_a)
% 0.99/1.22 & class_Rings_Ozero__neq__one(T_a) )
% 0.99/1.22 => ( c_Power_Opower__class_Opower(T_a,V_a_2,V_nb_2) = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.22 & V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__0__Suc,axiom,
% 0.99/1.22 ! [V_n,T_a] :
% 0.99/1.22 ( ( class_Power_Opower(T_a)
% 0.99/1.22 & class_Rings_Osemiring__0(T_a) )
% 0.99/1.22 => 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) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 0.99/1.22 ! [V_n,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Olinordered__idom(T_a)
% 0.99/1.22 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))))
% 0.99/1.22 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_odd__power__less__zero,axiom,
% 0.99/1.22 ! [V_n,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Olinordered__idom(T_a)
% 0.99/1.22 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 0.99/1.22 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power__m1__odd,axiom,
% 0.99/1.22 ! [V_n,T_a] :
% 0.99/1.22 ( class_Int_Onumber__ring(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_zero__le__even__power_H,axiom,
% 0.99/1.22 ! [V_n,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Olinordered__idom(T_a)
% 0.99/1.22 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n))) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_even__power__le__0__imp__0,axiom,
% 0.99/1.22 ! [V_k,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Olinordered__idom(T_a)
% 0.99/1.22 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_k)),c_Groups_Ozero__class_Ozero(T_a))
% 0.99/1.22 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_power2__sum,axiom,
% 0.99/1.22 ! [V_y,V_x,T_a] :
% 0.99/1.22 ( class_Int_Onumber__ring(T_a)
% 0.99/1.22 => c_Power_Opower__class_Opower(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_x),V_y)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_mult__right_Ozero,axiom,
% 0.99/1.22 ! [V_x,T_a] :
% 0.99/1.22 ( class_RealVector_Oreal__normed__algebra(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_mult_Ozero__right,axiom,
% 0.99/1.22 ! [V_a,T_a] :
% 0.99/1.22 ( class_RealVector_Oreal__normed__algebra(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_mult__left_Ozero,axiom,
% 0.99/1.22 ! [V_y,T_a] :
% 0.99/1.22 ( class_RealVector_Oreal__normed__algebra(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_mult_Ozero__left,axiom,
% 0.99/1.22 ! [V_b,T_a] :
% 0.99/1.22 ( class_RealVector_Oreal__normed__algebra(T_a)
% 0.99/1.22 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_less__zeroE,axiom,
% 0.99/1.22 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_le0,axiom,
% 0.99/1.22 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_lessI,axiom,
% 0.99/1.22 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_Suc__mono,axiom,
% 0.99/1.22 ! [V_n,V_m] :
% 0.99/1.22 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 0.99/1.22 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_zero__less__Suc,axiom,
% 0.99/1.22 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_bin__less__0__simps_I2_J,axiom,
% 0.99/1.22 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_pos__add__strict,axiom,
% 0.99/1.22 ! [V_c,V_b,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Olinordered__semidom(T_a)
% 0.99/1.22 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 0.99/1.22 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 0.99/1.22 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_even__less__0__iff,axiom,
% 0.99/1.22 ! [V_a_2,T_a] :
% 0.99/1.22 ( class_Rings_Olinordered__idom(T_a)
% 0.99/1.22 => ( 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))
% 0.99/1.22 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_add__number__of__left,axiom,
% 0.99/1.22 ! [V_z,V_w,V_v,T_a] :
% 0.99/1.22 ( class_Int_Onumber__ring(T_a)
% 0.99/1.22 => 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) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_add__number__of__eq,axiom,
% 0.99/1.22 ! [V_w,V_v,T_a] :
% 0.99/1.22 ( class_Int_Onumber__ring(T_a)
% 0.99/1.22 => 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)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_number__of__add,axiom,
% 0.99/1.22 ! [V_w,V_v,T_a] :
% 0.99/1.22 ( class_Int_Onumber__ring(T_a)
% 0.99/1.22 => 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)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.99/1.22 ! [V_c,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.99/1.22 ! [V_d,V_c,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => 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)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.99/1.22 ! [V_d,V_c,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => 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) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.99/1.22 ! [V_c,V_b,V_a,T_a] :
% 0.99/1.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.22 => 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)) ) ).
% 0.99/1.22
% 0.99/1.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.99/1.23 ! [V_c,V_b,V_a,T_a] :
% 0.99/1.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.23 => 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) ) ).
% 0.99/1.23
% 0.99/1.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.99/1.23 ! [V_d,V_c,V_b,V_a,T_a] :
% 0.99/1.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.23 => 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)) ) ).
% 0.99/1.23
% 0.99/1.23 fof(fact_le__number__of__eq__not__less,axiom,
% 0.99/1.23 ! [V_w_2,V_v_2,T_a] :
% 0.99/1.23 ( ( class_Int_Onumber(T_a)
% 0.99/1.23 & class_Orderings_Olinorder(T_a) )
% 0.99/1.23 => ( 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_w_2))
% 0.99/1.23 <=> ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) ) ) ).
% 0.99/1.23
% 0.99/1.23 fof(fact_less__number__of,axiom,
% 0.99/1.23 ! [V_y_2,V_x_2,T_a] :
% 0.99/1.23 ( ( class_Int_Onumber__ring(T_a)
% 0.99/1.23 & class_Rings_Olinordered__idom(T_a) )
% 0.99/1.23 => ( 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))
% 0.99/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 0.99/1.23
% 0.99/1.23 fof(fact_le__number__of,axiom,
% 0.99/1.23 ! [V_y_2,V_x_2,T_a] :
% 0.99/1.23 ( ( class_Int_Onumber__ring(T_a)
% 0.99/1.23 & class_Rings_Olinordered__idom(T_a) )
% 0.99/1.23 => ( 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))
% 0.99/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 0.99/1.23
% 0.99/1.23 fof(fact_rel__simps_I9_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I13_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I6_J,axiom,
% 1.04/1.23 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I3_J,axiom,
% 1.04/1.23 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I8_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_k_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I26_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I30_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I23_J,axiom,
% 1.04/1.23 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I20_J,axiom,
% 1.04/1.23 ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I28_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__gr__0,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( 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_nb_2))
% 1.04/1.23 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.04/1.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__add__Suc1,axiom,
% 1.04/1.23 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__add__Suc2,axiom,
% 1.04/1.23 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__iff__Suc__add,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.23 <=> ? [B_k] : V_nb_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__eq__Suc__le,axiom,
% 1.04/1.23 ! [V_m_2,V_nb_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__Suc__eq__le,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__le__eq,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_nb_2)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__imp__less__Suc,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__leI,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__less__Suc__eq,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
% 1.04/1.23 <=> V_nb_2 = V_m_2 ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__le__lessD,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I7_J,axiom,
% 1.04/1.23 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I24_J,axiom,
% 1.04/1.23 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I25_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_k_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I11_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_linorder__neqE__linordered__idom,axiom,
% 1.04/1.23 ! [V_y,V_x,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.23 => ( V_x != V_y
% 1.04/1.23 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult_Oadd__right,axiom,
% 1.04/1.23 ! [V_b_H,V_b,V_a,T_a] :
% 1.04/1.23 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.04/1.23 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__right_Oadd,axiom,
% 1.04/1.23 ! [V_y,V_x,V_xa,T_a] :
% 1.04/1.23 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.04/1.23 => c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult_Oadd__left,axiom,
% 1.04/1.23 ! [V_b,V_a_H,V_a,T_a] :
% 1.04/1.23 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.04/1.23 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__left_Oadd,axiom,
% 1.04/1.23 ! [V_ya,V_y,V_x,T_a] :
% 1.04/1.23 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.04/1.23 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__nat__number__of,axiom,
% 1.04/1.23 ! [V_v_H,V_v] :
% 1.04/1.23 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.04/1.23 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H) )
% 1.04/1.23 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.04/1.23 => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 1.04/1.23 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) )
% 1.04/1.23 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 1.04/1.23 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)) ) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_power__strict__mono,axiom,
% 1.04/1.23 ! [V_n,V_b,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_sum__squares__gt__zero__iff,axiom,
% 1.04/1.23 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)))
% 1.04/1.23 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.23 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_not__sum__squares__lt__zero,axiom,
% 1.04/1.23 ! [V_y,V_x,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__ring(T_a)
% 1.04/1.23 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_sum__squares__le__zero__iff,axiom,
% 1.04/1.23 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.23 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.23 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_sum__squares__ge__zero,axiom,
% 1.04/1.23 ! [V_y,V_x,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__ring(T_a)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y))) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__left__le__imp__le,axiom,
% 1.04/1.23 ! [V_b,V_a,V_c,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__right__le__imp__le,axiom,
% 1.04/1.23 ! [V_b,V_c,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__less__imp__less__left,axiom,
% 1.04/1.23 ! [V_b,V_a,V_c,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__left__less__imp__less,axiom,
% 1.04/1.23 ! [V_b,V_a,V_c,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__less__imp__less__right,axiom,
% 1.04/1.23 ! [V_b,V_c,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__right__less__imp__less,axiom,
% 1.04/1.23 ! [V_b,V_c,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__le__less__imp__less,axiom,
% 1.04/1.23 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__less__le__imp__less,axiom,
% 1.04/1.23 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__strict__mono_H,axiom,
% 1.04/1.23 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__strict__mono,axiom,
% 1.04/1.23 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__le__cancel__left__neg,axiom,
% 1.04/1.23 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_ba_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,V_a_2) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__le__cancel__left__pos,axiom,
% 1.04/1.23 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_ba_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_ba_2) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_power__less__imp__less__base,axiom,
% 1.04/1.23 ! [V_b,V_n,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I5_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I29_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I15_J,axiom,
% 1.04/1.23 ! [V_l_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__int__code_I14_J,axiom,
% 1.04/1.23 ! [V_k2_2,V_k1_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I33_J,axiom,
% 1.04/1.23 ! [V_l_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__eq__int__code_I15_J,axiom,
% 1.04/1.23 ! [V_k2_2,V_k1_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__nat__number__of,axiom,
% 1.04/1.23 ! [V_v_H_2,V_v_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
% 1.04/1.23 <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) )
% 1.04/1.23 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__nat__number__of,axiom,
% 1.04/1.23 ! [V_v_H_2,V_v_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
% 1.04/1.23 <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_nat__mult__le__cancel1,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_nb_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__le__cancel2,axiom,
% 1.04/1.23 ! [V_nb_2,V_k_2,V_m_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_nb_2,V_k_2))
% 1.04/1.23 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__le__cancel1,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_nb_2))
% 1.04/1.23 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_double__eq__0__iff,axiom,
% 1.04/1.23 ! [V_a_2,T_a] :
% 1.04/1.23 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.04/1.23 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.23 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__0__iff,axiom,
% 1.04/1.23 ! [V_a_2,V_ba_2,T_a] :
% 1.04/1.23 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.04/1.23 => ( V_ba_2 = c_Groups_Oplus__class_Oplus(T_a,V_ba_2,V_a_2)
% 1.04/1.23 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 1.04/1.23 ! [V_a,T_a] :
% 1.04/1.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.23 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 1.04/1.23 ! [V_a,T_a] :
% 1.04/1.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.23 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_comm__semiring__class_Odistrib,axiom,
% 1.04/1.23 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Ocomm__semiring(T_a)
% 1.04/1.23 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_combine__common__factor,axiom,
% 1.04/1.23 ! [V_c,V_b,V_e,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Osemiring(T_a)
% 1.04/1.23 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 1.04/1.23 ! [V_z,V_y,V_x,T_a] :
% 1.04/1.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.23 => c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_x,V_z)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_crossproduct__noteq,axiom,
% 1.04/1.23 ! [V_d_2,V_c_2,V_ba_2,V_a_2,T_a] :
% 1.04/1.23 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.04/1.23 => ( ( V_a_2 != V_ba_2
% 1.04/1.23 & V_c_2 != V_d_2 )
% 1.04/1.23 <=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_c_2)) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 1.04/1.23 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.23 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 1.04/1.23 ! [V_b,V_m,V_a,T_a] :
% 1.04/1.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.23 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),c_Groups_Otimes__class_Otimes(T_a,V_b,V_m)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_m) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_crossproduct__eq,axiom,
% 1.04/1.23 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 1.04/1.23 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.04/1.23 => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_y_2))
% 1.04/1.23 <=> ( V_w_2 = V_x_2
% 1.04/1.23 | V_y_2 = V_z_2 ) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Bit1__Min,axiom,
% 1.04/1.23 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I43_J,axiom,
% 1.04/1.23 ! [V_l_2] :
% 1.04/1.23 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 1.04/1.23 <=> c_Int_OMin = V_l_2 ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I47_J,axiom,
% 1.04/1.23 ! [V_k_2] :
% 1.04/1.23 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 1.04/1.23 <=> V_k_2 = c_Int_OMin ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I40_J,axiom,
% 1.04/1.23 c_Int_OMin != c_Int_OPls ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I37_J,axiom,
% 1.04/1.23 c_Int_OPls != c_Int_OMin ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I42_J,axiom,
% 1.04/1.23 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I45_J,axiom,
% 1.04/1.23 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__eq__self__zero,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 1.04/1.23 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__is__0,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.23 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.23 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Nat_Oadd__0__right,axiom,
% 1.04/1.23 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.04/1.23
% 1.04/1.23 fof(fact_plus__nat_Oadd__0,axiom,
% 1.04/1.23 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 1.04/1.23
% 1.04/1.23 fof(fact_zadd__0__right,axiom,
% 1.04/1.23 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 1.04/1.23
% 1.04/1.23 fof(fact_zadd__0,axiom,
% 1.04/1.23 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__Pls,axiom,
% 1.04/1.23 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__Pls__right,axiom,
% 1.04/1.23 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Bit0__def,axiom,
% 1.04/1.23 ! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__Bit0__Bit0,axiom,
% 1.04/1.23 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__Suc__right,axiom,
% 1.04/1.23 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__Suc,axiom,
% 1.04/1.23 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__Suc__shift,axiom,
% 1.04/1.23 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_zero__less__power__nat__eq,axiom,
% 1.04/1.23 ! [V_nb_2,V_x_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_nb_2))
% 1.04/1.23 <=> ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.23 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_gr0I,axiom,
% 1.04/1.23 ! [V_n] :
% 1.04/1.23 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_gr__implies__not0,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.04/1.23 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__nat__zero__code,axiom,
% 1.04/1.23 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_neq0__conv,axiom,
% 1.04/1.23 ! [V_nb_2] :
% 1.04/1.23 ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_not__less0,axiom,
% 1.04/1.23 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_nat__zero__less__power__iff,axiom,
% 1.04/1.23 ! [V_nb_2,V_x_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_nb_2))
% 1.04/1.23 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 1.04/1.23 | V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_nat__power__less__imp__less,axiom,
% 1.04/1.23 ! [V_n,V_m,V_i] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__0__eq,axiom,
% 1.04/1.23 ! [V_nb_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.04/1.23 <=> V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 1.04/1.23 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I17_J,axiom,
% 1.04/1.23 ! [V_l_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__int__code_I16_J,axiom,
% 1.04/1.23 ! [V_k2_2,V_k1_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I2_J,axiom,
% 1.04/1.23 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I14_J,axiom,
% 1.04/1.23 ! [V_l_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__int__code_I13_J,axiom,
% 1.04/1.23 ! [V_k2_2,V_k1_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_not__less__eq,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__Suc__eq,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 1.04/1.23 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.23 | V_m_2 = V_nb_2 ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__less__eq,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_nb_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_not__less__less__Suc__eq,axiom,
% 1.04/1.23 ! [V_m_2,V_nb_2] :
% 1.04/1.23 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
% 1.04/1.23 <=> V_nb_2 = V_m_2 ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__antisym,axiom,
% 1.04/1.23 ! [V_m,V_n] :
% 1.04/1.23 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 1.04/1.23 => V_m = V_n ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__SucI,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__lessI,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.04/1.23 => ( c_Nat_OSuc(V_m) != V_n
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__trans__Suc,axiom,
% 1.04/1.23 ! [V_k,V_j,V_i] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__SucE,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 1.04/1.23 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.04/1.23 => V_m = V_n ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__lessD,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__less__SucD,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 1.04/1.23 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I34_J,axiom,
% 1.04/1.23 ! [V_l_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__eq__int__code_I16_J,axiom,
% 1.04/1.23 ! [V_k2_2,V_k1_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__n__not__le__n,axiom,
% 1.04/1.23 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_not__less__eq__eq,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__Suc__eq,axiom,
% 1.04/1.23 ! [V_nb_2,V_m_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 1.04/1.23 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.23 | V_m_2 = c_Nat_OSuc(V_nb_2) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__le__mono,axiom,
% 1.04/1.23 ! [V_m_2,V_nb_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),c_Nat_OSuc(V_m_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,V_m_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__SucI,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__SucE,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 1.04/1.23 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.04/1.23 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_Suc__leD,axiom,
% 1.04/1.23 ! [V_n,V_m] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I19_J,axiom,
% 1.04/1.23 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_rel__simps_I31_J,axiom,
% 1.04/1.23 ! [V_l_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__eq__int__code_I13_J,axiom,
% 1.04/1.23 ! [V_k2_2,V_k1_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_plus__numeral__code_I9_J,axiom,
% 1.04/1.23 ! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_left__add__mult__distrib,axiom,
% 1.04/1.23 ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_u),V_k) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__mult__distrib2,axiom,
% 1.04/1.23 ! [V_n,V_m,V_k] : 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_add__mult__distrib,axiom,
% 1.04/1.23 ! [V_k,V_n,V_m] : 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_zadd__zmult__distrib2,axiom,
% 1.04/1.23 ! [V_z2,V_z1,V_w] : 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_zadd__zmult__distrib,axiom,
% 1.04/1.23 ! [V_w,V_z2,V_z1] : 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_not__real__square__gt__zero,axiom,
% 1.04/1.23 ! [V_x_2] :
% 1.04/1.23 ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2))
% 1.04/1.23 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__number__of__int__code,axiom,
% 1.04/1.23 ! [V_l_2,V_k_2] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
% 1.04/1.23 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__square,axiom,
% 1.04/1.23 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m)) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_le__cube,axiom,
% 1.04/1.23 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m))) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__le__mono1,axiom,
% 1.04/1.23 ! [V_k,V_j,V_i] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__le__mono2,axiom,
% 1.04/1.23 ! [V_k,V_j,V_i] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_mult__le__mono,axiom,
% 1.04/1.23 ! [V_l,V_k,V_j,V_i] :
% 1.04/1.23 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.04/1.23 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.04/1.23 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.04/1.23
% 1.04/1.23 fof(fact_less__eq__number__of__int__code,axiom,
% 1.04/1.23 ! [V_l_2,V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_even__sum__nat,axiom,
% 1.04/1.24 ! [V_y_2,V_x_2] :
% 1.04/1.24 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x_2,V_y_2))
% 1.04/1.24 <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.04/1.24 & c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_y_2) )
% 1.04/1.24 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.04/1.24 & ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_y_2) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_even__add,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2))
% 1.04/1.24 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_m_2)
% 1.04/1.24 <=> c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_odd__add,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2))
% 1.04/1.24 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_m_2)
% 1.04/1.24 <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__special_I1_J,axiom,
% 1.04/1.24 ! [V_y_2,T_a] :
% 1.04/1.24 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__special_I3_J,axiom,
% 1.04/1.24 ! [V_x_2,T_a] :
% 1.04/1.24 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__special_I1_J,axiom,
% 1.04/1.24 ! [V_y_2,T_a] :
% 1.04/1.24 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__special_I3_J,axiom,
% 1.04/1.24 ! [V_x_2,T_a] :
% 1.04/1.24 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__eq__imp__eq__base,axiom,
% 1.04/1.24 ! [V_b,V_n,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Power_Opower__class_Opower(T_a,V_a,V_n) = c_Power_Opower__class_Opower(T_a,V_b,V_n)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.04/1.24 => V_a = V_b ) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__0__number__of,axiom,
% 1.04/1.24 ! [V_v_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_sum__squares__eq__zero__iff,axiom,
% 1.04/1.24 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.24 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.24 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__scale__eq__noteq,axiom,
% 1.04/1.24 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 1.04/1.24 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.04/1.24 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.24 => ( ( V_a = V_b
% 1.04/1.24 & V_c != V_d )
% 1.04/1.24 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_r,V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,c_Groups_Otimes__class_Otimes(T_a,V_r,V_d)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_right__distrib__number__of,axiom,
% 1.04/1.24 ! [V_c,V_b,V_v,T_b] :
% 1.04/1.24 ( ( class_Int_Onumber(T_b)
% 1.04/1.24 & class_Rings_Osemiring(T_b) )
% 1.04/1.24 => c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_left__distrib__number__of,axiom,
% 1.04/1.24 ! [V_v,V_b,V_a,T_b] :
% 1.04/1.24 ( ( class_Int_Onumber(T_b)
% 1.04/1.24 & class_Rings_Osemiring(T_b) )
% 1.04/1.24 => c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__strict__left__mono__neg,axiom,
% 1.04/1.24 ! [V_c,V_a,V_b,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__strict__right__mono__neg,axiom,
% 1.04/1.24 ! [V_c,V_a,V_b,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_comm__mult__strict__left__mono,axiom,
% 1.04/1.24 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__strict__left__mono,axiom,
% 1.04/1.24 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__strict__right__mono,axiom,
% 1.04/1.24 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__neg__neg,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__neg__pos,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__less__cancel__left__neg,axiom,
% 1.04/1.24 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_ba_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(T_a,V_ba_2,V_a_2) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__less__mult__pos2,axiom,
% 1.04/1.24 ! [V_a,V_b,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__less__mult__pos,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__pos__neg2,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__pos__neg,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__pos__pos,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__less__cancel__left__pos,axiom,
% 1.04/1.24 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_ba_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__less__cancel__left__disj,axiom,
% 1.04/1.24 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_ba_2))
% 1.04/1.24 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) )
% 1.04/1.24 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 & c_Orderings_Oord__class_Oless(T_a,V_ba_2,V_a_2) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__less__cancel__right__disj,axiom,
% 1.04/1.24 ! [V_ba_2,V_c_2,V_a_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_c_2))
% 1.04/1.24 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) )
% 1.04/1.24 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 & c_Orderings_Oord__class_Oless(T_a,V_ba_2,V_a_2) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_not__square__less__zero,axiom,
% 1.04/1.24 ! [V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring(T_a)
% 1.04/1.24 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_split__mult__neg__le,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.04/1.24 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.04/1.24 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_split__mult__pos__le,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__ring(T_a)
% 1.04/1.24 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 1.04/1.24 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__mono,axiom,
% 1.04/1.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__mono_H,axiom,
% 1.04/1.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__left__mono__neg,axiom,
% 1.04/1.24 ! [V_c,V_a,V_b,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__ring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__right__mono__neg,axiom,
% 1.04/1.24 ! [V_c,V_a,V_b,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__ring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_comm__mult__left__mono,axiom,
% 1.04/1.24 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__comm__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__left__mono,axiom,
% 1.04/1.24 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__right__mono,axiom,
% 1.04/1.24 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__nonpos__nonpos,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__ring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__nonpos__nonneg,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__nonneg__nonpos2,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__nonneg__nonpos,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__nonneg__nonneg,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__le__0__iff,axiom,
% 1.04/1.24 ! [V_ba_2,V_a_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ba_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.04/1.24 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ba_2) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__mult__iff,axiom,
% 1.04/1.24 ! [V_ba_2,V_a_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ba_2))
% 1.04/1.24 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ba_2) )
% 1.04/1.24 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__square,axiom,
% 1.04/1.24 ! [V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__ring(T_a)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__numeral__0__right,axiom,
% 1.04/1.24 ! [V_a,T_a] :
% 1.04/1.24 ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__numeral__0,axiom,
% 1.04/1.24 ! [V_a,T_a] :
% 1.04/1.24 ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__less__power,axiom,
% 1.04/1.24 ! [V_n,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__power,axiom,
% 1.04/1.24 ! [V_n,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__mono,axiom,
% 1.04/1.24 ! [V_n,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__add,axiom,
% 1.04/1.24 ! [V_n,V_m,V_a,T_a] :
% 1.04/1.24 ( class_Groups_Omonoid__mult(T_a)
% 1.04/1.24 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 1.04/1.24 ! [V_q,V_p,V_x,T_a] :
% 1.04/1.24 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.24 => c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),c_Power_Opower__class_Opower(T_a,V_x,V_q)) = c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_eq__number__of__Pls__Min,axiom,
% 1.04/1.24 c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__Bit0__Bit1,axiom,
% 1.04/1.24 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__Bit1__Bit0,axiom,
% 1.04/1.24 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__is__1,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.04/1.24 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.04/1.24 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.04/1.24 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_one__is__add,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.24 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.04/1.24 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.04/1.24 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_bin__less__0__simps_I4_J,axiom,
% 1.04/1.24 ! [V_w_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_rel__simps_I12_J,axiom,
% 1.04/1.24 ! [V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_bin__less__0__simps_I1_J,axiom,
% 1.04/1.24 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 1.04/1.24 ! [V_x] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 1.04/1.24 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__Suc__eq__0__disj,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 1.04/1.24 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 | ? [B_j] :
% 1.04/1.24 ( V_m_2 = c_Nat_OSuc(B_j)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_nb_2) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__Suc0,axiom,
% 1.04/1.24 ! [V_nb_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 1.04/1.24 <=> V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_gr0__conv__Suc,axiom,
% 1.04/1.24 ! [V_nb_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
% 1.04/1.24 <=> ? [B_m] : V_nb_2 = c_Nat_OSuc(B_m) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_rel__simps_I16_J,axiom,
% 1.04/1.24 ! [V_l_2,V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__int__code_I15_J,axiom,
% 1.04/1.24 ! [V_k2_2,V_k1_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_bin__less__0__simps_I3_J,axiom,
% 1.04/1.24 ! [V_w_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_rel__simps_I4_J,axiom,
% 1.04/1.24 ! [V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_rel__simps_I10_J,axiom,
% 1.04/1.24 ! [V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__one__le__power,axiom,
% 1.04/1.24 ! [V_n,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_rel__simps_I22_J,axiom,
% 1.04/1.24 ! [V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__Suc__right,axiom,
% 1.04/1.24 ! [V_n,V_m] : 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__Suc,axiom,
% 1.04/1.24 ! [V_n,V_m] : 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_rel__simps_I32_J,axiom,
% 1.04/1.24 ! [V_l_2,V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__eq__int__code_I14_J,axiom,
% 1.04/1.24 ! [V_k2_2,V_k1_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_rel__simps_I21_J,axiom,
% 1.04/1.24 ! [V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_rel__simps_I27_J,axiom,
% 1.04/1.24 ! [V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__less__power__nat__eq__number__of,axiom,
% 1.04/1.24 ! [V_w_2,V_x_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)))
% 1.04/1.24 <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__mult__less__cancel1,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_nb_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__mult__eq__cancel1,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.04/1.24 => ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_nb_2)
% 1.04/1.24 <=> V_m_2 = V_nb_2 ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__less__mono2,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__less__mono1,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__less__cancel2,axiom,
% 1.04/1.24 ! [V_nb_2,V_k_2,V_m_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_nb_2,V_k_2))
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__less__cancel1,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_nb_2))
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__0__less__mult__iff,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2))
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zmult__zless__mono2,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_j)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_Suc__mult__less__cancel1,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_nb_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_Suc__mult__le__cancel1,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_nb_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__mono__odd,axiom,
% 1.04/1.24 ! [V_y,V_x,V_n,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_n)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_y,V_n)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_even__power__nat,axiom,
% 1.04/1.24 ! [V_y_2,V_x_2] :
% 1.04/1.24 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_y_2))
% 1.04/1.24 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_odd__pos,axiom,
% 1.04/1.24 ! [V_n] :
% 1.04/1.24 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_n)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zpower__zadd__distrib,axiom,
% 1.04/1.24 ! [V_z,V_y,V_x] : c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_z)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_not__sum__power2__lt__zero,axiom,
% 1.04/1.24 ! [V_y,V_x,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_sum__power2__gt__zero__iff,axiom,
% 1.04/1.24 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 1.04/1.24 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.24 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_sum__power2__ge__zero,axiom,
% 1.04/1.24 ! [V_y,V_x,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_sum__power2__le__zero__iff,axiom,
% 1.04/1.24 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.24 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power2__less__imp__less,axiom,
% 1.04/1.24 ! [V_y,V_x,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_number__of__Bit0,axiom,
% 1.04/1.24 ! [V_w,T_a] :
% 1.04/1.24 ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__inject__base,axiom,
% 1.04/1.24 ! [V_b,V_n,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)) = c_Power_Opower__class_Opower(T_a,V_b,c_Nat_OSuc(V_n))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => V_a = V_b ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__le__imp__le__base,axiom,
% 1.04/1.24 ! [V_b,V_n,V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)),c_Power_Opower__class_Opower(T_a,V_b,c_Nat_OSuc(V_n)))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_neg__one__odd__power,axiom,
% 1.04/1.24 ! [V_x,T_a] :
% 1.04/1.24 ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.04/1.24 => c_Power_Opower__class_Opower(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),V_x) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__less__zero__eq,axiom,
% 1.04/1.24 ! [V_nb_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,V_nb_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 <=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__Bit1,axiom,
% 1.04/1.24 ! [V_l,V_k] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(V_k),V_l) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_l)),V_l) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__odd__power,axiom,
% 1.04/1.24 ! [V_x_2,V_nb_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_x_2,V_nb_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__even__power,axiom,
% 1.04/1.24 ! [V_x,V_n,T_a] :
% 1.04/1.24 ( ( class_Groups_Omonoid__mult(T_a)
% 1.04/1.24 & class_Rings_Olinordered__ring(T_a) )
% 1.04/1.24 => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_n)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_x,V_n)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__power__iff,axiom,
% 1.04/1.24 ! [V_nb_2,V_a_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,V_nb_2))
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.04/1.24 | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__power__eq,axiom,
% 1.04/1.24 ! [V_nb_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_x_2,V_nb_2))
% 1.04/1.24 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.04/1.24 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_eq__0__number__of,axiom,
% 1.04/1.24 ! [V_v_2] :
% 1.04/1.24 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_eq__number__of__0,axiom,
% 1.04/1.24 ! [V_v_2] :
% 1.04/1.24 ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_n__less__m__mult__n,axiom,
% 1.04/1.24 ! [V_m,V_n] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_n__less__n__mult__m,axiom,
% 1.04/1.24 ! [V_m,V_n] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_one__less__mult,axiom,
% 1.04/1.24 ! [V_m,V_n] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_one__le__mult__iff,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2))
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_nb_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__less__power__eq,axiom,
% 1.04/1.24 ! [V_nb_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_x_2,V_nb_2))
% 1.04/1.24 <=> ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.04/1.24 & V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
% 1.04/1.24 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_Suc3__eq__add__3,axiom,
% 1.04/1.24 ! [V_n] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(V_n))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),V_n) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__less__zero__eq__number__of,axiom,
% 1.04/1.24 ! [V_w_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 <=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.04/1.24 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__le__zero__eq,axiom,
% 1.04/1.24 ! [V_nb_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,V_nb_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 <=> ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 & ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.04/1.24 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.04/1.24 & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__power__eq__number__of,axiom,
% 1.04/1.24 ! [V_w_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)))
% 1.04/1.24 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.04/1.24 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__2__right,axiom,
% 1.04/1.24 ! [V_z,T_a] :
% 1.04/1.24 ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 => c_Groups_Otimes__class_Otimes(T_a,V_z,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__2,axiom,
% 1.04/1.24 ! [V_z,T_a] :
% 1.04/1.24 ( class_Int_Onumber__ring(T_a)
% 1.04/1.24 => c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__less__power__eq__number__of,axiom,
% 1.04/1.24 ! [V_w_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)))
% 1.04/1.24 <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.04/1.24 & V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
% 1.04/1.24 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.04/1.24 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__2__eq__Suc_H,axiom,
% 1.04/1.24 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(V_n)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__2__eq__Suc,axiom,
% 1.04/1.24 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n) = c_Nat_OSuc(c_Nat_OSuc(V_n)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__mult__2__right,axiom,
% 1.04/1.24 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_z,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__mult__2,axiom,
% 1.04/1.24 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power__le__zero__eq__number__of,axiom,
% 1.04/1.24 ! [V_w_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.24 <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 & ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.04/1.24 & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.04/1.24 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.04/1.24 & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_pos2,axiom,
% 1.04/1.24 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,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_mult__nat__number__of,axiom,
% 1.04/1.24 ! [V_v_H,V_v] :
% 1.04/1.24 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.04/1.24 => 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) )
% 1.04/1.24 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.04/1.24 => 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_v_H)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__number__of__mult__left,axiom,
% 1.04/1.24 ! [V_k,V_v_H,V_v] :
% 1.04/1.24 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.04/1.24 => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),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) )
% 1.04/1.24 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.04/1.24 => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H),V_k)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_v_H)),V_k) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_sum__power2__eq__zero__iff,axiom,
% 1.04/1.24 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.24 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.24 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power2__less__0,axiom,
% 1.04/1.24 ! [V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__less__power2,axiom,
% 1.04/1.24 ! [V_a_2,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.04/1.24 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zero__le__power2,axiom,
% 1.04/1.24 ! [V_a,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power2__le__imp__le,axiom,
% 1.04/1.24 ! [V_y,V_x,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_power2__eq__imp__eq,axiom,
% 1.04/1.24 ! [V_y,V_x,T_a] :
% 1.04/1.24 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.24 => ( c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.04/1.24 => V_x = V_y ) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__2__cases,axiom,
% 1.04/1.24 ! [V_n] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 1.04/1.24 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.24 | V_n = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_real__sum__squared__expand,axiom,
% 1.04/1.24 ! [V_y,V_x] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_x),V_y)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_realpow__two__sum__zero__iff,axiom,
% 1.04/1.24 ! [V_y_2,V_x_2] :
% 1.04/1.24 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.04/1.24 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.04/1.24 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 1.04/1.24 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_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_number__of1,axiom,
% 1.04/1.24 ! [V_n] :
% 1.04/1.24 ( 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_n))
% 1.04/1.24 => ( 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_OBit0(V_n)))
% 1.04/1.24 & 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_OBit1(V_n))) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 1.04/1.24 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_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__pos__nonneg,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__nonneg__pos,axiom,
% 1.04/1.24 ! [V_b,V_a,T_a] :
% 1.04/1.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__strict__increasing,axiom,
% 1.04/1.24 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__strict__increasing2,axiom,
% 1.04/1.24 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.24 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__not__refl,axiom,
% 1.04/1.24 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_not__add__less1,axiom,
% 1.04/1.24 ! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_not__add__less2,axiom,
% 1.04/1.24 ! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__refl,axiom,
% 1.04/1.24 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zle__refl,axiom,
% 1.04/1.24 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__add2,axiom,
% 1.04/1.24 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__add1,axiom,
% 1.04/1.24 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__neq__iff,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( V_m_2 != V_nb_2
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.24 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__iff__add,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.24 <=> ? [B_k] : V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__add__commute,axiom,
% 1.04/1.24 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zadd__commute,axiom,
% 1.04/1.24 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__le__linear,axiom,
% 1.04/1.24 ! [V_n,V_m] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.04/1.24 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zle__linear,axiom,
% 1.04/1.24 ! [V_w,V_z] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.04/1.24 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__less__le,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.24 & V_m_2 != V_nb_2 ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zless__le,axiom,
% 1.04/1.24 ! [V_w_2,V_z_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2)
% 1.04/1.24 & V_z_2 != V_w_2 ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__eq__less__or__eq,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.24 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.24 | V_m_2 = V_nb_2 ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zless__linear,axiom,
% 1.04/1.24 ! [V_y,V_x] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 1.04/1.24 | V_x = V_y
% 1.04/1.24 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zadd__left__commute,axiom,
% 1.04/1.24 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__add__left__commute,axiom,
% 1.04/1.24 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__add__assoc,axiom,
% 1.04/1.24 ! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zadd__assoc,axiom,
% 1.04/1.24 ! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__add__left__cancel,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.24 ( 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_nb_2)
% 1.04/1.24 <=> V_m_2 = V_nb_2 ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__add__right__cancel,axiom,
% 1.04/1.24 ! [V_nb_2,V_k_2,V_m_2] :
% 1.04/1.24 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2)
% 1.04/1.24 <=> V_m_2 = V_nb_2 ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__add__left__cancel__less,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.24 ( 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_nb_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_nat__add__left__cancel__le,axiom,
% 1.04/1.24 ! [V_nb_2,V_m_2,V_k_2] :
% 1.04/1.24 ( 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_nb_2))
% 1.04/1.24 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_linorder__neqE__nat,axiom,
% 1.04/1.24 ! [V_y,V_x] :
% 1.04/1.24 ( V_x != V_y
% 1.04/1.24 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__irrefl__nat,axiom,
% 1.04/1.24 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__not__refl2,axiom,
% 1.04/1.24 ! [V_m,V_n] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.04/1.24 => V_m != V_n ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__not__refl3,axiom,
% 1.04/1.24 ! [V_t,V_s] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 1.04/1.24 => V_s != V_t ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_eq__imp__le,axiom,
% 1.04/1.24 ! [V_n,V_m] :
% 1.04/1.24 ( V_m = V_n
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_less__imp__le__nat,axiom,
% 1.04/1.24 ! [V_n,V_m] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_trans__less__add1,axiom,
% 1.04/1.24 ! [V_m,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_trans__less__add2,axiom,
% 1.04/1.24 ! [V_m,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_trans__le__add1,axiom,
% 1.04/1.24 ! [V_m,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_trans__le__add2,axiom,
% 1.04/1.24 ! [V_m,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zadd__strict__right__mono,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__less__mono1,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__le__mono1,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zadd__left__mono,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__neq__implies__less,axiom,
% 1.04/1.24 ! [V_n,V_m] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.04/1.24 => ( V_m != V_n
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zle__trans,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__trans,axiom,
% 1.04/1.24 ! [V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 1.04/1.24 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_le__antisym,axiom,
% 1.04/1.24 ! [V_n,V_m] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.04/1.24 => V_m = V_n ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_zle__antisym,axiom,
% 1.04/1.24 ! [V_w,V_z] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 1.04/1.24 => V_z = V_w ) ) ).
% 1.04/1.24
% 1.04/1.24 fof(fact_add__less__mono,axiom,
% 1.04/1.24 ! [V_l,V_k,V_j,V_i] :
% 1.04/1.24 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.04/1.24 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.04/1.24 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_zadd__zless__mono,axiom,
% 1.04/1.25 ! [V_z,V_z_H,V_w,V_w_H] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__le__mono,axiom,
% 1.04/1.25 ! [V_l,V_k,V_j,V_i] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_less__add__eq__less,axiom,
% 1.04/1.25 ! [V_n,V_m,V_l,V_k] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.04/1.25 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__lessD1,axiom,
% 1.04/1.25 ! [V_k,V_j,V_i] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__leD2,axiom,
% 1.04/1.25 ! [V_n,V_k,V_m] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__leD1,axiom,
% 1.04/1.25 ! [V_n,V_k,V_m] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__leE,axiom,
% 1.04/1.25 ! [V_n,V_k,V_m] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.04/1.25 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.04/1.25 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_less__or__eq__imp__le,axiom,
% 1.04/1.25 ! [V_n,V_m] :
% 1.04/1.25 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.04/1.25 | V_m = V_n )
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_nat__less__cases,axiom,
% 1.04/1.25 ! [V_P_2,V_nb_2,V_m_2] :
% 1.04/1.25 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.25 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 1.04/1.25 => ( ( V_m_2 = V_nb_2
% 1.04/1.25 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 1.04/1.25 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 1.04/1.25 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 1.04/1.25 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__add__left__mono,axiom,
% 1.04/1.25 ! [V_z,V_y,V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_less__eq__real__def,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.04/1.25 | V_x_2 = V_y_2 ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__less__def,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.04/1.25 & V_x_2 != V_y_2 ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_zero__reorient,axiom,
% 1.04/1.25 ! [V_x_2,T_a] :
% 1.04/1.25 ( class_Groups_Ozero(T_a)
% 1.04/1.25 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 1.04/1.25 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oab__semigroup__mult(T_a)
% 1.04/1.25 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oab__semigroup__add(T_a)
% 1.04/1.25 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__left__cancel,axiom,
% 1.04/1.25 ! [V_c_2,V_ba_2,V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.04/1.25 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ba_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
% 1.04/1.25 <=> V_ba_2 = V_c_2 ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__right__cancel,axiom,
% 1.04/1.25 ! [V_c_2,V_a_2,V_ba_2,T_a] :
% 1.04/1.25 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.04/1.25 => ( c_Groups_Oplus__class_Oplus(T_a,V_ba_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
% 1.04/1.25 <=> V_ba_2 = V_c_2 ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__left__imp__eq,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.04/1.25 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.04/1.25 => V_b = V_c ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__imp__eq,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.04/1.25 => V_b = V_c ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__right__imp__eq,axiom,
% 1.04/1.25 ! [V_c,V_a,V_b,T_a] :
% 1.04/1.25 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.04/1.25 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 1.04/1.25 => V_b = V_c ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 1.04/1.25 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 1.04/1.25 ! [V_y,V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__commute,axiom,
% 1.04/1.25 ! [V_w,V_z] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_w) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w,V_z) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__assoc,axiom,
% 1.04/1.25 ! [V_z3,V_z2,V_z1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_z2),V_z3) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_z3)) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__right__cancel,axiom,
% 1.04/1.25 ! [V_ba_2,V_a_2,V_c_2] :
% 1.04/1.25 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.04/1.25 => ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ba_2,V_c_2)
% 1.04/1.25 <=> V_a_2 = V_ba_2 ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__left__cancel,axiom,
% 1.04/1.25 ! [V_ba_2,V_a_2,V_c_2] :
% 1.04/1.25 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.04/1.25 => ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_ba_2)
% 1.04/1.25 <=> V_a_2 = V_ba_2 ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__less__iff1,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,V_z_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_z_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__order,axiom,
% 1.04/1.25 ! [V_y,V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__less__mono2,axiom,
% 1.04/1.25 ! [V_y,V_x,V_z] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__add__mult__distrib,axiom,
% 1.04/1.25 ! [V_w,V_z2,V_z1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w)) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__two__squares__add__zero__iff,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2] :
% 1.04/1.25 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.04/1.25 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.04/1.25 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__le__cancel__iff2,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,V_z_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z_2,V_x_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z_2,V_y_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__le__cancel__iff1,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,V_z_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2,V_z_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__0__left,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Omonoid__add(T_a)
% 1.04/1.25 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__0,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.04/1.25 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_double__zero__sym,axiom,
% 1.04/1.25 ! [V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.04/1.25 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 1.04/1.25 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__0__right,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Omonoid__add(T_a)
% 1.04/1.25 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add_Ocomm__neutral,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.04/1.25 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__le__cancel__right,axiom,
% 1.04/1.25 ! [V_ba_2,V_c_2,V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.04/1.25 => ( 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_ba_2,V_c_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_ba_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__le__cancel__left,axiom,
% 1.04/1.25 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.04/1.25 => ( 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_ba_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_ba_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__right__mono,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__left__mono,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__mono,axiom,
% 1.04/1.25 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__le__imp__le__right,axiom,
% 1.04/1.25 ! [V_b,V_c,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__le__imp__le__left,axiom,
% 1.04/1.25 ! [V_b,V_a,V_c,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__less__cancel__right,axiom,
% 1.04/1.25 ! [V_ba_2,V_c_2,V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.04/1.25 => ( 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_ba_2,V_c_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__less__cancel__left,axiom,
% 1.04/1.25 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.04/1.25 => ( 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_ba_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__strict__right__mono,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__strict__left__mono,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__strict__mono,axiom,
% 1.04/1.25 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__less__imp__less__right,axiom,
% 1.04/1.25 ! [V_b,V_c,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__less__imp__less__left,axiom,
% 1.04/1.25 ! [V_b,V_a,V_c,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.04/1.25 ! [V_y,V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 1.04/1.25 ! [V_n,V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__nonpos__nonpos,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__increasing2,axiom,
% 1.04/1.25 ! [V_a,V_b,V_c,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__increasing,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__nonneg__eq__0__iff,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 1.04/1.25 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.25 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.25 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__nonneg__nonneg,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.04/1.25 ! [V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.04/1.25 ! [V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__neg__neg,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__pos__pos,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.04/1.25 ! [V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.04/1.25 ! [V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__less__le__mono,axiom,
% 1.04/1.25 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__le__less__mono,axiom,
% 1.04/1.25 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_number__of2,axiom,
% 1.04/1.25 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)) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__nonpos__neg,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__neg__nonpos,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 1.04/1.25 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.04/1.25 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_unique__quotient__lemma__neg,axiom,
% 1.04/1.25 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q),V_r))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_zdiv__mono2__lemma,axiom,
% 1.04/1.25 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.04/1.25 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H)
% 1.04/1.25 => ( 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_unique__quotient__lemma,axiom,
% 1.04/1.25 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_q),V_r))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_q__neg__lemma,axiom,
% 1.04/1.25 ! [V_r_H,V_q_H,V_b_H] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__le__antisym,axiom,
% 1.04/1.25 ! [V_w,V_z] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 1.04/1.25 => V_z = V_w ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__le__trans,axiom,
% 1.04/1.25 ! [V_k,V_j,V_i] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__le__linear,axiom,
% 1.04/1.25 ! [V_w,V_z] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.04/1.25 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__le__refl,axiom,
% 1.04/1.25 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_q__pos__lemma,axiom,
% 1.04/1.25 ! [V_r_H,V_q_H,V_b_H] :
% 1.04/1.25 ( 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H,V_q_H),V_r_H))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_power2__i,axiom,
% 1.04/1.25 c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Complex_Oii,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__refl,axiom,
% 1.04/1.25 ! [V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 1.04/1.25 ! [V_ya,V_xa,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__le__iff,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_NthRoot_Osqrt(V_y_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__le__mono,axiom,
% 1.04/1.25 ! [V_y,V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_i__squared,axiom,
% 1.04/1.25 c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__eq__iff,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2] :
% 1.04/1.25 ( c_NthRoot_Osqrt(V_x_2) = c_NthRoot_Osqrt(V_y_2)
% 1.04/1.25 <=> V_x_2 = V_y_2 ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__power,axiom,
% 1.04/1.25 ! [V_k,V_x] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),V_k) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__mult,axiom,
% 1.04/1.25 ! [V_y,V_x] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__zero,axiom,
% 1.04/1.25 c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__eq__0__iff,axiom,
% 1.04/1.25 ! [V_x_2] :
% 1.04/1.25 ( c_NthRoot_Osqrt(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.04/1.25 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_complex__i__not__number__of,axiom,
% 1.04/1.25 ! [V_w] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__less__mono,axiom,
% 1.04/1.25 ! [V_y,V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__less__iff,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_NthRoot_Osqrt(V_y_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_complex__i__not__zero,axiom,
% 1.04/1.25 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__eq__zero__cancel,axiom,
% 1.04/1.25 ! [V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.04/1.25 => ( c_NthRoot_Osqrt(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.04/1.25 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__ge__zero,axiom,
% 1.04/1.25 ! [V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__le__0__iff,axiom,
% 1.04/1.25 ! [V_x_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__ge__0__iff,axiom,
% 1.04/1.25 ! [V_y_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__gt__0__iff,axiom,
% 1.04/1.25 ! [V_y_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__lt__0__iff,axiom,
% 1.04/1.25 ! [V_x_2] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__not__eq__zero,axiom,
% 1.04/1.25 ! [V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.04/1.25 => c_NthRoot_Osqrt(V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__gt__zero,axiom,
% 1.04/1.25 ! [V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_le__real__sqrt__sumsq,axiom,
% 1.04/1.25 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y,V_y)))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_le__fun__def,axiom,
% 1.04/1.25 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.04/1.25 ( class_Orderings_Oord(T_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.04/1.25 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__linear,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.25 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__eq__iff,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( V_x_2 = V_y_2
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.04/1.25 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__eq__refl,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( V_x = V_y
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_le__funD,axiom,
% 1.04/1.25 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.04/1.25 ( class_Orderings_Oord(T_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__antisym__conv,axiom,
% 1.04/1.25 ! [V_x_2,V_y_2,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_ord__eq__le__trans,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oord(T_a)
% 1.04/1.25 => ( V_a = V_b
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I3_J,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( V_a = V_b
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_ord__le__eq__trans,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oord(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.25 => ( V_b = V_c
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I4_J,axiom,
% 1.04/1.25 ! [V_c,V_a,V_b,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.04/1.25 => ( V_b = V_c
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__antisym,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.04/1.25 => V_x = V_y ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__trans,axiom,
% 1.04/1.25 ! [V_z,V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I5_J,axiom,
% 1.04/1.25 ! [V_x,V_y,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.25 => V_x = V_y ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I6_J,axiom,
% 1.04/1.25 ! [V_z,V_x,V_y,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_le__funE,axiom,
% 1.04/1.25 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.04/1.25 ( class_Orderings_Oord(T_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__le__cases,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__irrefl,axiom,
% 1.04/1.25 ! [V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__neq__iff,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( V_x_2 != V_y_2
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_not__less__iff__gr__or__eq,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.04/1.25 | V_x_2 = V_y_2 ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__less__linear,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 | V_x = V_y
% 1.04/1.25 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__antisym__conv3,axiom,
% 1.04/1.25 ! [V_x_2,V_y_2,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__neqE,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( V_x != V_y
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_less__imp__neq,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => V_x != V_y ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__not__sym,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__imp__not__less,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__imp__not__eq,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => V_x != V_y ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__imp__not__eq2,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => V_y != V_x ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__asym_H,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.25 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I9_J,axiom,
% 1.04/1.25 ! [V_a,V_b,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.04/1.25 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_ord__eq__less__trans,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oord(T_a)
% 1.04/1.25 => ( V_a = V_b
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I1_J,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( V_a = V_b
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_ord__less__eq__trans,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oord(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.04/1.25 => ( V_b = V_c
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I2_J,axiom,
% 1.04/1.25 ! [V_c,V_a,V_b,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.04/1.25 => ( V_b = V_c
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__trans,axiom,
% 1.04/1.25 ! [V_z,V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I10_J,axiom,
% 1.04/1.25 ! [V_z,V_x,V_y,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__asym,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__cases,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => ( V_x != V_y
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__mult__self__sum__ge__zero,axiom,
% 1.04/1.25 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y,V_y)))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__two__ge__zero,axiom,
% 1.04/1.25 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__two__gt__zero,axiom,
% 1.04/1.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__unique,axiom,
% 1.04/1.25 ! [V_x,V_y] :
% 1.04/1.25 ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.04/1.25 => c_NthRoot_Osqrt(V_x) = V_y ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__pow2,axiom,
% 1.04/1.25 ! [V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.04/1.25 => c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__pow2__iff,axiom,
% 1.04/1.25 ! [V_x_2] :
% 1.04/1.25 ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x_2
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__pow2__gt__zero,axiom,
% 1.04/1.25 ! [V_x] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__sum__squares__triangle__ineq,axiom,
% 1.04/1.25 ! [V_d,V_b,V_c,V_a] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__sum__squares__ge2,axiom,
% 1.04/1.25 ! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__sum__squares__ge1,axiom,
% 1.04/1.25 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__sum__squares__eq__cancel2,axiom,
% 1.04/1.25 ! [V_y,V_x] :
% 1.04/1.25 ( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_y
% 1.04/1.25 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__sum__squares__eq__cancel,axiom,
% 1.04/1.25 ! [V_y,V_x] :
% 1.04/1.25 ( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_x
% 1.04/1.25 => V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 1.04/1.25 ! [V_ya,V_xa,V_y,V_x] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__not__less,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__not__le,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__le__less__linear,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.25 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__le,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.04/1.25 & V_x_2 != V_y_2 ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_less__le__not__le,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.04/1.25 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__le__less,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 | V_x_2 = V_y_2 ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_leI,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_not__leE,axiom,
% 1.04/1.25 ! [V_x,V_y,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__antisym__conv1,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__neq__le__trans,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( V_a != V_b
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I12_J,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( V_a != V_b
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_leD,axiom,
% 1.04/1.25 ! [V_x,V_y,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.04/1.25 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__imp__le,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_linorder__antisym__conv2,axiom,
% 1.04/1.25 ! [V_y_2,V_x_2,T_a] :
% 1.04/1.25 ( class_Orderings_Olinorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.04/1.25 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.04/1.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__le__imp__less__or__eq,axiom,
% 1.04/1.25 ! [V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 | V_x = V_y ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__le__neq__trans,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.04/1.25 => ( V_a != V_b
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I11_J,axiom,
% 1.04/1.25 ! [V_a,V_b,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.04/1.25 => ( V_a != V_b
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__less__le__trans,axiom,
% 1.04/1.25 ! [V_z,V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I7_J,axiom,
% 1.04/1.25 ! [V_z,V_x,V_y,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_order__le__less__trans,axiom,
% 1.04/1.25 ! [V_z,V_y,V_x,T_a] :
% 1.04/1.25 ( class_Orderings_Opreorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_xt1_I8_J,axiom,
% 1.04/1.25 ! [V_z,V_x,V_y,T_a] :
% 1.04/1.25 ( class_Orderings_Oorder(T_a)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__sum__squares__ge__zero,axiom,
% 1.04/1.25 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_lemma__sqrt__hcomplex__capprox,axiom,
% 1.04/1.25 ! [V_y,V_x,V_u] :
% 1.04/1.25 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.04/1.25 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_power__m1__even,axiom,
% 1.04/1.25 ! [V_n,T_a] :
% 1.04/1.25 ( class_Int_Onumber__ring(T_a)
% 1.04/1.25 => c_Power_Opower__class_Opower(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__ge__abs2,axiom,
% 1.04/1.25 ! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_less__fun__def,axiom,
% 1.04/1.25 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.04/1.25 ( class_Orderings_Oord(T_b)
% 1.04/1.25 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.04/1.25 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.04/1.25 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__power__minus__one,axiom,
% 1.04/1.25 ! [V_n,T_a] :
% 1.04/1.25 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.25 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.25 => c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__eq__1__iff,axiom,
% 1.04/1.25 ! [V_x_2] :
% 1.04/1.25 ( c_NthRoot_Osqrt(V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 1.04/1.25 <=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__divide,axiom,
% 1.04/1.25 ! [V_y,V_x] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__sqrt__one,axiom,
% 1.04/1.25 c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__minus__one,axiom,
% 1.04/1.25 ! [T_a] :
% 1.04/1.25 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.25 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.25 => c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_complex__i__not__one,axiom,
% 1.04/1.25 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__add__abs,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.25 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__add__one__not__less__self,axiom,
% 1.04/1.25 ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_mult__1__left,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Omonoid__mult(T_a)
% 1.04/1.25 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_mult__1,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.04/1.25 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_mult__1__right,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Omonoid__mult(T_a)
% 1.04/1.25 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_mult_Ocomm__neutral,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.04/1.25 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__idempotent,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.25 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_one__reorient,axiom,
% 1.04/1.25 ! [V_x_2,T_a] :
% 1.04/1.25 ( class_Groups_Oone(T_a)
% 1.04/1.25 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 1.04/1.25 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__eq__0,axiom,
% 1.04/1.25 ! [V_a_2,T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.25 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.25 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__zero,axiom,
% 1.04/1.25 ! [T_a] :
% 1.04/1.25 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.25 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_right__inverse__eq,axiom,
% 1.04/1.25 ! [V_a_2,V_ba_2,T_a] :
% 1.04/1.25 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.25 => ( V_ba_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.25 => ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_ba_2) = c_Groups_Oone__class_Oone(T_a)
% 1.04/1.25 <=> V_a_2 = V_ba_2 ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_divide__self,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.25 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.25 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_divide__self__if,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.04/1.25 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.25 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.04/1.25 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.25 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__zero__not__eq__one,axiom,
% 1.04/1.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_real__mult__1,axiom,
% 1.04/1.25 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z) = V_z ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__mult__self,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.25 => 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)) = c_Groups_Otimes__class_Otimes(T_a,V_a,V_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_abs__mult,axiom,
% 1.04/1.25 ! [V_b,V_a,T_a] :
% 1.04/1.25 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.25 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = 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)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_power__abs,axiom,
% 1.04/1.25 ! [V_n,V_a,T_a] :
% 1.04/1.25 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.25 => c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_divide__zero__left,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.25 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_divide__zero,axiom,
% 1.04/1.25 ! [V_a,T_a] :
% 1.04/1.25 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.04/1.25 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_divide_Ozero,axiom,
% 1.04/1.25 ! [V_y,T_a] :
% 1.04/1.25 ( class_RealVector_Oreal__normed__field(T_a)
% 1.04/1.25 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_times__divide__eq__right,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.25 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_add__divide__distrib,axiom,
% 1.04/1.25 ! [V_c,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.25 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_divide_Oadd,axiom,
% 1.04/1.25 ! [V_ya,V_y,V_x,T_a] :
% 1.04/1.25 ( class_RealVector_Oreal__normed__field(T_a)
% 1.04/1.25 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_power__divide,axiom,
% 1.04/1.25 ! [V_n,V_b,V_a,T_a] :
% 1.04/1.25 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.04/1.25 => 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,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_one__neq__zero,axiom,
% 1.04/1.25 ! [T_a] :
% 1.04/1.25 ( class_Rings_Ozero__neq__one(T_a)
% 1.04/1.25 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.04/1.25
% 1.04/1.25 fof(fact_zero__neq__one,axiom,
% 1.04/1.25 ! [T_a] :
% 1.04/1.25 ( class_Rings_Ozero__neq__one(T_a)
% 1.04/1.25 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.26 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.26 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__divide__square__eq,axiom,
% 1.04/1.26 ! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_a),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__one,axiom,
% 1.04/1.26 ! [V_n,T_a] :
% 1.04/1.26 ( class_Groups_Omonoid__mult(T_a)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__one__right,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Groups_Omonoid__mult(T_a)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 1.04/1.26 ! [V_x,T_a] :
% 1.04/1.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_int__0__neq__1,axiom,
% 1.04/1.26 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_nat__mult__eq__1__iff,axiom,
% 1.04/1.26 ! [V_nb_2,V_m_2] :
% 1.04/1.26 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.04/1.26 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.04/1.26 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_nat__mult__1__right,axiom,
% 1.04/1.26 ! [V_n] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 1.04/1.26
% 1.04/1.26 fof(fact_nat__1__eq__mult__iff,axiom,
% 1.04/1.26 ! [V_nb_2,V_m_2] :
% 1.04/1.26 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.04/1.26 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.04/1.26 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_nat__mult__1,axiom,
% 1.04/1.26 ! [V_n] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) = V_n ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zmult__1__right,axiom,
% 1.04/1.26 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zmult__1,axiom,
% 1.04/1.26 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z) = V_z ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__one,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__1,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.26 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__one__over,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.04/1.26 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__add__one__gt__zero,axiom,
% 1.04/1.26 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_odd__1__nat,axiom,
% 1.04/1.26 ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__ge__self,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__le__D1,axiom,
% 1.04/1.26 ! [V_b,V_a,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__ge__zero,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__le__zero__iff,axiom,
% 1.04/1.26 ! [V_a_2,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__of__nonneg,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.26 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__not__less__zero,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zero__less__abs__iff,axiom,
% 1.04/1.26 ! [V_a_2,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
% 1.04/1.26 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__of__pos,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.26 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__mult__less,axiom,
% 1.04/1.26 ! [V_d,V_b,V_c,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,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)),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__triangle__ineq,axiom,
% 1.04/1.26 ! [V_b,V_a,T_a] :
% 1.04/1.26 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_eq__divide__imp,axiom,
% 1.04/1.26 ! [V_b,V_a,V_c,T_a] :
% 1.04/1.26 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.26 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => ( c_Groups_Otimes__class_Otimes(T_a,V_a,V_c) = V_b
% 1.04/1.26 => V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__eq__imp,axiom,
% 1.04/1.26 ! [V_a,V_b,V_c,T_a] :
% 1.04/1.26 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.26 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => ( V_b = c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)
% 1.04/1.26 => c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_nonzero__divide__eq__eq,axiom,
% 1.04/1.26 ! [V_a_2,V_ba_2,V_c_2,T_a] :
% 1.04/1.26 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.26 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => ( c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2) = V_a_2
% 1.04/1.26 <=> V_ba_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_nonzero__eq__divide__eq,axiom,
% 1.04/1.26 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.04/1.26 ( class_Rings_Odivision__ring(T_a)
% 1.04/1.26 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2)
% 1.04/1.26 <=> c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_ba_2 ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_nonzero__power__divide,axiom,
% 1.04/1.26 ! [V_n,V_a,V_b,T_a] :
% 1.04/1.26 ( class_Fields_Ofield(T_a)
% 1.04/1.26 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => 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,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__even__abs,axiom,
% 1.04/1.26 ! [V_x,V_n,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_n)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_n) = c_Power_Opower__class_Opower(T_a,V_x,V_n) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_not__one__le__zero,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zero__le__one,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_not__one__less__zero,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zero__less__one,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_less__1__mult,axiom,
% 1.04/1.26 ! [V_n,V_m,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__0__le__divide__iff,axiom,
% 1.04/1.26 ! [V_y_2,V_x_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.04/1.26 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) )
% 1.04/1.26 & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.04/1.26 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_less__add__one,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 1.04/1.26 ! [V_m,T_a] :
% 1.04/1.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.26 => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)),V_m) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 1.04/1.26 ! [V_a,V_m,T_a] :
% 1.04/1.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.26 => c_Groups_Oplus__class_Oplus(T_a,V_m,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 1.04/1.26 ! [V_m,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.26 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),V_m) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_one__le__power,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__inject__exp,axiom,
% 1.04/1.26 ! [V_nb_2,V_m_2,V_a_2,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
% 1.04/1.26 => ( c_Power_Opower__class_Opower(T_a,V_a_2,V_m_2) = c_Power_Opower__class_Opower(T_a,V_a_2,V_nb_2)
% 1.04/1.26 <=> V_m_2 = V_nb_2 ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__sqrt__abs2,axiom,
% 1.04/1.26 ! [V_x] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__0,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Power_Opower(T_a)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 1.04/1.26 ! [V_x,T_a] :
% 1.04/1.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_One__nat__def,axiom,
% 1.04/1.26 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_Suc__eq__plus1__left,axiom,
% 1.04/1.26 ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_Suc__eq__plus1,axiom,
% 1.04/1.26 ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_mult__eq__self__implies__10,axiom,
% 1.04/1.26 ! [V_n,V_m] :
% 1.04/1.26 ( V_m = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)
% 1.04/1.26 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.04/1.26 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 1.04/1.26 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_int__0__less__1,axiom,
% 1.04/1.26 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_Bit1__def,axiom,
% 1.04/1.26 ! [V_k] : c_Int_OBit1(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_odd__nonzero,axiom,
% 1.04/1.26 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zless__add1__eq,axiom,
% 1.04/1.26 ! [V_z_2,V_w_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.04/1.26 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
% 1.04/1.26 | V_w_2 = V_z_2 ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__sqrt__ge__one,axiom,
% 1.04/1.26 ! [V_x] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__sqrt__le__1__iff,axiom,
% 1.04/1.26 ! [V_x_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__sqrt__ge__1__iff,axiom,
% 1.04/1.26 ! [V_y_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__sqrt__gt__1__iff,axiom,
% 1.04/1.26 ! [V_y_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y_2))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__sqrt__lt__1__iff,axiom,
% 1.04/1.26 ! [V_x_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__eq__mult,axiom,
% 1.04/1.26 ! [V_b,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Oordered__ring__abs(T_a)
% 1.04/1.26 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.26 | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.04/1.26 & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.04/1.26 | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.04/1.26 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = 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)) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__mult__pos,axiom,
% 1.04/1.26 ! [V_y,V_x,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.04/1.26 => 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,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x)) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zero__le__power__abs,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_eq__divide__eq__number__of1,axiom,
% 1.04/1.26 ! [V_w_2,V_ba_2,V_a_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 <=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_ba_2 )
% 1.04/1.26 & ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_eq__divide__eq__number__of,axiom,
% 1.04/1.26 ! [V_c_2,V_ba_2,V_w_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2)
% 1.04/1.26 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2) = V_ba_2 )
% 1.04/1.26 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__eq__eq__number__of,axiom,
% 1.04/1.26 ! [V_w_2,V_c_2,V_ba_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2) = c_Int_Onumber__class_Onumber__of(T_a,V_w_2)
% 1.04/1.26 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => V_ba_2 = c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2) )
% 1.04/1.26 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__eq__eq__number__of1,axiom,
% 1.04/1.26 ! [V_a_2,V_w_2,V_ba_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_a_2
% 1.04/1.26 <=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => V_ba_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) )
% 1.04/1.26 & ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.04/1.26 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__mono__even,axiom,
% 1.04/1.26 ! [V_y,V_x,V_n,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_n)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),c_Groups_Oabs__class_Oabs(T_a,V_y))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_y,V_n)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__Numeral0,axiom,
% 1.04/1.26 ! [V_x,T_a] :
% 1.04/1.26 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber__ring(T_a) )
% 1.04/1.26 => c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__even__abs__number__of,axiom,
% 1.04/1.26 ! [V_x,V_w,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w))
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__numeral__1,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( ( class_Fields_Ofield(T_a)
% 1.04/1.26 & class_Int_Onumber__ring(T_a) )
% 1.04/1.26 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__Numeral1,axiom,
% 1.04/1.26 ! [V_x,T_a] :
% 1.04/1.26 ( ( class_Fields_Ofield(T_a)
% 1.04/1.26 & class_Int_Onumber__ring(T_a) )
% 1.04/1.26 => c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_mult__left__le__one__le,axiom,
% 1.04/1.26 ! [V_y,V_x,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x),V_x) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_mult__right__le__one__le,axiom,
% 1.04/1.26 ! [V_y,V_x,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_x) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zero__less__two,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__gt1__lemma,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__less__power__Suc,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__0__left,axiom,
% 1.04/1.26 ! [V_n,T_a] :
% 1.04/1.26 ( ( class_Power_Opower(T_a)
% 1.04/1.26 & class_Rings_Osemiring__0(T_a) )
% 1.04/1.26 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 1.04/1.26 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_number__of__Bit1,axiom,
% 1.04/1.26 ! [V_w,T_a] :
% 1.04/1.26 ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__gt1,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n))) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__strict__increasing,axiom,
% 1.04/1.26 ! [V_a,V_N,V_n,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__less__imp__less__exp,axiom,
% 1.04/1.26 ! [V_n,V_m,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__strict__increasing__iff,axiom,
% 1.04/1.26 ! [V_y_2,V_x_2,V_ba_2,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_ba_2)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_ba_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_ba_2,V_y_2))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__increasing,axiom,
% 1.04/1.26 ! [V_a,V_N,V_n,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_semiring__norm_I110_J,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 => c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_numeral__1__eq__1,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_Numeral1__eq1__nat,axiom,
% 1.04/1.26 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_nat__numeral__1__eq__1,axiom,
% 1.04/1.26 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_one__is__num__one,axiom,
% 1.04/1.26 c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_int__one__le__iff__zero__less,axiom,
% 1.04/1.26 ! [V_z_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_odd__less__0,axiom,
% 1.04/1.26 ! [V_z_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_pos__zmult__eq__1__iff,axiom,
% 1.04/1.26 ! [V_nb_2,V_m_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)
% 1.04/1.26 => ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m_2,V_nb_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.04/1.26 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.04/1.26 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zless__imp__add1__zle,axiom,
% 1.04/1.26 ! [V_z,V_w] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_add1__zle__eq,axiom,
% 1.04/1.26 ! [V_z_2,V_w_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zle__add1__eq__le,axiom,
% 1.04/1.26 ! [V_z_2,V_w_2] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_zmult__eq__1__iff,axiom,
% 1.04/1.26 ! [V_nb_2,V_m_2] :
% 1.04/1.26 ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m_2,V_nb_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.04/1.26 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.04/1.26 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 1.04/1.26 | ( V_m_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
% 1.04/1.26 & V_nb_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 1.04/1.26 ! [V_n,V_m] :
% 1.04/1.26 ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m,V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.04/1.26 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.04/1.26 | V_m = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_less__divide__eq__number__of1,axiom,
% 1.04/1.26 ! [V_w_2,V_ba_2,V_a_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_ba_2) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_less__divide__eq__number__of,axiom,
% 1.04/1.26 ! [V_c_2,V_ba_2,V_w_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2))
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2),V_ba_2) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__less__eq__number__of,axiom,
% 1.04/1.26 ! [V_w_2,V_c_2,V_ba_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2),V_ba_2) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__less__eq__number__of1,axiom,
% 1.04/1.26 ! [V_a_2,V_w_2,V_ba_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_a_2)
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_ba_2) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_convex__bound__le,axiom,
% 1.04/1.26 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semiring__1(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.04/1.26 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__Suc__less,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_realpow__Suc__le__self,axiom,
% 1.04/1.26 ! [V_n,V_r,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_r,c_Nat_OSuc(V_n)),V_r) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__Suc__less__one,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__strict__decreasing,axiom,
% 1.04/1.26 ! [V_a,V_N,V_n,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_double__number__of__Bit0,axiom,
% 1.04/1.26 ! [V_w,T_a] :
% 1.04/1.26 ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 => 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)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__decreasing,axiom,
% 1.04/1.26 ! [V_a,V_N,V_n,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__le__imp__le__exp,axiom,
% 1.04/1.26 ! [V_n,V_m,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__increasing__iff,axiom,
% 1.04/1.26 ! [V_y_2,V_x_2,V_ba_2,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_ba_2)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_ba_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_ba_2,V_y_2))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_one__less__power,axiom,
% 1.04/1.26 ! [V_n,V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semidom(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power__0__left__number__of,axiom,
% 1.04/1.26 ! [V_w,T_a] :
% 1.04/1.26 ( ( class_Power_Opower(T_a)
% 1.04/1.26 & class_Rings_Osemiring__0(T_a) )
% 1.04/1.26 => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.26 => 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) )
% 1.04/1.26 & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.04/1.26 => 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) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_neg__one__even__power,axiom,
% 1.04/1.26 ! [V_x,T_a] :
% 1.04/1.26 ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),V_x) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_neg__one__even__odd__power,axiom,
% 1.04/1.26 ! [V_x,T_a] :
% 1.04/1.26 ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 => ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),V_x) = c_Groups_Oone__class_Oone(T_a) )
% 1.04/1.26 & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin),V_x) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_le__imp__0__less,axiom,
% 1.04/1.26 ! [V_z] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_real__sqrt__sum__squares__less,axiom,
% 1.04/1.26 ! [V_y,V_u,V_x] :
% 1.04/1.26 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 1.04/1.26 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_abs__power2,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_power2__abs,axiom,
% 1.04/1.26 ! [V_a,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__idom(T_a)
% 1.04/1.26 => c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__le__eq__number__of1,axiom,
% 1.04/1.26 ! [V_a_2,V_w_2,V_ba_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_a_2)
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_ba_2) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_divide__le__eq__number__of,axiom,
% 1.04/1.26 ! [V_w_2,V_c_2,V_ba_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2),V_ba_2) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_le__divide__eq__number__of,axiom,
% 1.04/1.26 ! [V_c_2,V_ba_2,V_w_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2))
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2),V_ba_2) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.04/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),V_c_2)) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_le__divide__eq__number__of1,axiom,
% 1.04/1.26 ! [V_w_2,V_ba_2,V_a_2,T_a] :
% 1.04/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.04/1.26 & class_Int_Onumber(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
% 1.04/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_ba_2) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 1.04/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) )
% 1.04/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.04/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_convex__bound__lt,axiom,
% 1.04/1.26 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.04/1.26 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.04/1.26 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.04/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a) ) ) ) ) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_le__special_I2_J,axiom,
% 1.04/1.26 ! [V_y_2,T_a] :
% 1.04/1.26 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_le__special_I4_J,axiom,
% 1.04/1.26 ! [V_x_2,T_a] :
% 1.04/1.26 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_one__add__one__is__two,axiom,
% 1.04/1.26 ! [T_a] :
% 1.04/1.26 ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_less__special_I2_J,axiom,
% 1.04/1.26 ! [V_y_2,T_a] :
% 1.04/1.26 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 & class_Rings_Olinordered__idom(T_a) )
% 1.04/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.04/1.26 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ) ).
% 1.04/1.26
% 1.04/1.26 fof(fact_less__special_I4_J,axiom,
% 1.04/1.26 ! [V_x_2,T_a] :
% 1.04/1.26 ( ( class_Int_Onumber__ring(T_a)
% 1.04/1.26 & class_Rings_Olinordered__idom(T_a) )
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.14/1.26 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_add__special_I2_J,axiom,
% 1.14/1.26 ! [V_w,T_a] :
% 1.14/1.26 ( class_Int_Onumber__ring(T_a)
% 1.14/1.26 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_add__special_I3_J,axiom,
% 1.14/1.26 ! [V_v,T_a] :
% 1.14/1.26 ( class_Int_Onumber__ring(T_a)
% 1.14/1.26 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls))) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_one__power2,axiom,
% 1.14/1.26 ! [T_a] :
% 1.14/1.26 ( class_Rings_Osemiring__1(T_a)
% 1.14/1.26 => c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_nat__1__add__1,axiom,
% 1.14/1.26 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_self__quotient__aux2,axiom,
% 1.14/1.26 ! [V_q,V_r,V_a] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.14/1.26 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_q))
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_self__quotient__aux1,axiom,
% 1.14/1.26 ! [V_q,V_r,V_a] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.14/1.26 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_q))
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_half__gt__zero__iff,axiom,
% 1.14/1.26 ! [V_r_2,T_a] :
% 1.14/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 & class_Int_Onumber__ring(T_a) )
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.14/1.26 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r_2) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_half__gt__zero,axiom,
% 1.14/1.26 ! [V_r,T_a] :
% 1.14/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 & class_Int_Onumber__ring(T_a) )
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_real__sqrt__abs,axiom,
% 1.14/1.26 ! [V_x] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_real__less__half__sum,axiom,
% 1.14/1.26 ! [V_y,V_x] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_real__gt__half__sum,axiom,
% 1.14/1.26 ! [V_y,V_x] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_two__realpow__ge__one,axiom,
% 1.14/1.26 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_real__sqrt__two__gt__one,axiom,
% 1.14/1.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_lemma__real__divide__sqrt__less,axiom,
% 1.14/1.26 ! [V_u] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
% 1.14/1.26 ! [V_x] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 1.14/1.26 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.14/1.26 | V_x = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_real__sqrt__ge__abs1,axiom,
% 1.14/1.26 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_cos__x__y__le__one,axiom,
% 1.14/1.26 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_half,axiom,
% 1.14/1.26 ! [T_a] :
% 1.14/1.26 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 & class_Int_Onumber__ring(T_a) )
% 1.14/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_less__one__imp__sqr__less__one,axiom,
% 1.14/1.26 ! [V_x] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.14/1.26 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_abs__zmult__eq__1,axiom,
% 1.14/1.26 ! [V_n,V_m] :
% 1.14/1.26 ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m,V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.14/1.26 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_zabs__less__one__iff,axiom,
% 1.14/1.26 ! [V_z_2] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
% 1.14/1.26 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_zero__le__zpower__abs,axiom,
% 1.14/1.26 ! [V_n,V_x] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x),V_n)) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_zero__less__zpower__abs__iff,axiom,
% 1.14/1.26 ! [V_nb_2,V_x_2] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2),V_nb_2))
% 1.14/1.26 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.14/1.26 | V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_le__Suc__ex__iff,axiom,
% 1.14/1.26 ! [V_l_2,V_k_2] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 1.14/1.26 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_rabs__ratiotest__lemma,axiom,
% 1.14/1.26 ! [V_y,V_x,V_c] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
% 1.14/1.26 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_real__sum__of__halves,axiom,
% 1.14/1.26 ! [V_x] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x ).
% 1.14/1.26
% 1.14/1.26 fof(fact_eq__divide__2__times__iff,axiom,
% 1.14/1.26 ! [V_z_2,V_y_2,V_x_2] :
% 1.14/1.26 ( V_x_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_z_2))
% 1.14/1.26 <=> c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_x_2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_z_2) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_IH,axiom,
% 1.14/1.26 ! [B_m] :
% 1.14/1.26 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,v_na____)
% 1.14/1.26 => ( B_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.14/1.26 => ? [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),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_b,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,B_z,B_m)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_le__divide__eq,axiom,
% 1.14/1.26 ! [V_c_2,V_ba_2,V_a_2,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2))
% 1.14/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_ba_2) )
% 1.14/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.26 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) )
% 1.14/1.26 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_abs__norm__cancel,axiom,
% 1.14/1.26 ! [V_a,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__zero,axiom,
% 1.14/1.26 ! [T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__eq__zero,axiom,
% 1.14/1.26 ! [V_x_2,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.14/1.26 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__mult,axiom,
% 1.14/1.26 ! [V_y,V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.14/1.26 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_complex__mod__triangle__sub,axiom,
% 1.14/1.26 ! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__divide,axiom,
% 1.14/1.26 ! [V_b,V_a,T_a] :
% 1.14/1.26 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.26 & class_RealVector_Oreal__normed__field(T_a) )
% 1.14/1.26 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__power,axiom,
% 1.14/1.26 ! [V_n,V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.14/1.26 => c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__not__less__zero,axiom,
% 1.14/1.26 ! [V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__ge__zero,axiom,
% 1.14/1.26 ! [V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__one,axiom,
% 1.14/1.26 ! [T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.14/1.26 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__le__zero__iff,axiom,
% 1.14/1.26 ! [V_x_2,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.14/1.26 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_zero__less__norm__iff,axiom,
% 1.14/1.26 ! [V_x_2,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
% 1.14/1.26 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__mult__ineq,axiom,
% 1.14/1.26 ! [V_y,V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__mult__less,axiom,
% 1.14/1.26 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r,V_s)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_nonzero__norm__divide,axiom,
% 1.14/1.26 ! [V_a,V_b,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__field(T_a)
% 1.14/1.26 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__triangle__ineq,axiom,
% 1.14/1.26 ! [V_y,V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__add__less,axiom,
% 1.14/1.26 ! [V_s,V_y,V_r,V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__power__ineq,axiom,
% 1.14/1.26 ! [V_n,V_x,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_n)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__number__of,axiom,
% 1.14/1.26 ! [V_w,T_a] :
% 1.14/1.26 ( ( class_Int_Onumber__ring(T_a)
% 1.14/1.26 & class_RealVector_Oreal__normed__algebra__1(T_a) )
% 1.14/1.26 => c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_norm__ratiotest__lemma,axiom,
% 1.14/1.26 ! [V_y,V_x,V_c,T_a] :
% 1.14/1.26 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c,c_RealVector_Onorm__class_Onorm(T_a,V_y)))
% 1.14/1.26 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_times__divide__times__eq,axiom,
% 1.14/1.26 ! [V_w,V_z,V_y,V_x,T_a] :
% 1.14/1.26 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.26 => c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_abs__divide,axiom,
% 1.14/1.26 ! [V_b,V_a,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__right__mono__neg,axiom,
% 1.14/1.26 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__right__mono,axiom,
% 1.14/1.26 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__le__0__iff,axiom,
% 1.14/1.26 ! [V_ba_2,V_a_2,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_ba_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.14/1.26 & c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.14/1.26 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ba_2) ) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_zero__le__divide__iff,axiom,
% 1.14/1.26 ! [V_ba_2,V_a_2,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_ba_2))
% 1.14/1.26 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.14/1.26 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ba_2) )
% 1.14/1.26 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 & c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_zero__less__divide__iff,axiom,
% 1.14/1.26 ! [V_ba_2,V_a_2,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_ba_2))
% 1.14/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.14/1.26 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ba_2) )
% 1.14/1.26 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 & c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__less__0__iff,axiom,
% 1.14/1.26 ! [V_ba_2,V_a_2,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_ba_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.14/1.26 & c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.14/1.26 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ba_2) ) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__pos__pos,axiom,
% 1.14/1.26 ! [V_y,V_x,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__pos__neg,axiom,
% 1.14/1.26 ! [V_y,V_x,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__neg__pos,axiom,
% 1.14/1.26 ! [V_y,V_x,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__neg__neg,axiom,
% 1.14/1.26 ! [V_y,V_x,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__strict__right__mono,axiom,
% 1.14/1.26 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.14/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__strict__right__mono__neg,axiom,
% 1.14/1.26 ! [V_c,V_a,V_b,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_frac__eq__eq,axiom,
% 1.14/1.26 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] :
% 1.14/1.26 ( class_Fields_Ofield(T_a)
% 1.14/1.26 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => ( c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2)
% 1.14/1.26 <=> c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2) = c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2) ) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_mult__divide__mult__cancel__left,axiom,
% 1.14/1.26 ! [V_b,V_a,V_c,T_a] :
% 1.14/1.26 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.26 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_mult__divide__mult__cancel__right,axiom,
% 1.14/1.26 ! [V_b,V_a,V_c,T_a] :
% 1.14/1.26 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.26 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__eq__eq,axiom,
% 1.14/1.26 ! [V_a_2,V_c_2,V_ba_2,T_a] :
% 1.14/1.26 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.26 => ( c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2) = V_a_2
% 1.14/1.26 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => V_ba_2 = c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) )
% 1.14/1.26 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_eq__divide__eq,axiom,
% 1.14/1.26 ! [V_c_2,V_ba_2,V_a_2,T_a] :
% 1.14/1.26 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.26 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2)
% 1.14/1.26 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2) = V_ba_2 )
% 1.14/1.26 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_nonzero__abs__divide,axiom,
% 1.14/1.26 ! [V_a,V_b,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.26 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.26 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 1.14/1.26
% 1.14/1.26 fof(fact_divide__nonpos__neg,axiom,
% 1.14/1.26 ! [V_y,V_x,T_a] :
% 1.14/1.26 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.26 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__nonpos__pos,axiom,
% 1.14/1.27 ! [V_y,V_x,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_frac__le,axiom,
% 1.14/1.27 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_frac__less,axiom,
% 1.14/1.27 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_frac__less2,axiom,
% 1.14/1.27 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__nonneg__neg,axiom,
% 1.14/1.27 ! [V_y,V_x,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__nonneg__pos,axiom,
% 1.14/1.27 ! [V_y,V_x,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_less__divide__eq,axiom,
% 1.14/1.27 ! [V_c_2,V_ba_2,V_a_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2))
% 1.14/1.27 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_ba_2) )
% 1.14/1.27 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) )
% 1.14/1.27 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__less__eq,axiom,
% 1.14/1.27 ! [V_a_2,V_c_2,V_ba_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2),V_a_2)
% 1.14/1.27 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) )
% 1.14/1.27 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_ba_2) )
% 1.14/1.27 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_pos__less__divide__eq,axiom,
% 1.14/1.27 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2))
% 1.14/1.27 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_ba_2) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_pos__divide__less__eq,axiom,
% 1.14/1.27 ! [V_a_2,V_ba_2,V_c_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2),V_a_2)
% 1.14/1.27 <=> c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mult__imp__div__pos__less,axiom,
% 1.14/1.27 ! [V_z,V_x,V_y,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mult__imp__less__div__pos,axiom,
% 1.14/1.27 ! [V_x,V_z,V_y,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neg__less__divide__eq,axiom,
% 1.14/1.27 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2))
% 1.14/1.27 <=> c_Orderings_Oord__class_Oless(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neg__divide__less__eq,axiom,
% 1.14/1.27 ! [V_a_2,V_ba_2,V_c_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2),V_a_2)
% 1.14/1.27 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_ba_2) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__strict__left__mono,axiom,
% 1.14/1.27 ! [V_c,V_a,V_b,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__strict__left__mono__neg,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_add__num__frac,axiom,
% 1.14/1.27 ! [V_x,V_z,V_y,T_a] :
% 1.14/1.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.27 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.27 => c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_add__divide__eq__iff,axiom,
% 1.14/1.27 ! [V_y,V_x,V_z,T_a] :
% 1.14/1.27 ( class_Fields_Ofield(T_a)
% 1.14/1.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.27 => c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_add__frac__num,axiom,
% 1.14/1.27 ! [V_z,V_x,V_y,T_a] :
% 1.14/1.27 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.27 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.27 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__add__eq__iff,axiom,
% 1.14/1.27 ! [V_y,V_x,V_z,T_a] :
% 1.14/1.27 ( class_Fields_Ofield(T_a)
% 1.14/1.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.27 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_add__frac__eq,axiom,
% 1.14/1.27 ! [V_w,V_x,V_z,V_y,T_a] :
% 1.14/1.27 ( class_Fields_Ofield(T_a)
% 1.14/1.27 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.27 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.27 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_gt__half__sum,axiom,
% 1.14/1.27 ! [V_b,V_a,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_less__half__sum,axiom,
% 1.14/1.27 ! [V_b,V_a,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_abs__div__pos,axiom,
% 1.14/1.27 ! [V_x,V_y,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.27 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__left__mono__neg,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__left__mono,axiom,
% 1.14/1.27 ! [V_c,V_a,V_b,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neg__divide__le__eq,axiom,
% 1.14/1.27 ! [V_a_2,V_ba_2,V_c_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2),V_a_2)
% 1.14/1.27 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_ba_2) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neg__le__divide__eq,axiom,
% 1.14/1.27 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2))
% 1.14/1.27 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mult__imp__le__div__pos,axiom,
% 1.14/1.27 ! [V_x,V_z,V_y,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mult__imp__div__pos__le,axiom,
% 1.14/1.27 ! [V_z,V_x,V_y,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y))
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_pos__divide__le__eq,axiom,
% 1.14/1.27 ! [V_a_2,V_ba_2,V_c_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2),V_a_2)
% 1.14/1.27 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_pos__le__divide__eq,axiom,
% 1.14/1.27 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2))
% 1.14/1.27 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_ba_2) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divide__le__eq,axiom,
% 1.14/1.27 ! [V_a_2,V_c_2,V_ba_2,T_a] :
% 1.14/1.27 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_ba_2,V_c_2),V_a_2)
% 1.14/1.27 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2)) )
% 1.14/1.27 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.14/1.27 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_c_2),V_ba_2) )
% 1.14/1.27 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_calculation,axiom,
% 1.14/1.27 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
% 1.14/1.27 => ? [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),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_b,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,B_z,v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_arctan__half,axiom,
% 1.14/1.27 ! [V_x] : c_Transcendental_Oarctan(V_x) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_real__norm__def,axiom,
% 1.14/1.27 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_arctan__monotone_H,axiom,
% 1.14/1.27 ! [V_y,V_x] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_arctan__zero__zero,axiom,
% 1.14/1.27 c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_arctan__monotone,axiom,
% 1.14/1.27 ! [V_y,V_x] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_th0,axiom,
% 1.14/1.27 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_b)),v_b)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_pos__zmod__mult__2,axiom,
% 1.14/1.27 ! [V_b,V_a] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_b)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_a)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_norm__of__real,axiom,
% 1.14/1.27 ! [V_r,T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.14/1.27 => c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__neg__neg__trivial,axiom,
% 1.14/1.27 ! [V_b,V_a] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neg__mod__conj,axiom,
% 1.14/1.27 ! [V_a,V_b] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neg__mod__sign,axiom,
% 1.14/1.27 ! [V_a,V_b] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__pos__pos__trivial,axiom,
% 1.14/1.27 ! [V_b,V_a] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_pos__mod__conj,axiom,
% 1.14/1.27 ! [V_a,V_b] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))
% 1.14/1.27 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_pos__mod__sign,axiom,
% 1.14/1.27 ! [V_a,V_b] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_nonzero__of__real__divide,axiom,
% 1.14/1.27 ! [V_x,V_y,T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__field(T_a)
% 1.14/1.27 => ( V_y != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__minus1__right,axiom,
% 1.14/1.27 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__right__eq,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__left__eq,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__eq,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__mult1,axiom,
% 1.14/1.27 ! [V_b,V_a,V_c,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)) = c_Groups_Otimes__class_Otimes(T_a,V_c,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__mult2,axiom,
% 1.14/1.27 ! [V_b,V_c,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) = c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__simps_I4_J,axiom,
% 1.14/1.27 ! [V_b,V_c,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__cong,axiom,
% 1.14/1.27 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 1.14/1.27 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b_H),V_c) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__zmult1__eq,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__simps_I3_J,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_b),V_c) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__self2__is__0,axiom,
% 1.14/1.27 ! [V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__self1__is__0,axiom,
% 1.14/1.27 ! [V_a,V_b,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__0,axiom,
% 1.14/1.27 ! [T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real_Ozero,axiom,
% 1.14/1.27 ! [T_a] :
% 1.14/1.27 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__eq__0__iff,axiom,
% 1.14/1.27 ! [V_x_2,T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 => ( c_RealVector_Oof__real(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.14/1.27 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__mult,axiom,
% 1.14/1.27 ! [V_y,V_x,T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Otimes__class_Otimes(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__self,axiom,
% 1.14/1.27 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__zero,axiom,
% 1.14/1.27 ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__self,axiom,
% 1.14/1.27 ! [V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__by__0,axiom,
% 1.14/1.27 ! [V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__0,axiom,
% 1.14/1.27 ! [V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zpower__zmod,axiom,
% 1.14/1.27 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),V_m) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mod__trivial,axiom,
% 1.14/1.27 ! [V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__eq__iff,axiom,
% 1.14/1.27 ! [V_y_2,V_x_2,T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 => ( c_RealVector_Oof__real(T_a,V_x_2) = c_RealVector_Oof__real(T_a,V_y_2)
% 1.14/1.27 <=> V_x_2 = V_y_2 ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_complex__of__real__power,axiom,
% 1.14/1.27 ! [V_n,V_x] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,V_x),V_n) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_n)) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__divide,axiom,
% 1.14/1.27 ! [V_y,V_x,T_a] :
% 1.14/1.27 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.14/1.27 & class_RealVector_Oreal__field(T_a) )
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__eq__0__iff,axiom,
% 1.14/1.27 ! [V_d_2,V_m_2] :
% 1.14/1.27 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.14/1.27 <=> ? [B_q] : V_m_2 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_d_2,B_q) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__power,axiom,
% 1.14/1.27 ! [V_n,V_x,T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_n)) = c_Power_Opower__class_Opower(T_a,c_RealVector_Oof__real(T_a,V_x),V_n) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neg__mod__bound,axiom,
% 1.14/1.27 ! [V_a,V_b] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_pos__mod__bound,axiom,
% 1.14/1.27 ! [V_a,V_b] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.14/1.27 ! [V_y,V_x] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__le__nonneg__dividend,axiom,
% 1.14/1.27 ! [V_k,V_m] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k),V_m) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__number__of__eq,axiom,
% 1.14/1.27 ! [V_w,T_a] :
% 1.14/1.27 ( ( class_Int_Onumber__ring(T_a)
% 1.14/1.27 & class_RealVector_Oreal__algebra__1(T_a) )
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,V_w) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__by__1,axiom,
% 1.14/1.27 ! [V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__1,axiom,
% 1.14/1.27 ! [T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real__add,axiom,
% 1.14/1.27 ! [V_y,V_x,T_a] :
% 1.14/1.27 ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_of__real_Oadd,axiom,
% 1.14/1.27 ! [V_y,V_x,T_a] :
% 1.14/1.27 ( ( class_RealVector_Oreal__algebra__1(T_a)
% 1.14/1.27 & class_RealVector_Oreal__normed__vector(T_a) )
% 1.14/1.27 => c_RealVector_Oof__real(T_a,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__add__self2,axiom,
% 1.14/1.27 ! [V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__add__self1,axiom,
% 1.14/1.27 ! [V_a,V_b,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__add__right__eq,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__add__left__eq,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__add__eq,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__simps_I2_J,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__simps_I1_J,axiom,
% 1.14/1.27 ! [V_b,V_c,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__add__cong,axiom,
% 1.14/1.27 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 1.14/1.27 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_H,V_b_H),V_c) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__self2,axiom,
% 1.14/1.27 ! [V_c,V_b,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__mult__self1,axiom,
% 1.14/1.27 ! [V_b,V_c,V_a,T_a] :
% 1.14/1.27 ( class_Divides_Osemiring__div(T_a)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_mod__pos__neg__trivial,axiom,
% 1.14/1.27 ! [V_b,V_a] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_i__mult__eq,axiom,
% 1.14/1.27 c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Oii) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__number__of__Bit0,axiom,
% 1.14/1.27 ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_divmod__int__rel__mod__eq,axiom,
% 1.14/1.27 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 1.14/1.27 ( V_a_1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_1,V_q_1),V_y)
% 1.14/1.27 => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.14/1.27 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_b_1) ) )
% 1.14/1.27 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_y)
% 1.14/1.27 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
% 1.14/1.27 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.14/1.27 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmult2__lemma__aux2,axiom,
% 1.14/1.27 ! [V_q,V_r,V_b,V_c] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmult2__lemma__aux1,axiom,
% 1.14/1.27 ! [V_q,V_r,V_b,V_c] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_c),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmult2__lemma__aux4,axiom,
% 1.14/1.27 ! [V_q,V_b,V_r,V_c] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.14/1.27 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_c)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmult2__lemma__aux3,axiom,
% 1.14/1.27 ! [V_q,V_b,V_r,V_c] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.14/1.27 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.14/1.27 => 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c)),V_r)) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_split__zmod,axiom,
% 1.14/1.27 ! [V_k_2,V_nb_2,V_P_2] :
% 1.14/1.27 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_nb_2,V_k_2)))
% 1.14/1.27 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.14/1.27 => hBOOL(hAPP(V_P_2,V_nb_2)) )
% 1.14/1.27 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.14/1.27 => ! [B_i,B_j] :
% 1.14/1.27 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)
% 1.14/1.27 & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
% 1.14/1.27 & V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2,B_i),B_j) )
% 1.14/1.27 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 1.14/1.27 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => ! [B_i,B_j] :
% 1.14/1.27 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 1.14/1.27 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 & V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2,B_i),B_j) )
% 1.14/1.27 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neq__one__mod__two,axiom,
% 1.14/1.27 ! [V_x_2] :
% 1.14/1.27 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.14/1.27 <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_neg__zmod__mult__2,axiom,
% 1.14/1.27 ! [V_b,V_a] :
% 1.14/1.27 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.14/1.27 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_b)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_a)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_b,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(fact_zmod__number__of__Bit1,axiom,
% 1.14/1.27 ! [V_v,V_w] :
% 1.14/1.27 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))
% 1.14/1.27 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(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_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 1.14/1.27 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))
% 1.14/1.27 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_w))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ).
% 1.14/1.27
% 1.14/1.27 %----Arity declarations (191)
% 1.14/1.27 fof(arity_fun__Orderings_Opreorder,axiom,
% 1.14/1.27 ! [T_2,T_1] :
% 1.14/1.27 ( class_Orderings_Opreorder(T_1)
% 1.14/1.27 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_fun__Orderings_Oorder,axiom,
% 1.14/1.27 ! [T_2,T_1] :
% 1.14/1.27 ( class_Orderings_Oorder(T_1)
% 1.14/1.27 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_fun__Orderings_Oord,axiom,
% 1.14/1.27 ! [T_2,T_1] :
% 1.14/1.27 ( class_Orderings_Oord(T_1)
% 1.14/1.27 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.14/1.27 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.14/1.27 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 1.14/1.27 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 1.14/1.27 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 1.14/1.27 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 1.14/1.27 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 1.14/1.27 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 1.14/1.27 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 1.14/1.27 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 1.14/1.27 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 1.14/1.27 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 1.14/1.27 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 1.14/1.27 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 1.14/1.27 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 1.14/1.27 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 1.14/1.27 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 1.14/1.27 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 1.14/1.27 class_Orderings_Opreorder(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 1.14/1.27 class_Orderings_Olinorder(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 1.14/1.27 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 1.14/1.27 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 1.14/1.27 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 1.14/1.27 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 1.14/1.27 class_Rings_Omult__zero(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 1.14/1.27 class_Orderings_Oorder(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 1.14/1.27 class_Int_Oring__char__0(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 1.14/1.27 class_Int_Onumber__ring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 1.14/1.27 class_Rings_Osemiring(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 1.14/1.27 class_Orderings_Oord(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Power_Opower,axiom,
% 1.14/1.27 class_Power_Opower(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 1.14/1.27 class_Groups_Ozero(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Int_Onumber,axiom,
% 1.14/1.27 class_Int_Onumber(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Int__Oint__Groups_Oone,axiom,
% 1.14/1.27 class_Groups_Oone(tc_Int_Oint) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.14/1.27 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.14/1.27 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 1.14/1.27 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 1.14/1.27 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 1.14/1.27 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 1.14/1.27 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 1.14/1.27 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 1.14/1.27 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 1.14/1.27 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 1.14/1.27 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 1.14/1.27 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 1.14/1.27 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 1.14/1.27 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 1.14/1.27 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 1.14/1.27 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 1.14/1.27 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 1.14/1.27 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 1.14/1.27 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 1.14/1.27 class_Orderings_Oorder(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 1.14/1.27 class_Rings_Osemiring(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 1.14/1.27 class_Orderings_Oord(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Power_Opower,axiom,
% 1.14/1.27 class_Power_Opower(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 1.14/1.27 class_Groups_Ozero(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 1.14/1.27 class_Int_Onumber(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 1.14/1.27 class_Groups_Oone(tc_Nat_Onat) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 1.14/1.27 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 1.14/1.27 class_Orderings_Oorder(tc_HOL_Obool) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 1.14/1.27 class_Orderings_Oord(tc_HOL_Obool) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.14/1.27 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.14/1.27 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 1.14/1.27 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 1.14/1.27 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 1.14/1.27 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 1.14/1.27 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 1.14/1.27 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 1.14/1.27 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 1.14/1.27 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
% 1.14/1.27 class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 1.14/1.27 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 1.14/1.27 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 1.14/1.27 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 1.14/1.27 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 1.14/1.27 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 1.14/1.27 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 1.14/1.27 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 1.14/1.27 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 1.14/1.27 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 1.14/1.27 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 1.14/1.27 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__RealVector_Oreal__field,axiom,
% 1.14/1.27 class_RealVector_Oreal__field(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 1.14/1.27 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 1.14/1.27 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 1.14/1.27 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 1.14/1.27 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 1.14/1.27 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 1.14/1.27 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 1.14/1.27 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 1.14/1.27 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
% 1.14/1.27 class_Rings_Osemiring__1(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 1.14/1.27 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 1.14/1.27 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 1.14/1.27 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 1.14/1.27 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
% 1.14/1.27 class_Int_Onumber__ring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 1.14/1.27 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 1.14/1.27 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 1.14/1.27 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 1.14/1.27 class_Power_Opower(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 1.14/1.27 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Int_Onumber,axiom,
% 1.14/1.27 class_Int_Onumber(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 1.14/1.27 class_Groups_Oone(tc_RealDef_Oreal) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.14/1.27 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 1.14/1.27 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
% 1.14/1.27 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
% 1.14/1.27 class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 1.14/1.27 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 1.14/1.27 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 1.14/1.27 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 1.14/1.27 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 1.14/1.27 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 1.14/1.27 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 1.14/1.27 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
% 1.14/1.27 class_RealVector_Oreal__field(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 1.14/1.27 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 1.14/1.27 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 1.14/1.27 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 1.14/1.27 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 1.14/1.27 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
% 1.14/1.27 class_Rings_Osemiring__1(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 1.14/1.27 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 1.14/1.27 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 1.14/1.27 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
% 1.14/1.27 class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 1.14/1.27 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 1.14/1.27 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 1.14/1.27 class_Power_Opower(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 1.14/1.27 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
% 1.14/1.27 class_Int_Onumber(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 1.14/1.27 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 1.14/1.27
% 1.14/1.27 %----Conjectures (1)
% 1.14/1.27 fof(conj_0,conjecture,
% 1.14/1.27 ? [B_m] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)) ).
% 1.14/1.27
% 1.14/1.27 %------------------------------------------------------------------------------
% 1.14/1.27 %-------------------------------------------
% 1.14/1.27 % Proof found
% 1.14/1.27 % SZS status Theorem for theBenchmark
% 1.14/1.27 % SZS output start Proof
% 1.14/1.27 %ClaNum:1883(EqnAxiom:145)
% 1.14/1.27 %VarNum:9175(SingletonVarNum:3015)
% 1.14/1.27 %MaxLitNum:7
% 1.14/1.27 %MaxfuncDepth:12
% 1.14/1.27 %SharedTerms:298
% 1.14/1.27 %goalClause: 516
% 1.14/1.27 %singleGoalClaCount:1
% 1.14/1.27 [147]P1(a1)
% 1.14/1.27 [148]P1(a13)
% 1.14/1.27 [149]P1(a40)
% 1.14/1.27 [150]P27(a1)
% 1.14/1.27 [151]P27(a13)
% 1.14/1.27 [152]P27(a40)
% 1.14/1.27 [153]P2(a41)
% 1.14/1.27 [154]P2(a1)
% 1.14/1.27 [155]P2(a13)
% 1.14/1.27 [156]P2(a40)
% 1.14/1.27 [157]P3(a41)
% 1.14/1.27 [158]P3(a1)
% 1.14/1.27 [159]P3(a13)
% 1.14/1.27 [160]P3(a40)
% 1.14/1.27 [161]P28(a41)
% 1.14/1.27 [162]P28(a1)
% 1.14/1.27 [163]P28(a13)
% 1.14/1.27 [164]P28(a40)
% 1.14/1.27 [165]P55(a1)
% 1.14/1.27 [166]P55(a13)
% 1.14/1.27 [167]P55(a40)
% 1.14/1.27 [168]P29(a41)
% 1.14/1.27 [169]P29(a1)
% 1.14/1.27 [170]P29(a13)
% 1.14/1.27 [171]P29(a40)
% 1.14/1.27 [172]P34(a41)
% 1.14/1.27 [173]P34(a1)
% 1.14/1.27 [174]P34(a13)
% 1.14/1.27 [175]P34(a40)
% 1.14/1.27 [176]P62(a41)
% 1.14/1.27 [177]P62(a1)
% 1.14/1.27 [178]P62(a13)
% 1.14/1.27 [179]P62(a40)
% 1.14/1.27 [180]P63(a41)
% 1.14/1.27 [181]P63(a1)
% 1.14/1.27 [182]P63(a13)
% 1.14/1.27 [183]P63(a40)
% 1.14/1.27 [184]P56(a1)
% 1.14/1.27 [185]P56(a13)
% 1.14/1.27 [186]P56(a40)
% 1.14/1.27 [187]P35(a41)
% 1.14/1.27 [188]P35(a1)
% 1.14/1.27 [189]P35(a13)
% 1.14/1.27 [190]P35(a40)
% 1.14/1.27 [191]P4(a41)
% 1.14/1.27 [192]P4(a1)
% 1.14/1.27 [193]P4(a13)
% 1.14/1.27 [194]P4(a40)
% 1.14/1.27 [195]P64(a41)
% 1.14/1.27 [196]P64(a1)
% 1.14/1.27 [197]P64(a13)
% 1.14/1.27 [198]P64(a40)
% 1.14/1.27 [199]P44(a1)
% 1.14/1.27 [200]P44(a40)
% 1.14/1.27 [201]P36(a13)
% 1.14/1.27 [202]P36(a40)
% 1.14/1.27 [203]P48(a41)
% 1.14/1.27 [204]P48(a1)
% 1.14/1.27 [205]P48(a40)
% 1.14/1.27 [206]P30(a41)
% 1.14/1.27 [207]P30(a1)
% 1.14/1.27 [208]P30(a40)
% 1.14/1.27 [209]P49(a1)
% 1.14/1.27 [210]P49(a40)
% 1.14/1.27 [211]P50(a1)
% 1.14/1.27 [212]P50(a40)
% 1.14/1.27 [213]P51(a41)
% 1.14/1.27 [214]P51(a1)
% 1.14/1.27 [215]P51(a40)
% 1.14/1.27 [216]P52(a41)
% 1.14/1.27 [217]P52(a1)
% 1.14/1.27 [218]P52(a40)
% 1.14/1.27 [219]P18(a1)
% 1.14/1.27 [220]P18(a40)
% 1.14/1.27 [221]P66(a41)
% 1.14/1.27 [222]P66(a1)
% 1.14/1.27 [223]P66(a13)
% 1.14/1.27 [224]P66(a40)
% 1.14/1.27 [225]P39(a41)
% 1.14/1.27 [226]P39(a1)
% 1.14/1.27 [227]P39(a13)
% 1.14/1.27 [228]P39(a40)
% 1.14/1.27 [229]P65(a41)
% 1.14/1.27 [230]P65(a1)
% 1.14/1.27 [231]P65(a13)
% 1.14/1.27 [232]P65(a40)
% 1.14/1.27 [233]P45(a41)
% 1.14/1.27 [234]P45(a1)
% 1.14/1.27 [235]P45(a40)
% 1.14/1.27 [236]P57(a41)
% 1.14/1.27 [237]P57(a1)
% 1.14/1.27 [238]P57(a40)
% 1.14/1.27 [239]P58(a1)
% 1.14/1.27 [240]P58(a40)
% 1.14/1.27 [241]P60(a41)
% 1.14/1.27 [242]P60(a1)
% 1.14/1.27 [243]P60(a40)
% 1.14/1.27 [244]P59(a41)
% 1.14/1.27 [245]P59(a1)
% 1.14/1.27 [246]P59(a40)
% 1.14/1.27 [247]P20(a41)
% 1.14/1.27 [248]P20(a1)
% 1.14/1.27 [249]P20(a40)
% 1.14/1.27 [250]P26(a41)
% 1.14/1.27 [251]P26(a1)
% 1.14/1.27 [252]P26(a13)
% 1.14/1.27 [253]P26(a40)
% 1.14/1.27 [254]P5(a41)
% 1.14/1.27 [255]P5(a1)
% 1.14/1.27 [256]P5(a13)
% 1.14/1.27 [257]P5(a40)
% 1.14/1.27 [258]P6(a41)
% 1.14/1.27 [259]P6(a1)
% 1.14/1.27 [260]P6(a13)
% 1.14/1.27 [261]P6(a40)
% 1.14/1.27 [262]P15(a41)
% 1.14/1.27 [263]P15(a1)
% 1.14/1.27 [264]P15(a13)
% 1.14/1.27 [265]P15(a40)
% 1.14/1.27 [266]P16(a41)
% 1.14/1.27 [267]P16(a1)
% 1.14/1.27 [268]P16(a13)
% 1.14/1.27 [269]P16(a40)
% 1.14/1.27 [270]P19(a41)
% 1.14/1.27 [271]P19(a1)
% 1.14/1.27 [272]P19(a13)
% 1.14/1.27 [273]P19(a40)
% 1.14/1.27 [274]P17(a41)
% 1.14/1.27 [275]P17(a1)
% 1.14/1.27 [276]P17(a13)
% 1.14/1.27 [277]P17(a40)
% 1.14/1.27 [278]P21(a41)
% 1.14/1.27 [279]P21(a1)
% 1.14/1.27 [280]P21(a40)
% 1.14/1.27 [281]P22(a41)
% 1.14/1.27 [282]P22(a1)
% 1.14/1.27 [283]P22(a40)
% 1.14/1.27 [284]P25(a41)
% 1.14/1.27 [285]P25(a1)
% 1.14/1.27 [286]P25(a40)
% 1.14/1.27 [287]P31(a41)
% 1.14/1.27 [288]P31(a1)
% 1.14/1.27 [289]P31(a40)
% 1.14/1.27 [290]P31(a39)
% 1.14/1.27 [291]P32(a41)
% 1.14/1.27 [292]P32(a1)
% 1.14/1.27 [293]P32(a40)
% 1.14/1.27 [294]P32(a39)
% 1.14/1.27 [295]P33(a41)
% 1.14/1.27 [296]P33(a1)
% 1.14/1.27 [297]P33(a40)
% 1.14/1.27 [298]P33(a39)
% 1.14/1.27 [299]P23(a1)
% 1.14/1.27 [300]P23(a40)
% 1.14/1.27 [301]P24(a41)
% 1.14/1.27 [302]P24(a1)
% 1.14/1.27 [303]P24(a13)
% 1.14/1.27 [304]P24(a40)
% 1.14/1.27 [305]P46(a13)
% 1.14/1.27 [306]P46(a40)
% 1.14/1.27 [307]P47(a13)
% 1.14/1.27 [308]P47(a40)
% 1.14/1.27 [309]P40(a13)
% 1.14/1.27 [310]P40(a40)
% 1.14/1.27 [311]P7(a13)
% 1.14/1.27 [312]P7(a40)
% 1.14/1.27 [313]P8(a13)
% 1.14/1.27 [314]P8(a40)
% 1.14/1.27 [315]P61(a1)
% 1.14/1.27 [316]P61(a40)
% 1.14/1.27 [317]P13(a40)
% 1.14/1.27 [318]P53(a1)
% 1.14/1.27 [319]P53(a40)
% 1.14/1.27 [320]P54(a1)
% 1.14/1.27 [321]P54(a40)
% 1.14/1.27 [322]P43(a13)
% 1.14/1.27 [323]P43(a40)
% 1.14/1.27 [324]P41(a13)
% 1.14/1.27 [325]P41(a40)
% 1.14/1.27 [326]P42(a13)
% 1.14/1.27 [327]P42(a40)
% 1.14/1.27 [328]P14(a40)
% 1.14/1.27 [329]P37(a13)
% 1.14/1.27 [330]P37(a40)
% 1.14/1.27 [331]P9(a41)
% 1.14/1.27 [332]P9(a1)
% 1.14/1.27 [333]P38(a13)
% 1.14/1.27 [334]P38(a40)
% 1.14/1.27 [346]P11(a1,a12,a11)
% 1.14/1.27 [348]P12(a1,a12,a11)
% 1.14/1.27 [475]~E(a12,a11)
% 1.14/1.27 [483]~P10(a41,a44)
% 1.14/1.27 [487]~P11(a1,a11,a12)
% 1.14/1.27 [488]~P12(a1,a11,a11)
% 1.14/1.27 [489]~P12(a1,a11,a12)
% 1.14/1.27 [490]~P12(a1,a12,a12)
% 1.14/1.27 [146]E(f2(a1),a11)
% 1.14/1.27 [340]E(f15(a1,a11),f2(a1))
% 1.14/1.27 [341]E(f15(a41,a11),f2(a41))
% 1.14/1.27 [342]P10(a41,f2(a41))
% 1.14/1.27 [355]P12(a1,a12,f2(a1))
% 1.14/1.27 [372]P11(a1,f2(a1),f3(a1))
% 1.14/1.27 [373]P12(a1,f2(a1),f3(a1))
% 1.14/1.27 [374]E(f10(a13,a6,a6),f15(a13,a12))
% 1.14/1.27 [377]P11(a1,f2(a1),f15(a1,a11))
% 1.14/1.27 [476]~E(f2(a41),a44)
% 1.14/1.27 [477]~E(f2(a41),a45)
% 1.14/1.27 [478]~E(f2(a13),a42)
% 1.14/1.27 [479]~E(f2(a13),a6)
% 1.14/1.27 [480]~E(f3(a13),a6)
% 1.14/1.27 [481]~E(f3(a1),f2(a1))
% 1.14/1.27 [482]~E(f3(a40),f2(a40))
% 1.14/1.27 [485]~P10(a41,f3(a41))
% 1.14/1.27 [486]~E(f15(a1,a12),f15(a1,a11))
% 1.14/1.27 [495]~P12(a1,a11,f2(a1))
% 1.14/1.27 [335]E(f14(f2(a40)),f2(a40))
% 1.14/1.27 [336]E(f14(f3(a40)),f3(a40))
% 1.14/1.27 [337]E(f16(f2(a40)),f2(a40))
% 1.14/1.27 [378]E(f19(a13,f15(a40,a12)),f10(a13,a6,a6))
% 1.14/1.27 [389]E(f9(a1,f9(a1,f3(a1),a12),a12),a12)
% 1.14/1.27 [401]E(f17(a13,f20(a13,f19(a13,f17(a13,a42)),a42)),f3(a40))
% 1.14/1.27 [417]E(f15(a1,f9(a1,f9(a1,f3(a1),a11),a11)),f3(a1))
% 1.14/1.27 [418]E(f15(a41,f9(a1,f9(a1,f3(a1),a11),a11)),f3(a41))
% 1.14/1.27 [422]E(f15(a41,f9(a1,f9(a1,f3(a1),a11),a11)),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [441]E(f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f9(a41,f3(a41),f3(a41)))
% 1.14/1.27 [443]E(f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f9(a41,f9(a41,f2(a41),f3(a41)),f3(a41)))
% 1.14/1.27 [444]E(f15(a41,f9(a1,f9(a1,f3(a1),f9(a1,f9(a1,f3(a1),a11),a11)),f9(a1,f9(a1,f3(a1),a11),a11))),f9(a41,f9(a41,f9(a41,f2(a41),f3(a41)),f3(a41)),f3(a41)))
% 1.14/1.27 [445]P11(a1,f2(a1),f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))
% 1.14/1.27 [446]P12(a41,f2(a41),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))
% 1.14/1.27 [454]P11(a1,f2(a1),f15(a1,f9(a1,f9(a1,f3(a1),f9(a1,f9(a1,f3(a1),a11),a11)),f9(a1,f9(a1,f3(a1),a11),a11))))
% 1.14/1.27 [448]E(f18(a13,a6,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f15(a13,a12))
% 1.14/1.27 [456]P11(a40,f2(a40),f14(f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [457]P12(a40,f2(a40),f14(f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [458]P12(a40,f3(a40),f14(f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [352]P11(a41,x3521,x3521)
% 1.14/1.27 [353]P11(a1,x3531,x3531)
% 1.14/1.27 [354]P11(a40,x3541,x3541)
% 1.14/1.27 [494]~P12(a41,x4941,x4941)
% 1.14/1.27 [338]E(f15(a1,x3381),x3381)
% 1.14/1.27 [343]E(f4(a40,x3431),f17(a40,x3431))
% 1.14/1.27 [349]E(f10(a1,a11,x3491),a11)
% 1.14/1.27 [350]E(f9(a1,x3501,a11),x3501)
% 1.14/1.27 [351]E(f9(a1,a11,x3511),x3511)
% 1.14/1.27 [356]E(f5(a1,x3561,x3561),f2(a1))
% 1.14/1.27 [358]P11(a41,f2(a41),x3581)
% 1.14/1.27 [386]P11(a41,x3861,f10(a41,x3861,x3861))
% 1.14/1.27 [484]~E(f15(a13,x4841),a6)
% 1.14/1.27 [492]~E(f9(a1,x4921,x4921),a12)
% 1.14/1.27 [498]~P12(a41,x4981,f2(a41))
% 1.14/1.27 [359]E(f10(a41,x3591,f3(a41)),x3591)
% 1.14/1.27 [360]E(f10(a1,x3601,f3(a1)),x3601)
% 1.14/1.27 [361]E(f9(a41,x3611,f2(a41)),x3611)
% 1.14/1.27 [362]E(f9(a1,x3621,f2(a1)),x3621)
% 1.14/1.27 [363]E(f10(a41,f3(a41),x3631),x3631)
% 1.14/1.27 [364]E(f10(a1,f3(a1),x3641),x3641)
% 1.14/1.27 [365]E(f10(a40,f3(a40),x3651),x3651)
% 1.14/1.27 [366]E(f9(a41,f2(a41),x3661),x3661)
% 1.14/1.27 [367]E(f9(a1,f2(a1),x3671),x3671)
% 1.14/1.27 [368]E(f10(a41,x3681,f2(a41)),f2(a41))
% 1.14/1.27 [369]E(f10(a41,f2(a41),x3691),f2(a41))
% 1.14/1.27 [370]E(f5(a1,f2(a1),x3701),f2(a1))
% 1.14/1.27 [376]E(f5(a1,x3761,f15(a1,a12)),f2(a1))
% 1.14/1.27 [385]E(f14(f10(a40,x3851,x3851)),f4(a40,x3851))
% 1.14/1.27 [390]P12(a41,x3901,f9(a41,x3901,f3(a41)))
% 1.14/1.27 [391]P12(a41,f2(a41),f9(a41,x3911,f3(a41)))
% 1.14/1.27 [397]P12(a40,f2(a40),f9(a40,f3(a40),f4(a40,x3971)))
% 1.14/1.27 [419]P11(a41,x4191,f10(a41,x4191,f10(a41,x4191,x4191)))
% 1.14/1.27 [500]~E(f9(a41,x5001,f3(a41)),x5001)
% 1.14/1.27 [506]~E(f9(a41,x5061,f3(a41)),f2(a41))
% 1.14/1.27 [511]~P11(a41,f9(a41,x5111,f3(a41)),x5111)
% 1.14/1.27 [513]~P12(a40,f9(a40,f4(a40,x5131),f3(a40)),x5131)
% 1.14/1.27 [516]~E(f9(a41,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x5161),f3(a41)),a44)
% 1.14/1.27 [400]E(f18(a41,f9(a41,f2(a41),f3(a41)),x4001),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [510]~E(f9(a1,f9(a1,f3(a1),x5101),x5101),a11)
% 1.14/1.27 [512]~E(f9(a1,f9(a1,f3(a1),x5121),x5121),f2(a1))
% 1.14/1.27 [447]E(f18(a13,f7(x4471),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),x4471)
% 1.14/1.27 [449]E(f10(a41,x4491,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f9(a41,x4491,x4491))
% 1.14/1.27 [450]E(f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x4501),f9(a41,x4501,x4501))
% 1.14/1.27 [451]E(f9(a41,x4511,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f9(a41,f9(a41,x4511,f3(a41)),f3(a41)))
% 1.14/1.27 [452]E(f9(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x4521),f9(a41,f9(a41,x4521,f3(a41)),f3(a41)))
% 1.14/1.27 [455]E(f9(a41,f15(a41,f9(a1,f9(a1,f3(a1),f9(a1,f9(a1,f3(a1),a11),a11)),f9(a1,f9(a1,f3(a1),a11),a11))),x4551),f9(a41,f9(a41,f9(a41,x4551,f3(a41)),f3(a41)),f3(a41)))
% 1.14/1.27 [460]P11(a40,f3(a40),f18(a40,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x4601))
% 1.14/1.27 [459]E(f14(f18(a40,x4591,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f4(a40,x4591))
% 1.14/1.27 [461]E(f9(a40,f20(a40,x4611,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f20(a40,x4611,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),x4611)
% 1.14/1.27 [462]E(f10(a40,f15(a40,f9(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)),f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4621,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f18(a40,f10(a40,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x4621),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [471]E(f10(a40,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f16(f20(a40,x4711,f9(a40,f3(a40),f14(f9(a40,f3(a40),f18(a40,x4711,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))))))),f16(x4711))
% 1.14/1.27 [379]E(f10(a41,x3791,x3792),f10(a41,x3792,x3791))
% 1.14/1.27 [380]E(f10(a1,x3801,x3802),f10(a1,x3802,x3801))
% 1.14/1.27 [381]E(f10(a40,x3811,x3812),f10(a40,x3812,x3811))
% 1.14/1.27 [382]E(f9(a41,x3821,x3822),f9(a41,x3822,x3821))
% 1.14/1.27 [383]E(f9(a1,x3831,x3832),f9(a1,x3832,x3831))
% 1.14/1.27 [387]P11(a41,x3871,f9(a41,x3872,x3871))
% 1.14/1.27 [388]P11(a41,x3881,f9(a41,x3881,x3882))
% 1.14/1.27 [507]~P12(a41,f9(a41,x5071,x5072),x5072)
% 1.14/1.27 [508]~P12(a41,f9(a41,x5081,x5082),x5081)
% 1.14/1.27 [392]E(f14(f18(a40,x3921,x3922)),f18(a40,f14(x3921),x3922))
% 1.14/1.27 [393]E(f10(a40,f14(x3931),f14(x3932)),f14(f10(a40,x3931,x3932)))
% 1.14/1.27 [394]E(f20(a40,f14(x3941),f14(x3942)),f14(f20(a40,x3941,x3942)))
% 1.14/1.27 [395]E(f18(a13,f19(a13,x3951),x3952),f19(a13,f18(a40,x3951,x3952)))
% 1.14/1.27 [396]P11(a1,f2(a1),f18(a1,f4(a1,x3961),x3962))
% 1.14/1.27 [398]E(f10(a1,f15(a1,x3981),f15(a1,x3982)),f15(a1,f10(a1,x3981,x3982)))
% 1.14/1.27 [399]E(f9(a1,f15(a1,x3991),f15(a1,x3992)),f15(a1,f9(a1,x3991,x3992)))
% 1.14/1.27 [410]E(f20(a40,f10(a40,x4101,x4102),f10(a40,x4101,x4101)),f20(a40,x4102,x4101))
% 1.14/1.27 [420]P12(a41,x4201,f9(a41,f9(a41,x4202,x4201),f3(a41)))
% 1.14/1.27 [421]P12(a41,x4211,f9(a41,f9(a41,x4211,x4212),f3(a41)))
% 1.14/1.27 [433]E(f9(a1,f9(a1,x4331,x4331),f9(a1,x4332,x4332)),f9(a1,f9(a1,x4331,x4332),f9(a1,x4331,x4332)))
% 1.14/1.27 [434]P11(a40,f17(a13,x4341),f9(a40,f17(a13,f9(a13,x4341,x4342)),f17(a13,x4342)))
% 1.14/1.27 [438]E(f9(a1,f9(a1,f9(a1,f3(a1),x4381),x4381),f9(a1,x4382,x4382)),f9(a1,f9(a1,f3(a1),f9(a1,x4381,x4382)),f9(a1,x4381,x4382)))
% 1.14/1.27 [411]E(f10(a41,x4111,f9(a41,x4112,f3(a41))),f9(a41,x4111,f10(a41,x4111,x4112)))
% 1.14/1.27 [412]E(f10(a41,f9(a41,x4121,f3(a41)),x4122),f9(a41,x4122,f10(a41,x4121,x4122)))
% 1.14/1.27 [414]E(f9(a41,f9(a41,x4141,f3(a41)),x4142),f9(a41,f9(a41,x4141,x4142),f3(a41)))
% 1.14/1.27 [415]E(f9(a41,f9(a41,x4151,f3(a41)),x4152),f9(a41,x4151,f9(a41,x4152,f3(a41))))
% 1.14/1.27 [439]P11(a40,x4391,f14(f9(a40,f10(a40,x4391,x4391),f10(a40,x4392,x4392))))
% 1.14/1.27 [440]P11(a40,f2(a40),f14(f9(a40,f10(a40,x4401,x4401),f10(a40,x4402,x4402))))
% 1.14/1.27 [453]E(f5(a1,f15(a1,f9(a1,x4531,x4531)),f15(a1,f9(a1,x4532,x4532))),f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f5(a1,f15(a1,x4531),f15(a1,x4532))))
% 1.14/1.27 [515]~E(f9(a1,x5151,x5151),f9(a1,f9(a1,f3(a1),x5152),x5152))
% 1.14/1.27 [436]E(f9(a1,f9(a1,f10(a1,x4361,x4362),f10(a1,x4361,x4362)),x4362),f10(a1,f9(a1,f9(a1,f3(a1),x4361),x4361),x4362))
% 1.14/1.27 [437]E(f9(a1,f9(a1,x4371,x4371),f9(a1,f9(a1,f3(a1),x4372),x4372)),f9(a1,f9(a1,f3(a1),f9(a1,x4371,x4372)),f9(a1,x4371,x4372)))
% 1.14/1.27 [463]E(f9(a40,f9(a40,f18(a40,x4631,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4632,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f10(a40,f10(a40,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x4631),x4632)),f18(a40,f9(a40,x4631,x4632),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [464]P11(a40,x4641,f14(f9(a40,f18(a40,x4642,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4641,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))))
% 1.14/1.27 [465]P11(a40,x4651,f14(f9(a40,f18(a40,x4651,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4652,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))))
% 1.14/1.27 [466]P11(a40,f2(a40),f14(f9(a40,f18(a40,x4661,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4662,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))))
% 1.14/1.27 [467]P11(a40,f4(a40,x4671),f14(f9(a40,f18(a40,x4672,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4671,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))))
% 1.14/1.27 [468]P11(a40,f4(a40,x4681),f14(f9(a40,f18(a40,x4681,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4682,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))))
% 1.14/1.27 [470]P11(a40,f4(a40,f20(a40,x4701,f14(f9(a40,f18(a40,x4701,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4702,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))))),f3(a40))
% 1.14/1.27 [402]E(f9(a41,x4021,f9(a41,x4022,x4023)),f9(a41,x4022,f9(a41,x4021,x4023)))
% 1.14/1.27 [403]E(f9(a1,x4031,f9(a1,x4032,x4033)),f9(a1,x4032,f9(a1,x4031,x4033)))
% 1.14/1.27 [404]E(f10(a41,f10(a41,x4041,x4042),x4043),f10(a41,x4041,f10(a41,x4042,x4043)))
% 1.14/1.27 [405]E(f10(a1,f10(a1,x4051,x4052),x4053),f10(a1,x4051,f10(a1,x4052,x4053)))
% 1.14/1.27 [406]E(f10(a40,f10(a40,x4061,x4062),x4063),f10(a40,x4061,f10(a40,x4062,x4063)))
% 1.14/1.27 [407]E(f18(a1,f18(a1,x4071,x4072),x4073),f18(a1,x4071,f10(a41,x4072,x4073)))
% 1.14/1.27 [408]E(f9(a41,f9(a41,x4081,x4082),x4083),f9(a41,x4081,f9(a41,x4082,x4083)))
% 1.14/1.27 [409]E(f9(a1,f9(a1,x4091,x4092),x4093),f9(a1,x4091,f9(a1,x4092,x4093)))
% 1.14/1.27 [423]E(f9(a41,f10(a41,x4231,x4232),f10(a41,x4231,x4233)),f10(a41,x4231,f9(a41,x4232,x4233)))
% 1.14/1.27 [424]E(f9(a1,f10(a1,x4241,x4242),f10(a1,x4241,x4243)),f10(a1,x4241,f9(a1,x4242,x4243)))
% 1.14/1.27 [425]E(f10(a1,f18(a1,x4251,x4252),f18(a1,x4251,x4253)),f18(a1,x4251,f9(a41,x4252,x4253)))
% 1.14/1.27 [426]E(f9(a41,f10(a41,x4261,x4262),f10(a41,x4263,x4262)),f10(a41,f9(a41,x4261,x4263),x4262))
% 1.14/1.27 [427]E(f9(a1,f10(a1,x4271,x4272),f10(a1,x4273,x4272)),f10(a1,f9(a1,x4271,x4273),x4272))
% 1.14/1.27 [429]E(f9(a40,f10(a40,x4291,x4292),f10(a40,x4293,x4292)),f10(a40,f9(a40,x4291,x4293),x4292))
% 1.14/1.27 [431]E(f5(a1,f10(a1,x4311,f5(a1,x4312,x4313)),x4313),f5(a1,f10(a1,x4311,x4312),x4313))
% 1.14/1.27 [432]E(f5(a1,f18(a1,f5(a1,x4321,x4322),x4323),x4322),f5(a1,f18(a1,x4321,x4323),x4322))
% 1.14/1.27 [435]E(f9(a41,f10(a41,x4351,x4352),f9(a41,f10(a41,x4353,x4352),x4354)),f9(a41,f10(a41,f9(a41,x4351,x4353),x4352),x4354))
% 1.14/1.27 [473]E(f18(a40,f14(f10(a40,f9(a40,f18(a40,x4731,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4732,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f9(a40,f18(a40,x4733,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4734,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f10(a40,f9(a40,f18(a40,x4731,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4732,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f9(a40,f18(a40,x4733,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4734,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))))
% 1.14/1.27 [469]P11(a40,f2(a40),f14(f10(a40,f9(a40,f18(a40,x4691,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4692,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f9(a40,f18(a40,x4693,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4694,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))))
% 1.14/1.27 [472]P11(a40,f14(f9(a40,f18(a40,f9(a40,x4721,x4722),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,f9(a40,x4723,x4724),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))),f9(a40,f14(f9(a40,f18(a40,x4721,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4723,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))),f14(f9(a40,f18(a40,x4722,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x4724,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))))
% 1.14/1.27 [517]~E(x5171,f2(a40))+E(f14(x5171),f2(a40))
% 1.14/1.27 [518]~E(x5181,f3(a40))+E(f14(x5181),f3(a40))
% 1.14/1.27 [519]~E(f14(x5191),f2(a40))+E(x5191,f2(a40))
% 1.14/1.27 [520]~E(f14(x5201),f3(a40))+E(x5201,f3(a40))
% 1.14/1.27 [523]~P62(x5231)+~E(f3(x5231),f2(x5231))
% 1.14/1.27 [525]~P1(x5251)+E(f15(x5251,a11),f2(x5251))
% 1.14/1.27 [544]~E(a11,x5441)+E(f9(a1,x5441,x5441),a11)
% 1.14/1.27 [545]~E(x5451,a11)+E(f9(a1,x5451,x5451),a11)
% 1.14/1.27 [553]E(x5531,f2(a41))+P12(a41,f2(a41),x5531)
% 1.14/1.27 [588]P10(a41,x5881)+P12(a41,f2(a41),x5881)
% 1.14/1.27 [606]~P48(x6061)+P11(x6061,f2(x6061),f3(x6061))
% 1.14/1.27 [607]~P48(x6071)+P12(x6071,f2(x6071),f3(x6071))
% 1.14/1.27 [615]P11(a1,x6151,a11)+~E(f15(a41,x6151),f2(a41))
% 1.14/1.27 [620]~E(x6201,f2(a1))+P12(a1,f4(a1,x6201),f3(a1))
% 1.14/1.27 [621]E(x6211,a11)+~E(f9(a1,x6211,x6211),a11)
% 1.14/1.27 [622]E(a11,x6221)+~E(f9(a1,x6221,x6221),a11)
% 1.14/1.27 [643]E(x6431,f2(a41))+~P11(a41,x6431,f2(a41))
% 1.14/1.27 [653]~P11(a1,x6531,a11)+E(f15(a41,x6531),f2(a41))
% 1.14/1.27 [663]~E(f14(x6631),f2(a40))+~P12(a40,f2(a40),x6631)
% 1.14/1.27 [695]~P48(x6951)+~P11(x6951,f3(x6951),f2(x6951))
% 1.14/1.27 [696]~P48(x6961)+~P12(x6961,f3(x6961),f2(x6961))
% 1.14/1.27 [724]E(x7241,f2(a1))+~P12(a1,f4(a1,x7241),f3(a1))
% 1.14/1.27 [754]~P12(a1,f2(a1),x7541)+P11(a1,f3(a1),x7541)
% 1.14/1.27 [755]~P11(a1,f3(a1),x7551)+P12(a1,f2(a1),x7551)
% 1.14/1.27 [779]~P11(a40,x7791,f2(a40))+P11(a40,f14(x7791),f2(a40))
% 1.14/1.27 [780]~P11(a40,x7801,f3(a40))+P11(a40,f14(x7801),f3(a40))
% 1.14/1.27 [781]~P12(a40,x7811,f2(a40))+P12(a40,f14(x7811),f2(a40))
% 1.14/1.27 [782]~P12(a40,x7821,f3(a40))+P12(a40,f14(x7821),f3(a40))
% 1.14/1.27 [784]~P11(a40,f2(a40),x7841)+P11(a40,f2(a40),f14(x7841))
% 1.14/1.27 [786]~P11(a40,f3(a40),x7861)+P11(a40,f3(a40),f14(x7861))
% 1.14/1.27 [788]~P12(a40,f2(a40),x7881)+P12(a40,f2(a40),f14(x7881))
% 1.14/1.27 [789]~P12(a40,f3(a40),x7891)+P12(a40,f3(a40),f14(x7891))
% 1.14/1.27 [792]~P11(a40,f14(x7921),f2(a40))+P11(a40,x7921,f2(a40))
% 1.14/1.27 [793]~P11(a40,f14(x7931),f3(a40))+P11(a40,x7931,f3(a40))
% 1.14/1.27 [794]~P12(a40,f14(x7941),f2(a40))+P12(a40,x7941,f2(a40))
% 1.14/1.27 [795]~P12(a40,f14(x7951),f3(a40))+P12(a40,x7951,f3(a40))
% 1.14/1.27 [796]~P11(a40,f2(a40),f14(x7961))+P11(a40,f2(a40),x7961)
% 1.14/1.27 [797]~P11(a40,f3(a40),f14(x7971))+P11(a40,f3(a40),x7971)
% 1.14/1.27 [798]~P12(a40,f2(a40),f14(x7981))+P12(a40,f2(a40),x7981)
% 1.14/1.27 [799]~P12(a40,f3(a40),f14(x7991))+P12(a40,f3(a40),x7991)
% 1.14/1.27 [818]~P12(a1,a11,x8181)+P12(a41,f2(a41),f15(a41,x8181))
% 1.14/1.27 [821]E(x8211,f2(a40))+P12(a40,f2(a40),f10(a40,x8211,x8211))
% 1.14/1.27 [849]P12(a1,a11,x8491)+~P12(a41,f2(a41),f15(a41,x8491))
% 1.14/1.27 [976]~P11(a1,a11,x9761)+P11(a1,a11,f9(a1,x9761,x9761))
% 1.14/1.27 [977]~P12(a1,a12,x9771)+P11(a1,a12,f9(a1,x9771,x9771))
% 1.14/1.27 [978]~P12(a1,a11,x9781)+P12(a1,a11,f9(a1,x9781,x9781))
% 1.14/1.27 [979]~P12(a1,a12,x9791)+P12(a1,a12,f9(a1,x9791,x9791))
% 1.14/1.27 [980]~P11(a1,x9801,a11)+P11(a1,f9(a1,x9801,x9801),a11)
% 1.14/1.27 [981]~P11(a1,x9811,a12)+P11(a1,f9(a1,x9811,x9811),a12)
% 1.14/1.27 [982]~P12(a1,x9821,a11)+P12(a1,f9(a1,x9821,x9821),a11)
% 1.14/1.27 [983]~P11(a1,x9831,a12)+P12(a1,f9(a1,x9831,x9831),a12)
% 1.14/1.27 [1039]~P12(a1,x10391,f2(a1))+P12(a1,f9(a1,x10391,x10391),f2(a1))
% 1.14/1.27 [1044]~E(x10441,f2(a40))+~P12(a40,f2(a40),f10(a40,x10441,x10441))
% 1.14/1.27 [1082]P11(a1,x10821,a11)+~P11(a1,f9(a1,x10821,x10821),a11)
% 1.14/1.27 [1083]P11(a1,x10831,a12)+~P11(a1,f9(a1,x10831,x10831),a12)
% 1.14/1.27 [1084]P11(a1,x10841,a12)+~P12(a1,f9(a1,x10841,x10841),a12)
% 1.14/1.27 [1085]P12(a1,x10851,a11)+~P12(a1,f9(a1,x10851,x10851),a11)
% 1.14/1.27 [1086]P11(a1,a11,x10861)+~P11(a1,a11,f9(a1,x10861,x10861))
% 1.14/1.27 [1087]P12(a1,a11,x10871)+~P12(a1,a11,f9(a1,x10871,x10871))
% 1.14/1.27 [1088]P12(a1,a12,x10881)+~P11(a1,a12,f9(a1,x10881,x10881))
% 1.14/1.27 [1089]P12(a1,a12,x10891)+~P12(a1,a12,f9(a1,x10891,x10891))
% 1.14/1.27 [1111]P12(a1,x11111,f2(a1))+~P12(a1,f9(a1,x11111,x11111),f2(a1))
% 1.14/1.27 [526]~P38(x5261)+E(f19(x5261,f2(a40)),f2(x5261))
% 1.14/1.27 [527]~P38(x5271)+E(f19(x5271,f3(a40)),f3(x5271))
% 1.14/1.27 [528]~P43(x5281)+E(f17(x5281,f2(x5281)),f2(a40))
% 1.14/1.27 [529]~P42(x5291)+E(f17(x5291,f3(x5291)),f3(a40))
% 1.14/1.27 [531]~P23(x5311)+E(f4(x5311,f2(x5311)),f2(x5311))
% 1.14/1.27 [532]~P44(x5321)+E(f4(x5321,f3(x5321)),f3(x5321))
% 1.14/1.27 [728]P10(a41,x7281)+P10(a41,f9(a41,x7281,f3(a41)))
% 1.14/1.27 [790]~P12(a41,f2(a41),x7901)+E(f9(a41,f22(x7901),f3(a41)),x7901)
% 1.14/1.27 [898]~P48(x8981)+P12(x8981,f2(x8981),f9(x8981,f3(x8981),f3(x8981)))
% 1.14/1.27 [926]~P10(a41,x9261)+~P10(a41,f9(a41,x9261,f3(a41)))
% 1.14/1.27 [1042]~P11(a1,f2(a1),x10421)+P12(a1,f2(a1),f9(a1,f3(a1),x10421))
% 1.14/1.27 [1051]E(x10511,f2(a41))+~P12(a41,x10511,f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [1321]~P11(a1,f2(a1),f15(a1,x13211))+P11(a1,f2(a1),f15(a1,f9(a1,x13211,x13211)))
% 1.14/1.27 [1324]~P10(a41,x13241)+E(f10(a41,f9(a41,f9(a41,f2(a41),f3(a41)),f3(a41)),f32(x13241)),x13241)
% 1.14/1.27 [1758]P10(a41,x17581)+E(f9(a41,f10(a41,f9(a41,f9(a41,f2(a41),f3(a41)),f3(a41)),f33(x17581)),f3(a41)),x17581)
% 1.14/1.27 [1811]~P10(a41,x18111)+E(f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f34(x18111)),x18111)
% 1.14/1.27 [1831]P10(a41,x18311)+E(f9(a41,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f35(x18311)),f3(a41)),x18311)
% 1.14/1.27 [824]~E(a12,x8241)+E(f9(a1,f9(a1,f3(a1),x8241),x8241),a12)
% 1.14/1.27 [825]~E(x8251,a12)+E(f9(a1,f9(a1,f3(a1),x8251),x8251),a12)
% 1.14/1.27 [1045]E(x10451,a12)+~E(f9(a1,f9(a1,f3(a1),x10451),x10451),a12)
% 1.14/1.27 [1046]E(a12,x10461)+~E(f9(a1,f9(a1,f3(a1),x10461),x10461),a12)
% 1.14/1.27 [1395]~P11(a1,a11,x13951)+P11(a1,a11,f9(a1,f9(a1,f3(a1),x13951),x13951))
% 1.14/1.27 [1396]~P11(a1,a12,x13961)+P11(a1,a12,f9(a1,f9(a1,f3(a1),x13961),x13961))
% 1.14/1.27 [1397]~P11(a1,a11,x13971)+P12(a1,a11,f9(a1,f9(a1,f3(a1),x13971),x13971))
% 1.14/1.27 [1398]~P12(a1,a12,x13981)+P12(a1,a12,f9(a1,f9(a1,f3(a1),x13981),x13981))
% 1.14/1.27 [1399]~P12(a1,x13991,a11)+P11(a1,f9(a1,f9(a1,f3(a1),x13991),x13991),a11)
% 1.14/1.27 [1400]~P11(a1,x14001,a12)+P11(a1,f9(a1,f9(a1,f3(a1),x14001),x14001),a12)
% 1.14/1.27 [1401]~P12(a1,x14011,a11)+P12(a1,f9(a1,f9(a1,f3(a1),x14011),x14011),a11)
% 1.14/1.27 [1402]~P12(a1,x14021,a12)+P12(a1,f9(a1,f9(a1,f3(a1),x14021),x14021),a12)
% 1.14/1.27 [1443]~P12(a1,x14431,f2(a1))+P12(a1,f9(a1,f9(a1,f3(a1),x14431),x14431),f2(a1))
% 1.14/1.27 [1635]P11(a1,x16351,a12)+~P11(a1,f9(a1,f9(a1,f3(a1),x16351),x16351),a12)
% 1.14/1.27 [1636]P12(a1,x16361,a11)+~P11(a1,f9(a1,f9(a1,f3(a1),x16361),x16361),a11)
% 1.14/1.27 [1637]P12(a1,x16371,a11)+~P12(a1,f9(a1,f9(a1,f3(a1),x16371),x16371),a11)
% 1.14/1.27 [1638]P12(a1,x16381,a12)+~P12(a1,f9(a1,f9(a1,f3(a1),x16381),x16381),a12)
% 1.14/1.27 [1639]P11(a1,a11,x16391)+~P11(a1,a11,f9(a1,f9(a1,f3(a1),x16391),x16391))
% 1.14/1.27 [1640]P11(a1,a11,x16401)+~P12(a1,a11,f9(a1,f9(a1,f3(a1),x16401),x16401))
% 1.14/1.27 [1641]P11(a1,a12,x16411)+~P11(a1,a12,f9(a1,f9(a1,f3(a1),x16411),x16411))
% 1.14/1.27 [1642]P12(a1,a12,x16421)+~P12(a1,a12,f9(a1,f9(a1,f3(a1),x16421),x16421))
% 1.14/1.27 [1653]P12(a1,x16531,f2(a1))+~P12(a1,f9(a1,f9(a1,f3(a1),x16531),x16531),f2(a1))
% 1.14/1.27 [1182]~P1(x11821)+E(f15(x11821,f9(a1,f9(a1,f3(a1),a11),a11)),f3(x11821))
% 1.14/1.27 [1754]~P11(a1,f2(a1),f15(a1,x17541))+P11(a1,f2(a1),f15(a1,f9(a1,f9(a1,f3(a1),x17541),x17541)))
% 1.14/1.27 [1803]~P1(x18031)+E(f9(x18031,f3(x18031),f3(x18031)),f15(x18031,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))
% 1.14/1.27 [1808]~P63(x18081)+E(f18(x18081,f2(x18081),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f2(x18081))
% 1.14/1.27 [1809]~P63(x18091)+E(f18(x18091,f3(x18091),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f3(x18091))
% 1.14/1.27 [1817]~P11(a40,f2(a40),x18171)+E(f18(a40,f14(x18171),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),x18171)
% 1.14/1.27 [1823]P11(a40,f2(a40),x18231)+~E(f18(a40,f14(x18231),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),x18231)
% 1.14/1.27 [1827]E(f5(a1,x18271,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f3(a1))+E(f5(a1,x18271,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f2(a1))
% 1.14/1.27 [1834]~P12(a40,f2(a40),x18341)+P12(a40,f2(a40),f18(a40,f14(x18341),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1837]~P12(a40,f4(a40,x18371),f3(a40))+P12(a40,f18(a40,x18371,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f3(a40))
% 1.14/1.27 [1845]~E(f5(a1,x18451,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f3(a1))+~E(f5(a1,x18451,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f2(a1))
% 1.14/1.27 [1852]~P12(a40,f2(a40),x18521)+P12(a40,f20(a40,x18521,f14(f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),x18521)
% 1.14/1.27 [548]~E(x5481,x5482)+P11(a41,x5481,x5482)
% 1.14/1.27 [549]~E(x5491,x5492)+P11(a40,x5491,x5492)
% 1.14/1.27 [558]~P31(x5581)+P11(x5581,x5582,x5582)
% 1.14/1.27 [629]~E(x6291,x6292)+~P12(a41,x6291,x6292)
% 1.14/1.27 [630]~E(x6301,x6302)+~P12(a1,x6301,x6302)
% 1.14/1.27 [631]~E(x6311,x6312)+~P12(a40,x6311,x6312)
% 1.14/1.27 [645]~P12(x6451,x6452,x6452)+~P31(x6451)
% 1.14/1.27 [676]P11(a41,x6762,x6761)+P11(a41,x6761,x6762)
% 1.14/1.27 [677]P11(a1,x6772,x6771)+P11(a1,x6771,x6772)
% 1.14/1.27 [678]P11(a40,x6782,x6781)+P11(a40,x6781,x6782)
% 1.14/1.27 [735]~P12(a41,x7351,x7352)+P11(a41,x7351,x7352)
% 1.14/1.27 [736]~P12(a1,x7361,x7362)+P11(a1,x7361,x7362)
% 1.14/1.27 [738]~P12(a40,x7381,x7382)+P11(a40,x7381,x7382)
% 1.14/1.27 [521]E(x5211,x5212)+~E(f14(x5211),f14(x5212))
% 1.14/1.27 [536]~P31(x5362)+P31(f43(x5361,x5362))
% 1.14/1.27 [537]~P32(x5372)+P32(f43(x5371,x5372))
% 1.14/1.27 [538]~P33(x5382)+P33(f43(x5381,x5382))
% 1.14/1.27 [556]~E(x5562,f2(a41))+E(f10(a41,x5561,x5562),f2(a41))
% 1.14/1.27 [557]~E(x5571,f2(a41))+E(f10(a41,x5571,x5572),f2(a41))
% 1.14/1.27 [565]~P9(x5651)+E(f5(x5651,x5652,x5652),f2(x5651))
% 1.14/1.27 [632]~P23(x6321)+P11(x6321,x6322,f4(x6321,x6322))
% 1.14/1.27 [633]~E(f9(a41,x6332,x6331),x6332)+E(x6331,f2(a41))
% 1.14/1.27 [634]~P43(x6341)+P11(a40,f2(a40),f17(x6341,x6342))
% 1.14/1.27 [636]~P12(a41,x6362,x6361)+~E(x6361,f2(a41))
% 1.14/1.27 [639]E(x6391,f2(a41))+~E(f9(a41,x6392,x6391),f2(a41))
% 1.14/1.27 [640]E(x6401,f2(a41))+~E(f9(a41,x6401,x6402),f2(a41))
% 1.14/1.27 [641]E(x6411,f3(a41))+~E(f10(a41,x6412,x6411),f3(a41))
% 1.14/1.27 [642]E(x6421,f3(a41))+~E(f10(a41,x6421,x6422),f3(a41))
% 1.14/1.27 [647]~P23(x6471)+P11(x6471,f2(x6471),f4(x6471,x6472))
% 1.14/1.27 [729]~P43(x7291)+~P12(a40,f17(x7291,x7292),f2(a40))
% 1.14/1.27 [730]~P10(a41,x7302)+P10(a41,f10(a41,x7301,x7302))
% 1.14/1.27 [731]~P10(a41,x7311)+P10(a41,f10(a41,x7311,x7312))
% 1.14/1.27 [752]~P23(x7521)+~P12(x7521,f4(x7521,x7522),f2(x7521))
% 1.14/1.27 [765]~P11(a40,x7651,x7652)+P11(a40,f14(x7651),f14(x7652))
% 1.14/1.27 [766]~P11(a40,x7661,x7662)+P11(a40,f16(x7661),f16(x7662))
% 1.14/1.27 [768]~P12(a40,x7681,x7682)+P12(a40,f14(x7681),f14(x7682))
% 1.14/1.27 [769]~P12(a40,x7691,x7692)+P12(a40,f16(x7691),f16(x7692))
% 1.14/1.27 [811]P11(a40,x8111,x8112)+~P11(a40,f14(x8111),f14(x8112))
% 1.14/1.27 [812]P12(a40,x8121,x8122)+~P12(a40,f14(x8121),f14(x8122))
% 1.14/1.27 [827]~E(x8272,f2(a41))+P12(a41,f2(a41),f18(a41,x8271,x8272))
% 1.14/1.27 [834]E(x8341,x8342)+~E(f9(a1,x8341,x8341),f9(a1,x8342,x8342))
% 1.14/1.27 [847]~P50(x8471)+P11(x8471,f2(x8471),f10(x8471,x8472,x8472))
% 1.14/1.27 [866]~P11(a1,x8661,a11)+P11(a41,f15(a41,x8661),f15(a41,x8662))
% 1.14/1.27 [884]~P11(a1,x8841,x8842)+P11(a41,f15(a41,x8841),f15(a41,x8842))
% 1.14/1.27 [885]~P11(a1,x8851,x8852)+P11(a1,f15(a1,x8851),f15(a1,x8852))
% 1.14/1.27 [886]~P12(a1,x8861,x8862)+P12(a1,f15(a1,x8861),f15(a1,x8862))
% 1.14/1.27 [897]P10(a41,x8971)+~P10(a41,f18(a41,x8971,x8972))
% 1.14/1.27 [914]P11(a1,x9141,x9142)+~P11(a1,f15(a1,x9141),f15(a1,x9142))
% 1.14/1.27 [915]P12(a1,x9151,x9152)+~P12(a41,f15(a41,x9151),f15(a41,x9152))
% 1.14/1.27 [916]P12(a1,x9161,x9162)+~P12(a1,f15(a1,x9161),f15(a1,x9162))
% 1.14/1.27 [987]P12(a41,f2(a41),x9871)+~P10(a41,f18(a41,x9872,x9871))
% 1.14/1.27 [1012]P12(a1,x10121,f5(a1,x10122,x10121))+~P12(a1,x10121,f2(a1))
% 1.14/1.27 [1013]P11(a1,f5(a1,x10131,x10132),x10131)+~P11(a1,f2(a1),x10131)
% 1.14/1.27 [1015]P12(a1,f5(a1,x10151,x10152),x10152)+~P12(a1,f2(a1),x10152)
% 1.14/1.27 [1030]~P11(a1,f2(a1),x10301)+P11(a1,f2(a1),f18(a1,x10301,x10302))
% 1.14/1.27 [1032]~P12(a1,f2(a1),x10322)+P11(a1,f2(a1),f5(a1,x10321,x10322))
% 1.14/1.27 [1034]~P12(a41,f2(a41),x10341)+P12(a41,f2(a41),f18(a41,x10341,x10342))
% 1.14/1.27 [1038]~P12(a1,x10382,f2(a1))+P11(a1,f5(a1,x10381,x10382),f2(a1))
% 1.14/1.27 [1061]~P50(x10611)+~P12(x10611,f10(x10611,x10612,x10612),f2(x10611))
% 1.14/1.27 [1112]P12(a41,f2(a41),x11121)+~P12(a41,f2(a41),f10(a41,x11122,x11121))
% 1.14/1.27 [1113]P12(a41,f2(a41),x11131)+~P12(a41,f2(a41),f10(a41,x11131,x11132))
% 1.14/1.27 [1198]~P11(a1,x11981,x11982)+P11(a1,f9(a1,x11981,x11981),f9(a1,x11982,x11982))
% 1.14/1.27 [1204]~P12(a1,x12041,x12042)+P12(a1,f9(a1,x12041,x12041),f9(a1,x12042,x12042))
% 1.14/1.27 [1433]P11(a1,x14331,x14332)+~P11(a1,f9(a1,x14331,x14331),f9(a1,x14332,x14332))
% 1.14/1.27 [1438]P12(a1,x14381,x14382)+~P12(a1,f9(a1,x14381,x14381),f9(a1,x14382,x14382))
% 1.14/1.27 [550]~P42(x5501)+E(f17(x5501,f19(x5501,x5502)),f4(a40,x5502))
% 1.14/1.27 [551]~P43(x5511)+E(f4(a40,f17(x5511,x5512)),f17(x5511,x5512))
% 1.14/1.27 [555]~P23(x5551)+E(f4(x5551,f4(x5551,x5552)),f4(x5551,x5552))
% 1.14/1.27 [566]~P3(x5661)+E(f18(x5661,x5662,f3(a41)),x5662)
% 1.14/1.27 [567]~P35(x5671)+E(f18(x5671,x5672,f3(a41)),x5672)
% 1.14/1.27 [572]~P3(x5721)+E(f10(x5721,x5722,f3(x5721)),x5722)
% 1.14/1.27 [573]~P35(x5731)+E(f10(x5731,x5732,f3(x5731)),x5732)
% 1.14/1.27 [574]~P4(x5741)+E(f10(x5741,x5742,f3(x5741)),x5742)
% 1.14/1.27 [575]~P35(x5751)+E(f9(x5751,x5752,f2(x5751)),x5752)
% 1.14/1.27 [576]~P19(x5761)+E(f9(x5761,x5762,f2(x5761)),x5762)
% 1.14/1.27 [577]~P17(x5771)+E(f9(x5771,x5772,f2(x5771)),x5772)
% 1.14/1.27 [578]~P46(x5781)+E(f20(x5781,x5782,f3(x5781)),x5782)
% 1.14/1.27 [579]~P9(x5791)+E(f5(x5791,x5792,f2(x5791)),x5792)
% 1.14/1.27 [580]~P3(x5801)+E(f10(x5801,f3(x5801),x5802),x5802)
% 1.14/1.27 [581]~P35(x5811)+E(f10(x5811,f3(x5811),x5812),x5812)
% 1.14/1.27 [582]~P4(x5821)+E(f10(x5821,f3(x5821),x5822),x5822)
% 1.14/1.27 [583]~P35(x5831)+E(f9(x5831,f2(x5831),x5832),x5832)
% 1.14/1.27 [584]~P19(x5841)+E(f9(x5841,f2(x5841),x5842),x5842)
% 1.14/1.27 [585]~P17(x5851)+E(f9(x5851,f2(x5851),x5852),x5852)
% 1.14/1.27 [586]~P29(x5861)+E(f18(x5861,x5862,f2(a41)),f3(x5861))
% 1.14/1.27 [587]~P35(x5871)+E(f18(x5871,x5872,f2(a41)),f3(x5871))
% 1.14/1.27 [592]~P34(x5921)+E(f10(x5921,x5922,f2(x5921)),f2(x5921))
% 1.14/1.27 [593]~P35(x5931)+E(f10(x5931,x5932,f2(x5931)),f2(x5931))
% 1.14/1.27 [595]~P36(x5951)+E(f10(x5951,x5952,f2(x5951)),f2(x5951))
% 1.14/1.27 [596]~P47(x5961)+E(f20(x5961,x5962,f2(x5961)),f2(x5961))
% 1.14/1.27 [597]~P9(x5971)+E(f5(x5971,x5972,f3(x5971)),f2(x5971))
% 1.14/1.27 [598]~P34(x5981)+E(f10(x5981,f2(x5981),x5982),f2(x5981))
% 1.14/1.27 [599]~P35(x5991)+E(f10(x5991,f2(x5991),x5992),f2(x5991))
% 1.14/1.27 [601]~P36(x6011)+E(f10(x6011,f2(x6011),x6012),f2(x6011))
% 1.14/1.27 [602]~P3(x6021)+E(f18(x6021,f3(x6021),x6022),f3(x6021))
% 1.14/1.27 [603]~P46(x6031)+E(f20(x6031,f2(x6031),x6032),f2(x6031))
% 1.14/1.27 [604]~P40(x6041)+E(f20(x6041,f2(x6041),x6042),f2(x6041))
% 1.14/1.27 [605]~P9(x6051)+E(f5(x6051,f2(x6051),x6052),f2(x6051))
% 1.14/1.27 [623]~P1(x6231)+E(f9(x6231,x6232,f15(x6231,a11)),x6232)
% 1.14/1.27 [624]~P1(x6241)+E(f9(x6241,f15(x6241,a11),x6242),x6242)
% 1.14/1.27 [707]~E(x7072,f2(a41))+E(f18(a41,x7071,x7072),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [756]P12(a41,f2(a41),x7561)+~E(x7561,f9(a41,x7562,f3(a41)))
% 1.14/1.27 [822]~P11(a41,x8221,x8222)+E(f9(a41,x8221,f37(x8222,x8221)),x8222)
% 1.14/1.27 [823]~P11(a41,x8231,x8232)+E(f9(a41,x8231,f23(x8232,x8231)),x8232)
% 1.14/1.27 [828]~E(x8281,x8282)+P12(a41,x8281,f9(a41,x8282,f3(a41)))
% 1.14/1.27 [829]~E(x8291,x8292)+P12(a1,x8291,f9(a1,x8292,f3(a1)))
% 1.14/1.27 [830]~E(f5(a1,x8302,x8301),f2(a1))+E(f10(a1,x8301,f24(x8301,x8302)),x8302)
% 1.14/1.27 [831]~P44(x8311)+E(f10(x8311,f4(x8311,x8312),f4(x8311,x8312)),f10(x8311,x8312,x8312))
% 1.14/1.27 [835]~E(x8351,f2(a41))+P12(a41,x8351,f9(a41,x8352,f3(a41)))
% 1.14/1.27 [874]~P48(x8741)+P12(x8741,x8742,f9(x8741,x8742,f3(x8741)))
% 1.14/1.27 [883]~P12(a1,x8831,a11)+E(f10(a41,f15(a41,x8831),f15(a41,x8832)),f2(a41))
% 1.14/1.27 [894]~P12(a1,x8941,a11)+E(f9(a41,f15(a41,x8941),f15(a41,x8942)),f15(a41,x8942))
% 1.14/1.27 [900]E(f4(a1,x9001),f3(a1))+~E(f4(a1,f10(a1,x9001,x9002)),f3(a1))
% 1.14/1.27 [910]~E(x9101,f9(a41,f2(a41),f3(a41)))+E(f18(a41,x9101,x9102),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [920]E(x9201,f2(a1))+P12(a1,f2(a1),f18(a1,f4(a1,x9201),x9202))
% 1.14/1.27 [921]~E(x9212,f2(a41))+P12(a1,f2(a1),f18(a1,f4(a1,x9211),x9212))
% 1.14/1.27 [929]P12(a41,x9291,x9292)+P12(a41,x9292,f9(a41,x9291,f3(a41)))
% 1.14/1.27 [930]P11(a41,x9301,x9302)+P11(a41,f9(a41,x9302,f3(a41)),x9301)
% 1.14/1.27 [974]E(x9741,f9(a41,f2(a41),f3(a41)))+~E(f10(a41,x9742,x9741),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [975]E(x9751,f9(a41,f2(a41),f3(a41)))+~E(f10(a41,x9751,x9752),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [1019]~P11(a41,x10191,x10192)+P12(a41,x10191,f9(a41,x10192,f3(a41)))
% 1.14/1.27 [1022]~P11(a1,x10221,x10222)+P12(a1,x10221,f9(a1,x10222,f3(a1)))
% 1.14/1.27 [1023]~P12(a1,x10231,x10232)+P12(a1,x10231,f9(a1,x10232,f3(a1)))
% 1.14/1.27 [1026]~P12(a41,x10261,x10262)+P11(a41,f9(a41,x10261,f3(a41)),x10262)
% 1.14/1.27 [1028]~P12(a1,x10281,x10282)+P11(a1,f9(a1,x10281,f3(a1)),x10282)
% 1.14/1.27 [1050]P12(a1,x10501,a11)+E(f10(a41,f15(a41,x10501),f15(a41,x10502)),f15(a41,f10(a1,x10501,x10502)))
% 1.14/1.27 [1093]~P12(a41,x10931,x10932)+E(f9(a41,f9(a41,x10931,f31(x10932,x10931)),f3(a41)),x10932)
% 1.14/1.27 [1115]P11(a41,x11151,x11152)+~P12(a41,x11151,f9(a41,x11152,f3(a41)))
% 1.14/1.27 [1116]P11(a1,x11161,x11162)+~P12(a1,x11161,f9(a1,x11162,f3(a1)))
% 1.14/1.27 [1120]P12(a41,x11201,x11202)+~P11(a41,f9(a41,x11201,f3(a41)),x11202)
% 1.14/1.27 [1122]P12(a1,x11221,x11222)+~P11(a1,f9(a1,x11221,f3(a1)),x11222)
% 1.14/1.27 [1167]~P1(x11671)+E(f10(x11671,f9(x11671,f3(x11671),f3(x11671)),f15(x11671,x11672)),f15(x11671,f9(a1,x11672,x11672)))
% 1.14/1.27 [1183]~P12(a41,x11831,x11832)+~P12(a41,x11832,f9(a41,x11831,f3(a41)))
% 1.14/1.27 [1184]~P11(a41,x11841,x11842)+~P11(a41,f9(a41,x11842,f3(a41)),x11841)
% 1.14/1.27 [1283]~P1(x12831)+E(f9(x12831,f9(x12831,f2(x12831),f15(x12831,x12832)),f15(x12831,x12832)),f15(x12831,f9(a1,x12832,x12832)))
% 1.14/1.27 [1322]E(x13221,f2(a40))+~E(f9(a40,f10(a40,x13222,x13222),f10(a40,x13221,x13221)),f2(a40))
% 1.14/1.27 [1323]E(x13231,f2(a40))+~E(f9(a40,f10(a40,x13231,x13231),f10(a40,x13232,x13232)),f2(a40))
% 1.14/1.27 [1447]P11(a41,x14471,x14472)+~P11(a41,f9(a41,x14471,f3(a41)),f9(a41,x14472,f3(a41)))
% 1.14/1.27 [1449]P12(a41,x14491,x14492)+~P12(a41,f9(a41,x14491,f3(a41)),f9(a41,x14492,f3(a41)))
% 1.14/1.27 [1513]~P11(a41,f9(a41,f2(a41),f3(a41)),x15131)+P11(a41,f9(a41,f2(a41),f3(a41)),f18(a41,x15131,x15132))
% 1.14/1.27 [1602]P11(a41,f9(a41,f2(a41),f3(a41)),x16021)+~P11(a41,f9(a41,f2(a41),f3(a41)),f10(a41,x16022,x16021))
% 1.14/1.27 [1603]P11(a41,f9(a41,f2(a41),f3(a41)),x16031)+~P11(a41,f9(a41,f2(a41),f3(a41)),f10(a41,x16031,x16032))
% 1.14/1.27 [1800]~P10(a41,x18001)+~E(x18001,f9(a41,f10(a41,f9(a41,f9(a41,f2(a41),f3(a41)),f3(a41)),x18002),f3(a41)))
% 1.14/1.27 [1847]~P10(a41,x18471)+~E(x18471,f9(a41,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18472),f3(a41)))
% 1.14/1.27 [1029]~P35(x10291)+E(f9(x10291,x10292,x10292),f10(x10291,f9(x10291,f3(x10291),f3(x10291)),x10292))
% 1.14/1.27 [1470]E(x14701,x14702)+~E(f9(a1,f9(a1,f3(a1),x14701),x14701),f9(a1,f9(a1,f3(a1),x14702),x14702))
% 1.14/1.27 [1551]~P11(a1,x15511,x15512)+P11(a1,f9(a1,x15511,x15511),f9(a1,f9(a1,f3(a1),x15512),x15512))
% 1.14/1.27 [1553]~P11(a1,x15531,x15532)+P12(a1,f9(a1,x15531,x15531),f9(a1,f9(a1,f3(a1),x15532),x15532))
% 1.14/1.27 [1555]~P12(a1,x15551,x15552)+P11(a1,f9(a1,f9(a1,f3(a1),x15551),x15551),f9(a1,x15552,x15552))
% 1.14/1.27 [1557]~P12(a1,x15571,x15572)+P12(a1,f9(a1,f9(a1,f3(a1),x15571),x15571),f9(a1,x15572,x15572))
% 1.14/1.27 [1623]P10(a41,x16231)+~E(x16231,f10(a41,f9(a41,f9(a41,f2(a41),f3(a41)),f3(a41)),x16232))
% 1.14/1.27 [1728]~P11(a1,x17281,x17282)+P11(a1,f9(a1,f9(a1,f3(a1),x17281),x17281),f9(a1,f9(a1,f3(a1),x17282),x17282))
% 1.14/1.27 [1730]~P12(a1,x17301,x17302)+P12(a1,f9(a1,f9(a1,f3(a1),x17301),x17301),f9(a1,f9(a1,f3(a1),x17302),x17302))
% 1.14/1.27 [1743]P11(a1,x17431,x17432)+~P11(a1,f9(a1,x17431,x17431),f9(a1,f9(a1,f3(a1),x17432),x17432))
% 1.14/1.27 [1745]P11(a1,x17451,x17452)+~P12(a1,f9(a1,x17451,x17451),f9(a1,f9(a1,f3(a1),x17452),x17452))
% 1.14/1.27 [1747]P12(a1,x17471,x17472)+~P11(a1,f9(a1,f9(a1,f3(a1),x17471),x17471),f9(a1,x17472,x17472))
% 1.14/1.27 [1749]P12(a1,x17491,x17492)+~P12(a1,f9(a1,f9(a1,f3(a1),x17491),x17491),f9(a1,x17492,x17492))
% 1.14/1.27 [1796]P11(a1,x17961,x17962)+~P11(a1,f9(a1,f9(a1,f3(a1),x17961),x17961),f9(a1,f9(a1,f3(a1),x17962),x17962))
% 1.14/1.27 [1798]P12(a1,x17981,x17982)+~P12(a1,f9(a1,f9(a1,f3(a1),x17981),x17981),f9(a1,f9(a1,f3(a1),x17982),x17982))
% 1.14/1.27 [1841]~P11(a1,f2(a1),f15(a1,x18412))+E(f5(a1,f15(a1,f9(a1,f9(a1,f3(a1),x18411),x18411)),f15(a1,f9(a1,x18412,x18412))),f9(a1,f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f5(a1,f15(a1,x18411),f15(a1,x18412))),f3(a1)))
% 1.14/1.27 [1842]P11(a1,f2(a1),f15(a1,x18422))+E(f5(a1,f15(a1,f9(a1,f9(a1,f3(a1),x18421),x18421)),f15(a1,f9(a1,x18422,x18422))),f8(a1,f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f5(a1,f9(a1,f15(a1,x18421),f3(a1)),f15(a1,x18422))),f3(a1)))
% 1.14/1.27 [1856]~P1(x18561)+E(f18(x18561,f15(x18561,a12),f9(a41,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18562),f3(a41))),f15(x18561,a12))
% 1.14/1.27 [1601]~P1(x16011)+E(f9(x16011,f9(x16011,f3(x16011),f15(x16011,x16012)),f15(x16011,x16012)),f15(x16011,f9(a1,f9(a1,f3(a1),x16012),x16012)))
% 1.14/1.27 [1684]~P1(x16841)+E(f10(x16841,x16842,f15(x16841,f9(a1,f9(a1,f3(a1),a11),a11))),x16842)
% 1.14/1.27 [1685]~P1(x16851)+E(f10(x16851,f15(x16851,f9(a1,f9(a1,f3(a1),a11),a11)),x16852),x16852)
% 1.14/1.27 [1752]~P1(x17521)+E(f9(x17521,f3(x17521),f15(x17521,x17522)),f15(x17521,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),x17522)))
% 1.14/1.27 [1753]~P1(x17531)+E(f9(x17531,f15(x17531,x17532),f3(x17531)),f15(x17531,f9(a1,x17532,f9(a1,f9(a1,f3(a1),a11),a11))))
% 1.14/1.27 [1812]~P35(x18121)+E(f10(x18121,x18122,x18122),f18(x18121,x18122,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1813]~P3(x18131)+E(f18(x18131,x18132,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f10(x18131,x18132,x18132))
% 1.14/1.27 [1814]~P1(x18141)+E(f10(x18141,x18142,f15(x18141,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f9(x18141,x18142,x18142))
% 1.14/1.27 [1815]~P1(x18151)+E(f10(x18151,f15(x18151,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18152),f9(x18151,x18152,x18152))
% 1.14/1.27 [1820]P10(a41,x18201)+~E(x18201,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18202))
% 1.14/1.27 [1826]~P3(x18261)+E(f18(x18261,x18262,f15(a41,f9(a1,f9(a1,f3(a1),f9(a1,f9(a1,f3(a1),a11),a11)),f9(a1,f9(a1,f3(a1),a11),a11)))),f10(x18261,f10(x18261,x18262,x18262),x18262))
% 1.14/1.27 [1828]~P44(x18281)+E(f18(x18281,f4(x18281,x18282),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18281,x18282,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1829]~P44(x18291)+P11(x18291,f2(x18291),f18(x18291,x18292,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1839]~P12(a40,x18391,x18392)+P12(a40,x18391,f20(a40,f9(a40,x18391,x18392),f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1840]~P12(a40,x18401,x18402)+P12(a40,f20(a40,f9(a40,x18401,x18402),f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),x18402)
% 1.14/1.27 [1846]~P44(x18461)+~P12(x18461,f18(x18461,x18462,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f2(x18461))
% 1.14/1.27 [1832]~P1(x18321)+E(f18(x18321,f15(x18321,a12),f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18322)),f3(x18321))
% 1.14/1.27 [1843]~P44(x18431)+E(f4(x18431,f18(x18431,x18432,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f18(x18431,x18432,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1860]E(x18601,f2(a40))+~E(f9(a40,f18(a40,x18602,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x18601,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(a40))
% 1.14/1.27 [1861]E(x18611,f2(a40))+~E(f9(a40,f18(a40,x18611,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x18612,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(a40))
% 1.14/1.27 [1872]~P11(a1,f2(a1),x18722)+E(f5(a1,f9(a1,f3(a1),f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18721)),f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18722)),f9(a1,f3(a1),f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f5(a1,x18721,x18722))))
% 1.14/1.27 [1873]~P11(a1,x18732,f2(a1))+E(f5(a1,f9(a1,f3(a1),f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18731)),f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18732)),f8(a1,f10(a1,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),f5(a1,f9(a1,x18731,f3(a1)),x18732)),f3(a1)))
% 1.14/1.27 [1874]E(x18741,f2(a40))+~E(f14(f9(a40,f18(a40,x18742,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x18741,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))),x18742)
% 1.14/1.27 [1875]E(x18751,f2(a40))+~E(f14(f9(a40,f18(a40,x18751,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x18752,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))),x18752)
% 1.14/1.27 [692]E(f10(a41,x6921,x6922),f10(a41,x6923,x6922))+~E(x6922,f2(a41))
% 1.14/1.27 [694]E(f10(a41,x6941,x6942),f10(a41,x6941,x6943))+~E(x6941,f2(a41))
% 1.14/1.27 [697]~P35(x6971)+E(f10(x6971,x6972,x6973),f10(x6971,x6973,x6972))
% 1.14/1.27 [698]~P35(x6981)+E(f9(x6981,x6982,x6983),f9(x6981,x6983,x6982))
% 1.14/1.27 [740]P11(a41,x7401,x7402)+~E(x7402,f9(a41,x7401,x7403))
% 1.14/1.27 [747]~E(x7471,f10(a1,x7472,x7473))+E(f5(a1,x7471,x7472),f2(a1))
% 1.14/1.27 [832]E(x8321,x8322)+~E(f9(a41,x8323,x8321),f9(a41,x8323,x8322))
% 1.14/1.27 [833]E(x8331,x8332)+~E(f9(a41,x8331,x8333),f9(a41,x8332,x8333))
% 1.14/1.27 [997]~P11(a41,x9971,x9973)+P11(a41,x9971,f9(a41,x9972,x9973))
% 1.14/1.27 [998]~P11(a41,x9981,x9982)+P11(a41,x9981,f9(a41,x9982,x9983))
% 1.14/1.27 [999]~P12(a41,x9991,x9993)+P12(a41,x9991,f9(a41,x9992,x9993))
% 1.14/1.27 [1000]~P12(a41,x10001,x10002)+P12(a41,x10001,f9(a41,x10002,x10003))
% 1.14/1.27 [1100]P11(a41,x11001,x11002)+~P11(a41,f9(a41,x11003,x11001),x11002)
% 1.14/1.27 [1101]P11(a41,x11011,x11012)+~P11(a41,f9(a41,x11011,x11013),x11012)
% 1.14/1.27 [1102]P12(a41,x11021,x11022)+~P12(a41,f9(a41,x11021,x11023),x11022)
% 1.14/1.27 [1130]P11(a41,f10(a41,x11302,x11301),f10(a41,x11303,x11301))+P12(a41,f2(a41),x11301)
% 1.14/1.27 [1131]P11(a41,f10(a41,x11311,x11312),f10(a41,x11311,x11313))+P12(a41,f2(a41),x11311)
% 1.14/1.27 [1191]~P11(a41,x11912,x11913)+P11(a41,f10(a41,x11911,x11912),f10(a41,x11911,x11913))
% 1.14/1.27 [1193]~P11(a41,x11931,x11933)+P11(a41,f10(a41,x11931,x11932),f10(a41,x11933,x11932))
% 1.14/1.27 [1194]~P11(a41,x11942,x11943)+P11(a41,f9(a41,x11941,x11942),f9(a41,x11941,x11943))
% 1.14/1.27 [1195]~P11(a41,x11951,x11953)+P11(a41,f9(a41,x11951,x11952),f9(a41,x11953,x11952))
% 1.14/1.27 [1196]~P11(a1,x11962,x11963)+P11(a1,f9(a1,x11961,x11962),f9(a1,x11961,x11963))
% 1.14/1.27 [1199]~P11(a40,x11992,x11993)+P11(a40,f9(a40,x11991,x11992),f9(a40,x11991,x11993))
% 1.14/1.27 [1200]~P12(a41,x12002,x12003)+P12(a41,f9(a41,x12001,x12002),f9(a41,x12001,x12003))
% 1.14/1.27 [1201]~P12(a41,x12011,x12013)+P12(a41,f9(a41,x12011,x12012),f9(a41,x12013,x12012))
% 1.14/1.27 [1202]~P12(a1,x12021,x12023)+P12(a1,f9(a1,x12021,x12022),f9(a1,x12023,x12022))
% 1.14/1.27 [1431]P11(a41,x14311,x14312)+~P11(a41,f9(a41,x14313,x14311),f9(a41,x14313,x14312))
% 1.14/1.27 [1434]P12(a41,x14341,x14342)+~P12(a41,f9(a41,x14343,x14341),f9(a41,x14343,x14342))
% 1.14/1.27 [1435]P12(a41,x14351,x14352)+~P12(a41,f10(a41,x14353,x14351),f10(a41,x14353,x14352))
% 1.14/1.27 [1436]P12(a41,x14361,x14362)+~P12(a41,f10(a41,x14361,x14363),f10(a41,x14362,x14363))
% 1.14/1.27 [1440]~P12(a41,f10(a41,x14402,x14401),f10(a41,x14403,x14401))+P12(a41,f2(a41),x14401)
% 1.14/1.27 [1441]~P12(a41,f10(a41,x14411,x14412),f10(a41,x14411,x14413))+P12(a41,f2(a41),x14411)
% 1.14/1.27 [840]~P9(x8401)+E(f5(x8401,f10(x8401,x8402,x8403),x8403),f2(x8401))
% 1.14/1.27 [841]~P9(x8411)+E(f5(x8411,f10(x8411,x8412,x8413),x8412),f2(x8411))
% 1.14/1.27 [909]~P38(x9091)+E(f18(x9091,f19(x9091,x9092),x9093),f19(x9091,f18(a40,x9092,x9093)))
% 1.14/1.27 [911]~P41(x9111)+E(f17(x9111,f18(x9111,x9112,x9113)),f18(a40,f17(x9111,x9112),x9113))
% 1.14/1.27 [913]~P44(x9131)+E(f18(x9131,f4(x9131,x9132),x9133),f4(x9131,f18(x9131,x9132,x9133)))
% 1.14/1.27 [943]~P9(x9431)+E(f5(x9431,f9(x9431,x9432,x9433),x9433),f5(x9431,x9432,x9433))
% 1.14/1.27 [944]~P9(x9441)+E(f5(x9441,f9(x9441,x9442,x9443),x9442),f5(x9441,x9443,x9442))
% 1.14/1.27 [945]~P9(x9451)+E(f5(x9451,f5(x9451,x9452,x9453),x9453),f5(x9451,x9452,x9453))
% 1.14/1.27 [949]~P44(x9491)+P11(x9491,f2(x9491),f18(x9491,f4(x9491,x9492),x9493))
% 1.14/1.27 [954]~P38(x9541)+E(f10(x9541,f19(x9541,x9542),f19(x9541,x9543)),f19(x9541,f10(a40,x9542,x9543)))
% 1.14/1.27 [955]~P38(x9551)+E(f9(x9551,f19(x9551,x9552),f19(x9551,x9553)),f19(x9551,f9(a40,x9552,x9553)))
% 1.14/1.27 [956]~P1(x9561)+E(f10(x9561,f15(x9561,x9562),f15(x9561,x9563)),f15(x9561,f10(a1,x9562,x9563)))
% 1.14/1.27 [957]~P1(x9571)+E(f9(x9571,f15(x9571,x9572),f15(x9571,x9573)),f15(x9571,f9(a1,x9572,x9573)))
% 1.14/1.27 [960]~P41(x9601)+E(f10(a40,f17(x9601,x9602),f17(x9601,x9603)),f17(x9601,f10(x9601,x9602,x9603)))
% 1.14/1.27 [961]~P44(x9611)+E(f10(x9611,f4(x9611,x9612),f4(x9611,x9613)),f4(x9611,f10(x9611,x9612,x9613)))
% 1.14/1.27 [962]~P13(x9621)+E(f20(x9621,f4(x9621,x9622),f4(x9621,x9623)),f4(x9621,f20(x9621,x9622,x9623)))
% 1.14/1.27 [1110]P12(a41,x11101,x11102)+~E(x11102,f9(a41,f9(a41,x11101,x11103),f3(a41)))
% 1.14/1.27 [1137]~P68(x11371,x11373,x11372)+P67(f21(x11371,f5(a1,x11372,x11373)))
% 1.14/1.27 [1147]~P3(x11471)+E(f10(x11471,f18(x11471,x11472,x11473),x11472),f10(x11471,x11472,f18(x11471,x11472,x11473)))
% 1.14/1.27 [1340]P68(x13401,x13402,x13403)+~P67(f21(x13401,f5(a1,x13403,x13402)))
% 1.14/1.27 [1392]~P42(x13921)+P11(a40,f17(x13921,f18(x13921,x13922,x13923)),f18(a40,f17(x13921,x13922),x13923))
% 1.14/1.27 [1466]~P36(x14661)+P11(a40,f17(x14661,f10(x14661,x14662,x14663)),f10(a40,f17(x14661,x14662),f17(x14661,x14663)))
% 1.14/1.27 [1467]~P43(x14671)+P11(a40,f17(x14671,f9(x14671,x14672,x14673)),f9(a40,f17(x14671,x14672),f17(x14671,x14673)))
% 1.14/1.27 [1468]~P23(x14681)+P11(x14681,f4(x14681,f9(x14681,x14682,x14683)),f9(x14681,f4(x14681,x14682),f4(x14681,x14683)))
% 1.14/1.27 [1604]~P50(x16041)+P11(x16041,f2(x16041),f9(x16041,f10(x16041,x16042,x16042),f10(x16041,x16043,x16043)))
% 1.14/1.27 [1762]~P50(x17621)+~P12(x17621,f9(x17621,f10(x17621,x17622,x17622),f10(x17621,x17623,x17623)),f2(x17621))
% 1.14/1.27 [1114]~P12(a1,x11141,a11)+E(f10(a41,f15(a41,x11141),f10(a41,f15(a41,x11142),x11143)),f2(a41))
% 1.14/1.27 [1159]~P35(x11591)+E(f10(x11591,x11592,f18(x11591,x11592,x11593)),f18(x11591,x11592,f9(a41,x11593,f3(a41))))
% 1.14/1.27 [1160]~P35(x11601)+E(f10(x11601,f18(x11601,x11602,x11603),x11602),f18(x11601,x11602,f9(a41,x11603,f3(a41))))
% 1.14/1.27 [1161]~P29(x11611)+E(f18(x11611,x11612,f9(a41,x11613,f3(a41))),f10(x11611,x11612,f18(x11611,x11612,x11613)))
% 1.14/1.27 [1162]~P35(x11621)+E(f18(x11621,x11622,f9(a41,x11623,f3(a41))),f10(x11621,x11622,f18(x11621,x11622,x11623)))
% 1.14/1.27 [1163]~P3(x11631)+E(f18(x11631,x11632,f9(a41,x11633,f3(a41))),f10(x11631,f18(x11631,x11632,x11633),x11632))
% 1.14/1.27 [1179]~P23(x11791)+E(f4(x11791,f9(x11791,f4(x11791,x11792),f4(x11791,x11793))),f9(x11791,f4(x11791,x11792),f4(x11791,x11793)))
% 1.14/1.27 [1185]~P35(x11851)+E(f9(x11851,x11852,f10(x11851,x11853,x11852)),f10(x11851,f9(x11851,x11853,f3(x11851)),x11852))
% 1.14/1.27 [1186]~P35(x11861)+E(f9(x11861,f10(x11861,x11862,x11863),x11863),f10(x11861,f9(x11861,x11862,f3(x11861)),x11863))
% 1.14/1.27 [1209]~P7(x12091)+E(f20(x12091,f3(x12091),f18(x12091,x12092,x12093)),f18(x12091,f20(x12091,f3(x12091),x12092),x12093))
% 1.14/1.27 [1469]E(x14691,x14692)+~E(f10(a41,f9(a41,x14693,f3(a41)),x14691),f10(a41,f9(a41,x14693,f3(a41)),x14692))
% 1.14/1.27 [1549]P12(a1,x15491,a11)+E(f10(a41,f15(a41,x15491),f10(a41,f15(a41,x15492),x15493)),f10(a41,f15(a41,f10(a1,x15491,x15492)),x15493))
% 1.14/1.27 [1726]~P12(a41,x17262,x17263)+P12(a41,f10(a41,f9(a41,x17261,f3(a41)),x17262),f10(a41,f9(a41,x17261,f3(a41)),x17263))
% 1.14/1.27 [1793]P11(a41,x17931,x17932)+~P11(a41,f10(a41,f9(a41,x17933,f3(a41)),x17931),f10(a41,f9(a41,x17933,f3(a41)),x17932))
% 1.14/1.27 [1858]~P35(x18581)+E(f18(x18581,x18582,f9(a41,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18583),f3(a41))),f10(x18581,x18582,f10(x18581,f18(x18581,x18582,x18583),f18(x18581,x18582,x18583))))
% 1.14/1.27 [1838]~P35(x18381)+E(f18(x18381,x18382,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18383)),f10(x18381,f18(x18381,x18382,x18383),f18(x18381,x18382,x18383)))
% 1.14/1.27 [1844]~P3(x18441)+E(f18(x18441,f18(x18441,x18442,x18443),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18441,x18442,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18443)))
% 1.14/1.27 [1851]~E(f10(a40,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18511),f20(a40,x18512,x18513))+E(x18511,f20(a40,x18512,f10(a40,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18513)))
% 1.14/1.27 [1855]~P44(x18551)+P11(x18551,f2(x18551),f18(x18551,x18552,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18553)))
% 1.14/1.27 [1857]E(f10(a40,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18571),f20(a40,x18572,x18573))+~E(x18571,f20(a40,x18572,f10(a40,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18573)))
% 1.14/1.27 [1859]~P3(x18591)+E(f18(x18591,x18592,f9(a41,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18593),f3(a41))),f10(x18591,x18592,f18(x18591,f18(x18591,x18592,x18593),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))
% 1.14/1.27 [1867]~P44(x18671)+P11(x18671,f2(x18671),f9(x18671,f18(x18671,x18672,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18671,x18673,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))
% 1.14/1.27 [1876]~P44(x18761)+~P12(x18761,f9(x18761,f18(x18761,x18762,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18761,x18763,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(x18761))
% 1.14/1.27 [1881]~P1(x18811)+E(f9(x18811,f9(x18811,f18(x18811,x18812,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18811,x18813,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f10(x18811,f10(x18811,f15(x18811,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18812),x18813)),f18(x18811,f9(x18811,x18812,x18813),f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1138]~P35(x11381)+E(f18(x11381,f18(x11381,x11382,x11383),x11384),f18(x11381,x11382,f10(a41,x11383,x11384)))
% 1.14/1.27 [1139]~P3(x11391)+E(f18(x11391,f18(x11391,x11392,x11393),x11394),f18(x11391,x11392,f10(a41,x11393,x11394)))
% 1.14/1.27 [1140]~P35(x11401)+E(f10(x11401,x11402,f10(x11401,x11403,x11404)),f10(x11401,x11403,f10(x11401,x11402,x11404)))
% 1.14/1.27 [1141]~P35(x11411)+E(f9(x11411,x11412,f9(x11411,x11413,x11414)),f9(x11411,x11413,f9(x11411,x11412,x11414)))
% 1.14/1.27 [1143]~P46(x11431)+E(f20(x11431,f10(x11431,x11432,x11433),x11434),f10(x11431,x11432,f20(x11431,x11433,x11434)))
% 1.14/1.27 [1145]~P35(x11451)+E(f10(x11451,f10(x11451,x11452,x11453),x11454),f10(x11451,x11452,f10(x11451,x11453,x11454)))
% 1.14/1.27 [1146]~P5(x11461)+E(f10(x11461,f10(x11461,x11462,x11463),x11464),f10(x11461,x11462,f10(x11461,x11463,x11464)))
% 1.14/1.27 [1148]~P35(x11481)+E(f9(x11481,f9(x11481,x11482,x11483),x11484),f9(x11481,x11482,f9(x11481,x11483,x11484)))
% 1.14/1.27 [1149]~P6(x11491)+E(f9(x11491,f9(x11491,x11492,x11493),x11494),f9(x11491,x11492,f9(x11491,x11493,x11494)))
% 1.14/1.27 [1150]~P35(x11501)+E(f10(x11501,f10(x11501,x11502,x11503),x11504),f10(x11501,f10(x11501,x11502,x11504),x11503))
% 1.14/1.27 [1151]~P35(x11511)+E(f9(x11511,f9(x11511,x11512,x11513),x11514),f9(x11511,f9(x11511,x11512,x11514),x11513))
% 1.14/1.27 [1353]~P3(x13531)+E(f10(x13531,f18(x13531,x13532,x13533),f18(x13531,x13532,x13534)),f18(x13531,x13532,f9(a41,x13533,x13534)))
% 1.14/1.27 [1354]~P35(x13541)+E(f10(x13541,f18(x13541,x13542,x13543),f18(x13541,x13542,x13544)),f18(x13541,x13542,f9(a41,x13543,x13544)))
% 1.14/1.27 [1357]~P35(x13571)+E(f9(x13571,f10(x13571,x13572,x13573),f10(x13571,x13572,x13574)),f10(x13571,x13572,f9(x13571,x13573,x13574)))
% 1.14/1.27 [1359]~P36(x13591)+E(f9(x13591,f10(x13591,x13592,x13593),f10(x13591,x13592,x13594)),f10(x13591,x13592,f9(x13591,x13593,x13594)))
% 1.14/1.27 [1362]~P36(x13621)+E(f9(x13621,f10(x13621,x13622,x13623),f10(x13621,x13624,x13623)),f10(x13621,f9(x13621,x13622,x13624),x13623))
% 1.14/1.27 [1363]~P39(x13631)+E(f9(x13631,f10(x13631,x13632,x13633),f10(x13631,x13634,x13633)),f10(x13631,f9(x13631,x13632,x13634),x13633))
% 1.14/1.27 [1364]~P35(x13641)+E(f10(x13641,f18(x13641,x13642,x13643),f18(x13641,x13644,x13643)),f18(x13641,f10(x13641,x13642,x13644),x13643))
% 1.14/1.27 [1365]~P4(x13651)+E(f10(x13651,f18(x13651,x13652,x13653),f18(x13651,x13654,x13653)),f18(x13651,f10(x13651,x13652,x13654),x13653))
% 1.14/1.27 [1366]~P7(x13661)+E(f20(x13661,f18(x13661,x13662,x13663),f18(x13661,x13664,x13663)),f18(x13661,f20(x13661,x13662,x13664),x13663))
% 1.14/1.27 [1367]~P46(x13671)+E(f9(x13671,f20(x13671,x13672,x13673),f20(x13671,x13674,x13673)),f20(x13671,f9(x13671,x13672,x13674),x13673))
% 1.14/1.27 [1368]~P40(x13681)+E(f9(x13681,f20(x13681,x13682,x13683),f20(x13681,x13684,x13683)),f20(x13681,f9(x13681,x13682,x13684),x13683))
% 1.14/1.27 [1369]~P9(x13691)+E(f5(x13691,f10(x13691,x13692,x13693),f10(x13691,x13692,x13694)),f10(x13691,x13692,f5(x13691,x13693,x13694)))
% 1.14/1.27 [1370]~P35(x13701)+E(f9(x13701,f10(x13701,x13702,x13703),f10(x13701,x13704,x13703)),f10(x13701,f9(x13701,x13702,x13704),x13703))
% 1.14/1.27 [1371]~P9(x13711)+E(f5(x13711,f10(x13711,x13712,x13713),f10(x13711,x13714,x13713)),f10(x13711,f5(x13711,x13712,x13714),x13713))
% 1.14/1.27 [1355]~P9(x13551)+E(f5(x13551,f9(x13551,x13552,f10(x13551,x13553,x13554)),x13554),f5(x13551,x13552,x13554))
% 1.14/1.27 [1356]~P9(x13561)+E(f5(x13561,f9(x13561,x13562,f10(x13561,x13563,x13564)),x13563),f5(x13561,x13562,x13563))
% 1.14/1.27 [1508]~P1(x15081)+E(f10(x15081,f15(x15081,x15082),f10(x15081,f15(x15081,x15083),x15084)),f10(x15081,f15(x15081,f10(a1,x15082,x15083)),x15084))
% 1.14/1.27 [1509]~P1(x15091)+E(f9(x15091,f15(x15091,x15092),f9(x15091,f15(x15091,x15093),x15094)),f9(x15091,f15(x15091,f9(a1,x15092,x15093)),x15094))
% 1.14/1.27 [1516]~P9(x15161)+E(f5(x15161,f10(x15161,x15162,f5(x15161,x15163,x15164)),x15164),f5(x15161,f10(x15161,x15162,x15163),x15164))
% 1.14/1.27 [1520]~P9(x15201)+E(f5(x15201,f9(x15201,x15202,f5(x15201,x15203,x15204)),x15204),f5(x15201,f9(x15201,x15202,x15203),x15204))
% 1.14/1.27 [1521]~P9(x15211)+E(f5(x15211,f10(x15211,f5(x15211,x15212,x15213),x15214),x15213),f5(x15211,f10(x15211,x15212,x15214),x15213))
% 1.14/1.27 [1522]~P9(x15221)+E(f5(x15221,f9(x15221,f5(x15221,x15222,x15223),x15224),x15223),f5(x15221,f9(x15221,x15222,x15224),x15223))
% 1.14/1.27 [1715]~P9(x17151)+E(f5(x17151,f10(x17151,f5(x17151,x17152,x17153),f5(x17151,x17154,x17153)),x17153),f5(x17151,f10(x17151,x17152,x17154),x17153))
% 1.14/1.27 [1716]~P9(x17161)+E(f5(x17161,f9(x17161,f5(x17161,x17162,x17163),f5(x17161,x17164,x17163)),x17163),f5(x17161,f9(x17161,x17162,x17164),x17163))
% 1.14/1.27 [1523]~P35(x15231)+E(f10(x15231,f10(x15231,x15232,x15233),f10(x15231,x15234,x15235)),f10(x15231,f10(x15231,x15232,x15234),f10(x15231,x15233,x15235)))
% 1.14/1.27 [1524]~P35(x15241)+E(f9(x15241,f9(x15241,x15242,x15243),f9(x15241,x15244,x15245)),f9(x15241,f9(x15241,x15242,x15244),f9(x15241,x15243,x15245)))
% 1.14/1.27 [1525]~P7(x15251)+E(f20(x15251,f10(x15251,x15252,x15253),f10(x15251,x15254,x15255)),f10(x15251,f20(x15251,x15252,x15254),f20(x15251,x15253,x15255)))
% 1.14/1.27 [1757]~P65(x17571)+E(f9(x17571,f10(x17571,x17572,x17573),f9(x17571,f10(x17571,x17574,x17573),x17575)),f9(x17571,f10(x17571,f9(x17571,x17572,x17574),x17573),x17575))
% 1.14/1.27 [543]~P1(x5431)+~P44(x5431)+E(f4(x5431,f15(x5431,a12)),f3(x5431))
% 1.14/1.27 [1665]E(x16651,f2(a41))+E(x16651,f9(a41,f2(a41),f3(a41)))+~P12(a41,x16651,f9(a41,f9(a41,f2(a41),f3(a41)),f3(a41)))
% 1.14/1.27 [1807]~P12(a41,x18071,a44)+E(x18071,f2(a41))+P12(a40,f17(a13,f9(a13,f3(a13),f10(a13,a42,f18(a13,f26(x18071),x18071)))),f3(a40))
% 1.14/1.27 [1822]E(x18221,f2(a41))+E(x18221,f9(a41,f2(a41),f3(a41)))+~P12(a41,x18221,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))
% 1.14/1.27 [1833]~P1(x18331)+~P13(x18331)+P12(x18331,f2(x18331),f20(x18331,f3(x18331),f15(x18331,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [683]E(x6831,x6832)+P12(a41,x6832,x6831)+P12(a41,x6831,x6832)
% 1.14/1.27 [684]E(x6841,x6842)+P12(a1,x6842,x6841)+P12(a1,x6841,x6842)
% 1.14/1.27 [743]E(x7431,x7432)+P12(a41,x7431,x7432)+~P11(a41,x7431,x7432)
% 1.14/1.27 [744]E(x7441,x7442)+P12(a1,x7441,x7442)+~P11(a1,x7441,x7442)
% 1.14/1.27 [746]E(x7461,x7462)+P12(a40,x7461,x7462)+~P11(a40,x7461,x7462)
% 1.14/1.27 [836]E(x8361,x8362)+~P11(a41,x8362,x8361)+~P11(a41,x8361,x8362)
% 1.14/1.27 [837]E(x8371,x8372)+~P11(a1,x8372,x8371)+~P11(a1,x8371,x8372)
% 1.14/1.27 [838]E(x8381,x8382)+~P11(a40,x8382,x8381)+~P11(a40,x8381,x8382)
% 1.14/1.27 [530]~P38(x5301)+E(f19(x5301,x5302),f2(x5301))+~E(x5302,f2(a40))
% 1.14/1.27 [533]~P43(x5331)+~E(x5332,f2(x5331))+E(f17(x5331,x5332),f2(a40))
% 1.14/1.27 [534]~P23(x5341)+~E(x5342,f2(x5341))+E(f4(x5341,x5342),f2(x5341))
% 1.14/1.27 [539]~P43(x5392)+E(x5391,f2(x5392))+~E(f17(x5392,x5391),f2(a40))
% 1.14/1.27 [540]~P38(x5402)+~E(f19(x5402,x5401),f2(x5402))+E(x5401,f2(a40))
% 1.14/1.27 [541]~P23(x5412)+~E(f4(x5412,x5411),f2(x5412))+E(x5411,f2(x5412))
% 1.14/1.27 [569]~E(x5692,f3(a41))+~E(x5691,f3(a41))+E(f10(a41,x5691,x5692),f3(a41))
% 1.14/1.27 [570]~E(x5702,f3(a1))+~E(x5701,f3(a1))+E(f10(a1,x5701,x5702),f3(a1))
% 1.14/1.27 [571]~E(x5712,f2(a41))+~E(x5711,f2(a41))+E(f9(a41,x5711,x5712),f2(a41))
% 1.14/1.27 [589]~P46(x5892)+E(f20(x5892,x5891,x5891),f3(x5892))+E(x5891,f2(x5892))
% 1.14/1.27 [590]~P47(x5902)+E(f20(x5902,x5901,x5901),f3(x5902))+E(x5901,f2(x5902))
% 1.14/1.27 [611]~P18(x6111)+~E(x6112,f2(x6111))+E(f9(x6111,x6112,x6112),f2(x6111))
% 1.14/1.27 [612]~P47(x6121)+~E(x6122,f2(x6121))+E(f20(x6121,x6122,x6122),f2(x6121))
% 1.14/1.27 [644]~E(f10(a41,x6442,x6441),x6442)+E(x6441,f3(a41))+E(x6442,f2(a41))
% 1.14/1.27 [646]~E(x6461,f15(a1,a12))+~E(x6462,f15(a1,a12))+E(f10(a1,x6461,x6462),f3(a1))
% 1.14/1.27 [649]~P43(x6492)+E(x6491,f2(x6492))+P12(a40,f2(a40),f17(x6492,x6491))
% 1.14/1.27 [650]E(x6501,f2(a41))+E(x6502,f2(a41))+~E(f10(a41,x6502,x6501),f2(a41))
% 1.14/1.27 [661]~P43(x6611)+~E(x6612,f2(x6611))+P11(a40,f17(x6611,x6612),f2(a40))
% 1.14/1.27 [662]~P23(x6622)+P12(x6622,f2(x6622),f4(x6622,x6621))+E(x6621,f2(x6622))
% 1.14/1.27 [666]~P23(x6661)+P11(x6661,f4(x6661,x6662),f2(x6661))+~E(x6662,f2(x6661))
% 1.14/1.27 [668]E(x6682,f15(a1,a12))+E(x6681,f3(a1))+~E(f10(a1,x6681,x6682),f3(a1))
% 1.14/1.27 [669]E(x6692,f15(a1,a12))+E(x6691,f3(a1))+~E(f10(a1,x6692,x6691),f3(a1))
% 1.14/1.27 [670]E(x6701,f15(a1,a12))+E(x6701,f3(a1))+~E(f10(a1,x6702,x6701),f3(a1))
% 1.14/1.27 [672]E(x6721,f15(a1,a12))+E(x6721,f3(a1))+~E(f10(a1,x6721,x6722),f3(a1))
% 1.14/1.27 [675]~P18(x6752)+~E(f9(x6752,x6751,x6751),f2(x6752))+E(x6751,f2(x6752))
% 1.14/1.27 [708]~P23(x7081)+~P11(x7081,f2(x7081),x7082)+E(f4(x7081,x7082),x7082)
% 1.14/1.27 [709]~P23(x7091)+~P12(x7091,f2(x7091),x7092)+E(f4(x7091,x7092),x7092)
% 1.14/1.27 [748]~P43(x7482)+E(x7481,f2(x7482))+~P11(a40,f17(x7482,x7481),f2(a40))
% 1.14/1.27 [751]P10(a41,x7511)+P10(a41,x7512)+P10(a41,f9(a41,x7512,x7511))
% 1.14/1.27 [753]~P43(x7532)+~E(x7531,f2(x7532))+~P12(a40,f2(a40),f17(x7532,x7531))
% 1.14/1.27 [763]~P23(x7632)+~P11(x7632,f4(x7632,x7631),f2(x7632))+E(x7631,f2(x7632))
% 1.14/1.27 [791]~P23(x7912)+~P12(x7912,f2(x7912),f4(x7912,x7911))+~E(x7911,f2(x7912))
% 1.14/1.27 [815]~P10(a41,x8152)+~P10(a41,x8151)+P10(a41,f9(a41,x8151,x8152))
% 1.14/1.27 [864]E(x8641,f3(a1))+~P12(a1,f2(a1),x8642)+~E(f10(a1,x8642,x8641),f3(a1))
% 1.14/1.27 [865]E(x8651,f3(a1))+~P12(a1,f2(a1),x8651)+~E(f10(a1,x8651,x8652),f3(a1))
% 1.14/1.27 [919]P10(a41,x9191)+P10(a41,x9192)+~P10(a41,f10(a41,x9192,x9191))
% 1.14/1.27 [937]P10(a41,x9371)+~P10(a41,x9372)+~P10(a41,f9(a41,x9372,x9371))
% 1.14/1.27 [938]P10(a41,x9381)+~P10(a41,x9382)+~P10(a41,f9(a41,x9381,x9382))
% 1.14/1.27 [946]~P10(a41,x9461)+~P12(a41,f2(a41),x9462)+P10(a41,f18(a41,x9461,x9462))
% 1.14/1.27 [947]~P12(a1,x9472,x9471)+E(f5(a1,x9471,x9472),x9471)+~P11(a1,x9471,f2(a1))
% 1.14/1.27 [948]~P12(a1,x9481,x9482)+E(f5(a1,x9481,x9482),x9481)+~P11(a1,f2(a1),x9481)
% 1.14/1.27 [1047]P11(a1,x10471,x10472)+P11(a1,x10471,a11)+~P11(a41,f15(a41,x10471),f15(a41,x10472))
% 1.14/1.27 [1049]~P12(a1,x10491,x10492)+~P12(a1,a11,x10492)+P12(a41,f15(a41,x10491),f15(a41,x10492))
% 1.14/1.27 [1054]~P18(x10541)+~P11(x10541,f2(x10541),x10542)+P11(x10541,f2(x10541),f9(x10541,x10542,x10542))
% 1.14/1.27 [1057]~P18(x10571)+~P12(x10571,f2(x10571),x10572)+P12(x10571,f2(x10571),f9(x10571,x10572,x10572))
% 1.14/1.27 [1058]~P18(x10581)+~P11(x10581,x10582,f2(x10581))+P11(x10581,f9(x10581,x10582,x10582),f2(x10581))
% 1.14/1.27 [1059]~P44(x10591)+~P12(x10591,x10592,f2(x10591))+P12(x10591,f9(x10591,x10592,x10592),f2(x10591))
% 1.14/1.27 [1060]~P18(x10601)+~P12(x10601,x10602,f2(x10601))+P12(x10601,f9(x10601,x10602,x10602),f2(x10601))
% 1.14/1.27 [1078]~P12(a1,x10782,x10781)+P12(a1,a11,x10781)+~P12(a41,f15(a41,x10782),f15(a41,x10781))
% 1.14/1.27 [1124]E(x11241,f2(a41))+P12(a41,f2(a41),x11242)+~P12(a41,f2(a41),f18(a41,x11242,x11241))
% 1.14/1.27 [1153]~P18(x11531)+~P11(x11531,f9(x11531,x11532,x11532),f2(x11531))+P11(x11531,x11532,f2(x11531))
% 1.14/1.27 [1155]~P44(x11551)+~P12(x11551,f9(x11551,x11552,x11552),f2(x11551))+P12(x11551,x11552,f2(x11551))
% 1.14/1.27 [1156]~P18(x11561)+~P12(x11561,f9(x11561,x11562,x11562),f2(x11561))+P12(x11561,x11562,f2(x11561))
% 1.14/1.27 [1157]~P18(x11571)+~P11(x11571,f2(x11571),f9(x11571,x11572,x11572))+P11(x11571,f2(x11571),x11572)
% 1.14/1.27 [1158]~P18(x11581)+~P12(x11581,f2(x11581),f9(x11581,x11582,x11582))+P12(x11581,f2(x11581),x11582)
% 1.14/1.27 [1170]~P11(a40,x11701,f2(a40))+~P11(a40,x11702,f2(a40))+P11(a40,f2(a40),f20(a40,x11701,x11702))
% 1.14/1.27 [1171]~P11(a40,x11712,f2(a40))+~P11(a40,f2(a40),x11712)+P11(a40,f2(a40),f20(a40,x11711,x11712))
% 1.14/1.27 [1172]~P11(a40,x11721,f2(a40))+~P11(a40,f2(a40),x11721)+P11(a40,f2(a40),f20(a40,x11721,x11722))
% 1.14/1.27 [1173]~P11(a1,f2(a1),x11732)+~P11(a1,f2(a1),x11731)+P11(a1,f2(a1),f10(a1,x11731,x11732))
% 1.14/1.27 [1174]~P11(a1,f2(a1),x11742)+~P11(a1,f2(a1),x11741)+P11(a1,f2(a1),f9(a1,x11741,x11742))
% 1.14/1.27 [1175]~P11(a1,f2(a1),x11752)+~P11(a1,f2(a1),x11751)+P11(a1,f2(a1),f5(a1,x11751,x11752))
% 1.14/1.27 [1176]~P11(a40,f2(a40),x11762)+~P11(a40,f2(a40),x11761)+P11(a40,f2(a40),f20(a40,x11761,x11762))
% 1.14/1.27 [1177]~P12(a41,f2(a41),x11772)+~P12(a41,f2(a41),x11771)+P12(a41,f2(a41),f10(a41,x11771,x11772))
% 1.14/1.27 [1178]~P12(a40,f2(a40),x11782)+~P12(a40,f2(a40),x11781)+P12(a40,f2(a40),f10(a40,x11781,x11782))
% 1.14/1.27 [1232]P11(a40,x12321,f2(a40))+P11(a40,f2(a40),x12322)+~P11(a40,f2(a40),f20(a40,x12322,x12321))
% 1.14/1.27 [1233]P11(a40,x12331,f2(a40))+P11(a40,f2(a40),x12332)+~P11(a40,f2(a40),f20(a40,x12331,x12332))
% 1.14/1.27 [1234]P12(a41,f2(a41),x12341)+P12(a41,f2(a41),x12342)+~P12(a41,f2(a41),f9(a41,x12342,x12341))
% 1.14/1.27 [1381]E(f5(a1,x13811,x13812),f9(a1,x13811,x13812))+~P12(a1,f2(a1),x13811)+~P11(a1,f9(a1,x13811,x13812),f2(a1))
% 1.14/1.27 [560]~P1(x5601)+~P38(x5601)+E(f19(x5601,f15(a40,x5602)),f15(x5601,x5602))
% 1.14/1.27 [635]~P1(x6351)+~P42(x6351)+E(f17(x6351,f15(x6351,x6352)),f4(a40,f15(a40,x6352)))
% 1.14/1.27 [651]~P1(x6511)+~P7(x6511)+E(f20(x6511,x6512,f15(x6511,a11)),f2(x6511))
% 1.14/1.27 [686]~P1(x6861)+~P10(a41,x6862)+E(f18(x6861,f15(x6861,a12),x6862),f3(x6861))
% 1.14/1.27 [688]~P1(x6881)+P10(a41,x6882)+E(f18(x6881,f15(x6881,a12),x6882),f15(x6881,a12))
% 1.14/1.27 [888]E(x8881,f2(a41))+E(x8882,f2(a41))+~E(f9(a41,x8882,x8881),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [889]E(x8891,f2(a41))+E(x8892,f2(a41))+~E(f9(a41,f2(a41),f3(a41)),f9(a41,x8892,x8891))
% 1.14/1.27 [922]~E(x9222,f2(a41))+~E(x9221,f9(a41,f2(a41),f3(a41)))+E(f9(a41,x9221,x9222),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [923]~E(x9231,f2(a41))+~E(x9232,f9(a41,f2(a41),f3(a41)))+E(f9(a41,x9231,x9232),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [924]~E(x9242,f2(a41))+~E(x9241,f9(a41,f2(a41),f3(a41)))+E(f9(a41,f2(a41),f3(a41)),f9(a41,x9241,x9242))
% 1.14/1.27 [925]~E(x9251,f2(a41))+~E(x9252,f9(a41,f2(a41),f3(a41)))+E(f9(a41,f2(a41),f3(a41)),f9(a41,x9251,x9252))
% 1.14/1.27 [992]E(x9921,f2(a41))+E(x9922,f9(a41,f2(a41),f3(a41)))+~E(f18(a41,x9922,x9921),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [993]E(x9931,f2(a41))+E(x9931,f9(a41,f2(a41),f3(a41)))+~E(f9(a41,x9932,x9931),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [994]E(x9941,f2(a41))+E(x9941,f9(a41,f2(a41),f3(a41)))+~E(f9(a41,x9941,x9942),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [995]E(x9951,f2(a41))+E(x9951,f9(a41,f2(a41),f3(a41)))+~E(f9(a41,f2(a41),f3(a41)),f9(a41,x9952,x9951))
% 1.14/1.27 [996]E(x9961,f2(a41))+E(x9961,f9(a41,f2(a41),f3(a41)))+~E(f9(a41,f2(a41),f3(a41)),f9(a41,x9961,x9962))
% 1.14/1.27 [1009]P12(a1,x10091,a11)+~P12(a1,x10092,a11)+E(f9(a41,f15(a41,x10091),f15(a41,x10092)),f15(a41,x10091))
% 1.14/1.27 [1063]~E(x10632,f2(a40))+~E(x10631,f2(a40))+E(f9(a40,f10(a40,x10631,x10631),f10(a40,x10632,x10632)),f2(a40))
% 1.14/1.27 [1094]E(x10941,f9(a41,f2(a41),f3(a41)))+E(x10942,f9(a41,f2(a41),f3(a41)))+~E(f9(a41,x10941,x10942),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [1095]E(x10951,f9(a41,f2(a41),f3(a41)))+E(x10952,f9(a41,f2(a41),f3(a41)))+~E(f9(a41,f2(a41),f3(a41)),f9(a41,x10951,x10952))
% 1.14/1.27 [1104]~E(x11042,f9(a41,f2(a41),f3(a41)))+~E(x11041,f9(a41,f2(a41),f3(a41)))+E(f10(a41,x11041,x11042),f9(a41,f2(a41),f3(a41)))
% 1.14/1.27 [1107]~P12(a41,x11071,x11072)+P12(a41,f9(a41,x11071,f3(a41)),x11072)+E(f9(a41,x11071,f3(a41)),x11072)
% 1.14/1.27 [1128]E(x11281,x11282)+P12(a41,x11281,x11282)+~P12(a41,x11281,f9(a41,x11282,f3(a41)))
% 1.14/1.27 [1129]E(x11291,x11292)+P12(a1,x11291,x11292)+~P12(a1,x11291,f9(a1,x11292,f3(a1)))
% 1.14/1.27 [1132]P12(a1,x11321,a11)+P12(a1,x11322,a11)+E(f9(a41,f15(a41,x11321),f15(a41,x11322)),f15(a41,f9(a1,x11321,x11322)))
% 1.14/1.27 [1164]E(x11641,f2(a41))+~E(x11642,f2(a1))+~P12(a1,f2(a1),f18(a1,f4(a1,x11642),x11641))
% 1.14/1.27 [1180]P12(a41,f36(x11802,x11801),x11802)+E(x11801,f2(a41))+~P12(a41,x11801,f9(a41,x11802,f3(a41)))
% 1.14/1.27 [1187]E(x11871,x11872)+~P11(a41,x11872,x11871)+~P12(a41,x11871,f9(a41,x11872,f3(a41)))
% 1.14/1.27 [1188]E(x11881,f2(a41))+~P12(a41,x11881,f9(a41,x11882,f3(a41)))+E(f9(a41,f36(x11882,x11881),f3(a41)),x11881)
% 1.14/1.27 [1280]P11(a41,x12801,x12802)+~P11(a41,x12801,f9(a41,x12802,f3(a41)))+E(x12801,f9(a41,x12802,f3(a41)))
% 1.14/1.27 [1666]P12(a41,x16661,f10(a41,x16662,x16661))+~P12(a41,f9(a41,f2(a41),f3(a41)),x16662)+~P12(a41,f9(a41,f2(a41),f3(a41)),x16661)
% 1.14/1.27 [1667]P12(a41,x16671,f10(a41,x16671,x16672))+~P12(a41,f9(a41,f2(a41),f3(a41)),x16672)+~P12(a41,f9(a41,f2(a41),f3(a41)),x16671)
% 1.14/1.27 [1739]~P11(a41,f9(a41,f2(a41),f3(a41)),x17392)+~P11(a41,f9(a41,f2(a41),f3(a41)),x17391)+P11(a41,f9(a41,f2(a41),f3(a41)),f10(a41,x17391,x17392))
% 1.14/1.27 [1740]~P12(a41,f9(a41,f2(a41),f3(a41)),x17401)+~P12(a41,f9(a41,f2(a41),f3(a41)),x17402)+P12(a41,f9(a41,f2(a41),f3(a41)),f10(a41,x17401,x17402))
% 1.14/1.27 [890]~P1(x8901)+~P44(x8901)+E(f4(x8901,f18(x8901,f15(x8901,a12),x8902)),f3(x8901))
% 1.14/1.27 [891]~P29(x8911)+~P64(x8911)+E(f18(x8911,f2(x8911),f9(a41,x8912,f3(a41))),f2(x8911))
% 1.14/1.27 [1692]~P1(x16921)+~P8(x16921)+E(f20(x16921,x16922,f15(x16921,f9(a1,f9(a1,f3(a1),a11),a11))),x16922)
% 1.14/1.27 [1810]~P56(x18101)+~E(x18102,f2(x18101))+E(f18(x18101,x18102,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f2(x18101))
% 1.14/1.27 [1824]E(f14(x18241),x18242)+~P11(a40,f2(a40),x18242)+~E(f18(a40,x18242,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),x18241)
% 1.14/1.27 [1830]~P44(x18302)+E(x18301,f2(x18302))+P12(x18302,f2(x18302),f18(x18302,x18301,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1848]~P44(x18482)+~E(x18481,f2(x18482))+~P12(x18482,f2(x18482),f18(x18482,x18481,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1853]~E(x18532,f2(a40))+~E(x18531,f2(a40))+E(f9(a40,f18(a40,x18531,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x18532,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(a40))
% 1.14/1.27 [562]~E(x5622,x5623)+~P31(x5621)+P11(x5621,x5622,x5623)
% 1.14/1.27 [564]~E(x5642,x5643)+~P33(x5641)+P11(x5641,x5642,x5643)
% 1.14/1.27 [659]~P12(x6593,x6591,x6592)+~E(x6591,x6592)+~P30(x6593)
% 1.14/1.27 [660]~P12(x6603,x6601,x6602)+~E(x6601,x6602)+~P33(x6603)
% 1.14/1.27 [700]P11(x7001,x7003,x7002)+~P30(x7001)+P11(x7001,x7002,x7003)
% 1.14/1.27 [705]P12(x7051,x7053,x7052)+~P30(x7051)+P11(x7051,x7052,x7053)
% 1.14/1.27 [758]~P31(x7581)+~P12(x7581,x7582,x7583)+P11(x7581,x7582,x7583)
% 1.14/1.27 [760]~P33(x7601)+~P12(x7601,x7602,x7603)+P11(x7601,x7602,x7603)
% 1.14/1.27 [856]~P12(x8561,x8563,x8562)+~P30(x8561)+~P11(x8561,x8562,x8563)
% 1.14/1.27 [857]~P12(x8571,x8573,x8572)+~P30(x8571)+~P12(x8571,x8572,x8573)
% 1.14/1.27 [858]~P12(x8581,x8583,x8582)+~P31(x8581)+~P11(x8581,x8582,x8583)
% 1.14/1.27 [862]~P12(x8621,x8623,x8622)+~P31(x8621)+~P12(x8621,x8622,x8623)
% 1.14/1.27 [863]~P12(x8631,x8633,x8632)+~P33(x8631)+~P12(x8631,x8632,x8633)
% 1.14/1.27 [940]~P11(a41,x9401,x9403)+P11(a41,x9401,x9402)+~P11(a41,x9403,x9402)
% 1.14/1.27 [941]~P11(a1,x9411,x9413)+P11(a1,x9411,x9412)+~P11(a1,x9413,x9412)
% 1.14/1.27 [942]~P11(a40,x9421,x9423)+P11(a40,x9421,x9422)+~P11(a40,x9423,x9422)
% 1.14/1.27 [542]~P38(x5423)+E(x5421,x5422)+~E(f19(x5423,x5421),f19(x5423,x5422))
% 1.14/1.27 [591]~P66(x5911)+~E(x5913,f2(x5911))+E(f9(x5911,x5912,x5913),x5912)
% 1.14/1.27 [609]~P55(x6091)+~E(x6093,f2(x6091))+E(f10(x6091,x6092,x6093),f2(x6091))
% 1.14/1.27 [610]~P55(x6101)+~E(x6102,f2(x6101))+E(f10(x6101,x6102,x6103),f2(x6101))
% 1.14/1.27 [665]~P66(x6652)+~E(f9(x6652,x6653,x6651),x6653)+E(x6651,f2(x6652))
% 1.14/1.27 [674]~P56(x6742)+~E(f18(x6742,x6741,x6743),f2(x6742))+E(x6741,f2(x6742))
% 1.14/1.27 [720]~P68(x7201,x7203,x7202)+~E(x7203,f2(a1))+P67(f21(x7201,x7202))
% 1.14/1.27 [843]E(x8431,x8432)+~E(f10(a41,x8433,x8431),f10(a41,x8433,x8432))+E(x8433,f2(a41))
% 1.14/1.27 [844]E(x8441,x8442)+~E(f10(a40,x8443,x8441),f10(a40,x8443,x8442))+E(x8443,f2(a40))
% 1.14/1.27 [845]E(x8451,x8452)+~E(f10(a41,x8451,x8453),f10(a41,x8452,x8453))+E(x8453,f2(a41))
% 1.14/1.27 [846]E(x8461,x8462)+~E(f10(a40,x8461,x8463),f10(a40,x8462,x8463))+E(x8463,f2(a40))
% 1.14/1.27 [872]~P44(x8721)+P12(x8721,f2(x8721),f18(x8721,x8722,x8723))+~E(x8723,f2(a41))
% 1.14/1.27 [892]~P23(x8921)+P11(x8921,x8922,x8923)+~P11(x8921,f4(x8921,x8922),x8923)
% 1.14/1.27 [896]~P44(x8961)+P11(x8961,f2(x8961),f18(x8961,x8962,x8963))+~P10(a41,x8963)
% 1.14/1.27 [1043]E(x10431,x10432)+~E(f10(a41,x10433,x10431),f10(a41,x10433,x10432))+~P12(a41,f2(a41),x10433)
% 1.14/1.27 [1052]~P44(x10521)+~P11(x10521,f2(x10521),x10522)+P11(x10521,f2(x10521),f18(x10521,x10522,x10523))
% 1.14/1.27 [1053]~P48(x10531)+~P11(x10531,f2(x10531),x10532)+P11(x10531,f2(x10531),f18(x10531,x10532,x10533))
% 1.14/1.27 [1055]~P48(x10551)+~P11(x10551,f3(x10551),x10552)+P11(x10551,f3(x10551),f18(x10551,x10552,x10553))
% 1.14/1.27 [1056]~P48(x10561)+~P12(x10561,f2(x10561),x10562)+P12(x10561,f2(x10561),f18(x10561,x10562,x10563))
% 1.14/1.27 [1067]~P44(x10672)+~P11(x10672,f18(x10672,x10673,x10671),f2(x10672))+~E(x10671,f2(a41))
% 1.14/1.27 [1077]~P44(x10771)+~P12(x10771,f18(x10771,x10773,x10772),f2(x10771))+~P10(a41,x10772)
% 1.14/1.27 [1154]~P44(x11541)+~P12(x11541,f18(x11541,x11542,x11543),f2(x11541))+P12(x11541,x11542,f2(x11541))
% 1.14/1.27 [1343]~P11(a40,x13432,x13433)+P11(a40,f10(a40,x13431,x13432),f10(a40,x13431,x13433))+~P12(a40,f2(a40),x13431)
% 1.14/1.27 [1344]~P11(a40,x13441,x13443)+P11(a40,f10(a40,x13441,x13442),f10(a40,x13443,x13442))+~P12(a40,f2(a40),x13442)
% 1.14/1.27 [1348]~P12(a41,x13481,x13483)+P12(a41,f10(a41,x13481,x13482),f10(a41,x13483,x13482))+~P12(a41,f2(a41),x13482)
% 1.14/1.27 [1349]~P12(a41,x13492,x13493)+P12(a41,f10(a41,x13491,x13492),f10(a41,x13491,x13493))+~P12(a41,f2(a41),x13491)
% 1.14/1.27 [1350]~P12(a1,x13502,x13503)+P12(a1,f10(a1,x13501,x13502),f10(a1,x13501,x13503))+~P12(a1,f2(a1),x13501)
% 1.14/1.27 [1351]~P12(a40,x13511,x13513)+P12(a40,f10(a40,x13511,x13512),f10(a40,x13513,x13512))+~P12(a40,f2(a40),x13512)
% 1.14/1.27 [1352]~P12(a40,x13522,x13523)+P12(a40,f10(a40,x13521,x13522),f10(a40,x13521,x13523))+~P12(a40,f2(a40),x13521)
% 1.14/1.27 [1542]P11(a41,x15421,x15422)+~P11(a41,f10(a41,x15423,x15421),f10(a41,x15423,x15422))+~P12(a41,f2(a41),x15423)
% 1.14/1.27 [1543]P11(a41,x15431,x15432)+~P11(a41,f10(a41,x15431,x15433),f10(a41,x15432,x15433))+~P12(a41,f2(a41),x15433)
% 1.14/1.27 [1544]P11(a40,x15441,x15442)+~P11(a40,f10(a40,x15443,x15441),f10(a40,x15443,x15442))+~P12(a40,f2(a40),x15443)
% 1.14/1.27 [1545]P11(a40,x15451,x15452)+~P11(a40,f10(a40,x15451,x15453),f10(a40,x15452,x15453))+~P12(a40,f2(a40),x15453)
% 1.14/1.27 [1547]P12(a41,x15471,x15472)+~P12(a41,f18(a41,x15473,x15471),f18(a41,x15473,x15472))+~P12(a41,f2(a41),x15473)
% 1.14/1.27 [1548]P12(a40,x15481,x15482)+~P12(a40,f10(a40,x15481,x15483),f10(a40,x15482,x15483))+~P12(a40,f2(a40),x15483)
% 1.14/1.27 [820]~P44(x8201)+~P10(a41,x8203)+E(f18(x8201,f4(x8201,x8202),x8203),f18(x8201,x8202,x8203))
% 1.14/1.27 [971]~P37(x9712)+E(x9711,f2(a40))+E(f20(x9712,f19(x9712,x9713),f19(x9712,x9711)),f19(x9712,f20(a40,x9713,x9711)))
% 1.14/1.27 [984]~P40(x9842)+E(x9841,f2(x9842))+E(f20(a40,f17(x9842,x9843),f17(x9842,x9841)),f17(x9842,f20(x9842,x9843,x9841)))
% 1.14/1.27 [986]~P7(x9861)+~P37(x9861)+E(f20(x9861,f19(x9861,x9862),f19(x9861,x9863)),f19(x9861,f20(a40,x9862,x9863)))
% 1.14/1.27 [988]~P14(x9882)+E(x9881,f2(x9882))+E(f20(x9882,f4(x9882,x9883),f4(x9882,x9881)),f4(x9882,f20(x9882,x9883,x9881)))
% 1.14/1.27 [991]~P40(x9911)+~P7(x9911)+E(f20(a40,f17(x9911,x9912),f17(x9911,x9913)),f17(x9911,f20(x9911,x9912,x9913)))
% 1.14/1.27 [1108]~P44(x11081)+~P11(x11081,f2(x11081),x11083)+E(f10(x11081,f4(x11081,x11082),x11083),f4(x11081,f10(x11081,x11082,x11083)))
% 1.14/1.27 [1109]~P13(x11091)+~P12(x11091,f2(x11091),x11093)+E(f20(x11091,f4(x11091,x11092),x11093),f4(x11091,f20(x11091,x11092,x11093)))
% 1.14/1.27 [1152]~P12(a41,x11521,x11523)+~P12(a41,x11523,x11522)+P12(a41,f9(a41,x11521,f3(a41)),x11522)
% 1.14/1.27 [1168]~P12(a41,x11683,x11682)+P12(a41,x11681,f9(a41,x11682,f3(a41)))+~E(x11681,f9(a41,x11683,f3(a41)))
% 1.14/1.27 [1374]~P49(x13742)+E(x13741,f2(x13742))+~E(f9(x13742,f10(x13742,x13743,x13743),f10(x13742,x13741,x13741)),f2(x13742))
% 1.14/1.27 [1375]~P49(x13752)+E(x13751,f2(x13752))+~E(f9(x13752,f10(x13752,x13751,x13751),f10(x13752,x13753,x13753)),f2(x13752))
% 1.14/1.27 [1382]E(x13821,f2(a40))+~P11(a40,x13822,f2(a40))+~P11(a40,f4(a40,x13821),f10(a40,x13822,f4(a40,x13823)))
% 1.14/1.27 [1458]~P48(x14581)+~P12(x14581,f3(x14581),x14582)+P12(x14581,f3(x14581),f10(x14581,x14582,f18(x14581,x14582,x14583)))
% 1.14/1.27 [1597]~P48(x15971)+~P12(x15971,f3(x15971),x15972)+P12(x15971,f18(x15971,x15972,x15973),f10(x15971,x15972,f18(x15971,x15972,x15973)))
% 1.14/1.27 [1609]~P49(x16092)+E(x16091,f2(x16092))+P12(x16092,f2(x16092),f9(x16092,f10(x16092,x16093,x16093),f10(x16092,x16091,x16091)))
% 1.14/1.27 [1610]~P49(x16102)+E(x16101,f2(x16102))+P12(x16102,f2(x16102),f9(x16102,f10(x16102,x16101,x16101),f10(x16102,x16103,x16103)))
% 1.14/1.27 [1763]~P49(x17632)+E(x17631,f2(x17632))+~P11(x17632,f9(x17632,f10(x17632,x17633,x17633),f10(x17632,x17631,x17631)),f2(x17632))
% 1.14/1.27 [1764]~P49(x17642)+E(x17641,f2(x17642))+~P11(x17642,f9(x17642,f10(x17642,x17641,x17641),f10(x17642,x17643,x17643)),f2(x17642))
% 1.14/1.27 [1459]~P48(x14591)+~P12(x14591,f3(x14591),x14592)+P12(x14591,f3(x14591),f18(x14591,x14592,f9(a41,x14593,f3(a41))))
% 1.14/1.27 [1693]~P14(x16931)+~P12(x16931,x16932,x16933)+P12(x16931,x16932,f20(x16931,f9(x16931,x16932,x16933),f9(x16931,f3(x16931),f3(x16931))))
% 1.14/1.27 [1694]~P14(x16941)+~P12(x16941,x16942,x16943)+P12(x16941,f20(x16941,f9(x16941,x16942,x16943),f9(x16941,f3(x16941),f3(x16941))),x16943)
% 1.14/1.27 [1871]~P44(x18711)+~P12(x18711,x18712,f2(x18711))+P12(x18711,f18(x18711,x18712,f9(a41,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18713),f3(a41))),f2(x18711))
% 1.14/1.27 [1880]~P44(x18801)+P11(x18801,f2(x18801),x18802)+~P11(x18801,f2(x18801),f18(x18801,x18802,f9(a41,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18803),f3(a41))))
% 1.14/1.27 [1862]~P44(x18622)+E(x18621,f2(x18622))+~E(f9(x18622,f18(x18622,x18623,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18622,x18621,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(x18622))
% 1.14/1.27 [1863]~P44(x18632)+E(x18631,f2(x18632))+~E(f9(x18632,f18(x18632,x18631,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18632,x18633,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(x18632))
% 1.14/1.27 [1866]~P44(x18662)+E(x18661,f2(x18662))+~P11(x18662,f18(x18662,x18661,f10(a41,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))),x18663)),f2(x18662))
% 1.14/1.27 [1868]~P44(x18682)+E(x18681,f2(x18682))+P12(x18682,f2(x18682),f9(x18682,f18(x18682,x18683,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18682,x18681,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))
% 1.14/1.27 [1869]~P44(x18692)+E(x18691,f2(x18692))+P12(x18692,f2(x18692),f9(x18692,f18(x18692,x18691,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18692,x18693,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))
% 1.14/1.27 [1877]~P44(x18772)+E(x18771,f2(x18772))+~P11(x18772,f9(x18772,f18(x18772,x18773,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18772,x18771,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(x18772))
% 1.14/1.27 [1878]~P44(x18782)+E(x18781,f2(x18782))+~P11(x18782,f9(x18782,f18(x18782,x18781,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18782,x18783,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(x18782))
% 1.14/1.27 [1883]~P12(a40,f4(a40,x18831),f20(a40,x18833,f14(f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))+~P12(a40,f4(a40,x18832),f20(a40,x18833,f14(f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))+P12(a40,f14(f9(a40,f18(a40,x18831,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x18832,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))),x18833)
% 1.14/1.27 [868]~P15(x8683)+E(x8681,x8682)+~E(f9(x8683,x8684,x8681),f9(x8683,x8684,x8682))
% 1.14/1.27 [869]~P16(x8693)+E(x8691,x8692)+~E(f9(x8693,x8694,x8691),f9(x8693,x8694,x8692))
% 1.14/1.27 [871]~P15(x8713)+E(x8711,x8712)+~E(f9(x8713,x8711,x8714),f9(x8713,x8712,x8714))
% 1.14/1.27 [927]~P32(x9272)+~P12(f43(x9271,x9272),x9273,x9274)+P11(f43(x9271,x9272),x9273,x9274)
% 1.14/1.27 [1048]~P32(x10481)+~P12(f43(x10482,x10481),x10484,x10483)+~P11(f43(x10482,x10481),x10483,x10484)
% 1.14/1.27 [1106]~P12(a41,x11063,x11064)+P12(a41,x11061,x11062)+~E(f9(a41,x11063,x11062),f9(a41,x11061,x11064))
% 1.14/1.27 [1224]~P21(x12241)+~P11(x12241,x12243,x12244)+P11(x12241,f9(x12241,x12242,x12243),f9(x12241,x12242,x12244))
% 1.14/1.27 [1225]~P22(x12251)+~P11(x12251,x12253,x12254)+P11(x12251,f9(x12251,x12252,x12253),f9(x12251,x12252,x12254))
% 1.14/1.27 [1226]~P21(x12261)+~P11(x12261,x12262,x12264)+P11(x12261,f9(x12261,x12262,x12263),f9(x12261,x12264,x12263))
% 1.14/1.27 [1227]~P22(x12271)+~P11(x12271,x12272,x12274)+P11(x12271,f9(x12271,x12272,x12273),f9(x12271,x12274,x12273))
% 1.14/1.27 [1228]~P21(x12281)+~P12(x12281,x12283,x12284)+P12(x12281,f9(x12281,x12282,x12283),f9(x12281,x12282,x12284))
% 1.14/1.27 [1229]~P25(x12291)+~P12(x12291,x12293,x12294)+P12(x12291,f9(x12291,x12292,x12293),f9(x12291,x12292,x12294))
% 1.14/1.27 [1230]~P21(x12301)+~P12(x12301,x12302,x12304)+P12(x12301,f9(x12301,x12302,x12303),f9(x12301,x12304,x12303))
% 1.14/1.27 [1231]~P25(x12311)+~P12(x12311,x12312,x12314)+P12(x12311,f9(x12311,x12312,x12313),f9(x12311,x12314,x12313))
% 1.14/1.27 [1336]~P11(a41,x13362,x13364)+~P11(a41,x13361,x13363)+P11(a41,f10(a41,x13361,x13362),f10(a41,x13363,x13364))
% 1.14/1.27 [1337]~P11(a41,x13372,x13374)+~P11(a41,x13371,x13373)+P11(a41,f9(a41,x13371,x13372),f9(a41,x13373,x13374))
% 1.14/1.27 [1338]~P12(a41,x13382,x13384)+~P12(a41,x13381,x13383)+P12(a41,f9(a41,x13381,x13382),f9(a41,x13383,x13384))
% 1.14/1.27 [1339]~P11(a1,x13392,x13394)+~P12(a1,x13391,x13393)+P12(a1,f9(a1,x13391,x13392),f9(a1,x13393,x13394))
% 1.14/1.27 [1451]~P21(x14511)+P11(x14511,x14512,x14513)+~P11(x14511,f9(x14511,x14514,x14512),f9(x14511,x14514,x14513))
% 1.14/1.27 [1453]~P21(x14531)+P11(x14531,x14532,x14533)+~P11(x14531,f9(x14531,x14532,x14534),f9(x14531,x14533,x14534))
% 1.14/1.27 [1455]~P21(x14551)+P12(x14551,x14552,x14553)+~P12(x14551,f9(x14551,x14554,x14552),f9(x14551,x14554,x14553))
% 1.14/1.27 [1457]~P21(x14571)+P12(x14571,x14572,x14573)+~P12(x14571,f9(x14571,x14572,x14574),f9(x14571,x14573,x14574))
% 1.14/1.27 [1165]~P7(x11652)+E(x11651,f2(x11652))+E(f20(x11652,f10(x11652,x11653,x11651),f10(x11652,x11654,x11651)),f20(x11652,x11653,x11654))
% 1.14/1.27 [1166]~P7(x11662)+E(x11661,f2(x11662))+E(f20(x11662,f10(x11662,x11661,x11663),f10(x11662,x11661,x11664)),f20(x11662,x11663,x11664))
% 1.14/1.27 [1376]~P8(x13762)+E(x13761,f2(x13762))+E(f20(x13762,f18(x13762,x13763,x13764),f18(x13762,x13761,x13764)),f18(x13762,f20(x13762,x13763,x13761),x13764))
% 1.14/1.27 [1819]~P32(x18192)+P11(f43(x18191,x18192),x18193,x18194)+~P11(x18192,f21(x18193,f38(x18194,x18193,x18191,x18192)),f21(x18194,f38(x18194,x18193,x18191,x18192)))
% 1.14/1.27 [1533]~P7(x15332)+E(x15331,f2(x15332))+E(f20(x15332,f9(x15332,x15333,f10(x15332,x15334,x15331)),x15331),f9(x15332,x15334,f20(x15332,x15333,x15331)))
% 1.14/1.27 [1534]~P8(x15342)+E(x15341,f2(x15342))+E(f20(x15342,f9(x15342,f10(x15342,x15341,x15343),x15344),x15341),f9(x15342,x15343,f20(x15342,x15344,x15341)))
% 1.14/1.27 [1535]~P7(x15352)+E(x15351,f2(x15352))+E(f20(x15352,f9(x15352,x15353,f10(x15352,x15354,x15351)),x15351),f9(x15352,f20(x15352,x15353,x15351),x15354))
% 1.14/1.27 [1536]~P8(x15362)+E(x15361,f2(x15362))+E(f20(x15362,f9(x15362,x15363,f10(x15362,x15361,x15364)),x15361),f9(x15362,f20(x15362,x15363,x15361),x15364))
% 1.14/1.27 [1559]~P2(x15591)+~P65(x15591)+E(f9(x15591,f10(x15591,f15(x15591,x15592),x15593),f10(x15591,f15(x15591,x15592),x15594)),f10(x15591,f15(x15591,x15592),f9(x15591,x15593,x15594)))
% 1.14/1.27 [1560]~P2(x15601)+~P65(x15601)+E(f9(x15601,f10(x15601,x15602,f15(x15601,x15603)),f10(x15601,x15604,f15(x15601,x15603))),f10(x15601,f9(x15601,x15602,x15604),f15(x15601,x15603)))
% 1.14/1.27 [1003]~P32(x10031)+P11(x10031,f21(x10032,x10033),f21(x10034,x10033))+~P11(f43(x10035,x10031),x10032,x10034)
% 1.14/1.27 [1532]~E(x15322,x15324)+~P66(x15321)+E(f9(x15321,f10(x15321,x15322,x15323),f10(x15321,x15324,x15325)),f9(x15321,f10(x15321,x15322,x15325),f10(x15321,x15324,x15323)))
% 1.14/1.27 [1825]E(x18251,f3(a1))+E(x18251,f2(a1))+~P11(a1,f2(a1),x18251)+~P12(a1,x18251,f15(a1,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))
% 1.14/1.27 [879]~P1(x8791)+~P44(x8791)+P11(x8791,f2(x8791),f15(x8791,x8792))+~P11(a1,a11,x8792)
% 1.14/1.27 [880]~P1(x8801)+~P44(x8801)+P12(x8801,f2(x8801),f15(x8801,x8802))+~P12(a1,a11,x8802)
% 1.14/1.27 [881]~P1(x8811)+~P44(x8811)+P11(x8811,f15(x8811,x8812),f2(x8811))+~P11(a1,x8812,a11)
% 1.14/1.27 [882]~P1(x8821)+~P44(x8821)+P12(x8821,f15(x8821,x8822),f2(x8821))+~P12(a1,x8822,a11)
% 1.14/1.27 [902]~P44(x9022)+~P1(x9022)+~P11(x9022,f15(x9022,x9021),f2(x9022))+P11(a1,x9021,a11)
% 1.14/1.27 [903]~P44(x9032)+~P1(x9032)+~P12(x9032,f15(x9032,x9031),f2(x9032))+P12(a1,x9031,a11)
% 1.14/1.27 [904]~P44(x9042)+~P1(x9042)+~P11(x9042,f2(x9042),f15(x9042,x9041))+P11(a1,a11,x9041)
% 1.14/1.27 [905]~P44(x9052)+~P1(x9052)+~P12(x9052,f2(x9052),f15(x9052,x9051))+P12(a1,a11,x9051)
% 1.14/1.27 [618]~P29(x6182)+~P64(x6182)+E(x6181,f2(a41))+E(f18(x6182,f2(x6182),x6181),f2(x6182))
% 1.14/1.27 [619]~P29(x6191)+~P64(x6191)+~E(x6192,f2(a41))+E(f18(x6191,f2(x6191),x6192),f3(x6191))
% 1.14/1.27 [1475]~P44(x14752)+~P1(x14752)+~P11(x14752,f15(x14752,x14751),f3(x14752))+P11(a1,x14751,f9(a1,f9(a1,f3(a1),a11),a11))
% 1.14/1.27 [1476]~P44(x14762)+~P1(x14762)+~P12(x14762,f15(x14762,x14761),f3(x14762))+P12(a1,x14761,f9(a1,f9(a1,f3(a1),a11),a11))
% 1.14/1.27 [1477]~P44(x14772)+~P1(x14772)+~P11(x14772,f3(x14772),f15(x14772,x14771))+P11(a1,f9(a1,f9(a1,f3(a1),a11),a11),x14771)
% 1.14/1.27 [1478]~P44(x14782)+~P1(x14782)+~P12(x14782,f3(x14782),f15(x14782,x14781))+P12(a1,f9(a1,f9(a1,f3(a1),a11),a11),x14781)
% 1.14/1.27 [1656]~P1(x16561)+~P44(x16561)+P11(x16561,f3(x16561),f15(x16561,x16562))+~P11(a1,f9(a1,f9(a1,f3(a1),a11),a11),x16562)
% 1.14/1.27 [1657]~P1(x16571)+~P44(x16571)+P12(x16571,f3(x16571),f15(x16571,x16572))+~P12(a1,f9(a1,f9(a1,f3(a1),a11),a11),x16572)
% 1.14/1.27 [1658]~P1(x16581)+~P44(x16581)+P11(x16581,f15(x16581,x16582),f3(x16581))+~P11(a1,x16582,f9(a1,f9(a1,f3(a1),a11),a11))
% 1.14/1.27 [1659]~P1(x16591)+~P44(x16591)+P12(x16591,f15(x16591,x16592),f3(x16591))+~P12(a1,x16592,f9(a1,f9(a1,f3(a1),a11),a11))
% 1.14/1.27 [1836]~P1(x18361)+~P13(x18361)+~P12(x18361,f2(x18361),x18362)+P12(x18361,f2(x18361),f20(x18361,x18362,f15(x18361,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1849]~P1(x18491)+~P13(x18491)+P12(x18491,f2(x18491),x18492)+~P12(x18491,f2(x18491),f20(x18491,x18492,f15(x18491,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [710]P12(x7103,x7101,x7102)+~P44(x7103)+E(x7101,x7102)+P12(x7103,x7102,x7101)
% 1.14/1.27 [716]P12(x7163,x7161,x7162)+~P30(x7163)+E(x7161,x7162)+P12(x7163,x7162,x7161)
% 1.14/1.27 [719]P12(x7191,x7192,x7193)+~E(x7192,x7193)+~P30(x7191)+P11(x7191,x7192,x7193)
% 1.14/1.27 [770]~P33(x7703)+~P11(x7703,x7702,x7701)+E(x7701,x7702)+P12(x7703,x7702,x7701)
% 1.14/1.27 [772]~P30(x7723)+~P11(x7723,x7721,x7722)+E(x7721,x7722)+P12(x7723,x7721,x7722)
% 1.14/1.27 [778]~P33(x7783)+~P11(x7783,x7781,x7782)+E(x7781,x7782)+P12(x7783,x7781,x7782)
% 1.14/1.27 [878]~P11(x8783,x8782,x8781)+~P11(x8783,x8781,x8782)+E(x8781,x8782)+~P33(x8783)
% 1.14/1.27 [906]P12(x9061,x9063,x9062)+~P31(x9061)+~P11(x9061,x9063,x9062)+P11(x9061,x9062,x9063)
% 1.14/1.27 [554]~P1(x5543)+~P27(x5543)+E(x5541,x5542)+~E(f15(x5543,x5541),f15(x5543,x5542))
% 1.14/1.27 [613]~E(x6133,x6131)+~P46(x6132)+E(f20(x6132,x6133,x6131),f3(x6132))+E(x6131,f2(x6132))
% 1.14/1.27 [679]~P46(x6793)+E(x6791,x6792)+~E(f20(x6793,x6791,x6792),f3(x6793))+E(x6792,f2(x6793))
% 1.14/1.27 [690]~P28(x6902)+~E(f10(x6902,x6903,x6901),f2(x6902))+E(x6901,f2(x6902))+E(x6903,f2(x6902))
% 1.14/1.27 [691]~P55(x6912)+~E(f10(x6912,x6913,x6911),f2(x6912))+E(x6911,f2(x6912))+E(x6913,f2(x6912))
% 1.14/1.27 [899]~P44(x8992)+P12(x8992,f2(x8992),f18(x8992,x8991,x8993))+~P10(a41,x8993)+E(x8991,f2(x8992))
% 1.14/1.27 [901]~P3(x9011)+~P50(x9011)+P11(x9011,f2(x9011),f18(x9011,x9012,x9013))+~P10(a41,x9013)
% 1.14/1.27 [907]~P1(x9071)+~P44(x9071)+~P11(a1,x9072,x9073)+P11(x9071,f15(x9071,x9072),f15(x9071,x9073))
% 1.14/1.27 [908]~P1(x9081)+~P44(x9081)+~P12(a1,x9082,x9083)+P12(x9081,f15(x9081,x9082),f15(x9081,x9083))
% 1.14/1.27 [928]P68(x9281,x9282,x9283)+P12(a1,x9282,f2(a1))+P12(a1,f2(a1),x9282)+~P67(f21(x9281,x9283))
% 1.14/1.27 [972]~P44(x9723)+~P1(x9723)+~P11(x9723,f15(x9723,x9721),f15(x9723,x9722))+P11(a1,x9721,x9722)
% 1.14/1.27 [973]~P44(x9733)+~P1(x9733)+~P12(x9733,f15(x9733,x9731),f15(x9733,x9732))+P12(a1,x9731,x9732)
% 1.14/1.27 [1064]P68(x10642,x10641,x10643)+P12(a1,f27(x10643,x10641,x10642),x10641)+E(x10641,f2(a1))+P12(a1,x10641,f2(a1))
% 1.14/1.27 [1065]P68(x10652,x10651,x10653)+P12(a1,x10651,f29(x10653,x10651,x10652))+E(x10651,f2(a1))+P12(a1,f2(a1),x10651)
% 1.14/1.27 [1069]P68(x10692,x10691,x10693)+E(x10691,f2(a1))+P12(a1,x10691,f2(a1))+P11(a1,f2(a1),f27(x10693,x10691,x10692))
% 1.14/1.27 [1070]P68(x10702,x10701,x10703)+E(x10701,f2(a1))+P12(a1,f2(a1),x10701)+P11(a1,f29(x10703,x10701,x10702),f2(a1))
% 1.14/1.27 [1074]~P44(x10742)+~P12(x10742,f2(x10742),x10743)+P12(x10742,f2(x10742),f18(x10742,x10743,x10741))+P10(a41,x10741)
% 1.14/1.27 [1075]~P44(x10752)+~P12(x10752,x10753,f2(x10752))+P12(x10752,f18(x10752,x10753,x10751),f2(x10752))+P10(a41,x10751)
% 1.14/1.27 [1090]~P44(x10902)+~P11(x10902,f18(x10902,x10901,x10903),f2(x10902))+E(x10901,f2(x10902))+~P10(a41,x10903)
% 1.14/1.27 [1133]P68(x11331,x11332,x11333)+P12(a1,f27(x11333,x11332,x11331),x11332)+P12(a1,x11332,f2(a1))+~P67(f21(x11331,x11333))
% 1.14/1.27 [1134]P68(x11341,x11342,x11343)+P12(a1,x11342,f29(x11343,x11342,x11341))+P12(a1,f2(a1),x11342)+~P67(f21(x11341,x11343))
% 1.14/1.27 [1135]P68(x11351,x11352,x11353)+P12(a1,x11352,f2(a1))+P11(a1,f2(a1),f27(x11353,x11352,x11351))+~P67(f21(x11351,x11353))
% 1.14/1.27 [1136]P68(x11361,x11362,x11363)+P12(a1,f2(a1),x11362)+P11(a1,f29(x11363,x11362,x11361),f2(a1))+~P67(f21(x11361,x11363))
% 1.14/1.27 [1169]~P44(x11692)+~P11(x11692,f18(x11692,x11691,x11693),f2(x11692))+P11(x11692,x11691,f2(x11692))+E(x11691,f2(x11692))
% 1.14/1.27 [1205]~P44(x12052)+~P11(x12052,f18(x12052,x12053,x12051),f2(x12052))+P11(x12052,x12053,f2(x12052))+P10(a41,x12051)
% 1.14/1.27 [1208]~P44(x12082)+~P11(x12082,f2(x12082),f18(x12082,x12083,x12081))+P11(x12082,f2(x12082),x12083)+P10(a41,x12081)
% 1.14/1.27 [1223]~P48(x12231)+~P12(x12231,f3(x12231),x12232)+P12(x12231,f3(x12231),f18(x12231,x12232,x12233))+~P12(a41,f2(a41),x12233)
% 1.14/1.27 [1235]~P49(x12351)+~P11(x12351,x12353,f2(x12351))+~P11(x12351,x12352,f2(x12351))+P11(x12351,f2(x12351),f10(x12351,x12352,x12353))
% 1.14/1.27 [1237]~P58(x12371)+~P11(x12371,x12373,f2(x12371))+~P11(x12371,x12372,f2(x12371))+P11(x12371,f2(x12371),f10(x12371,x12372,x12373))
% 1.14/1.27 [1238]~P13(x12381)+~P11(x12381,x12383,f2(x12381))+~P11(x12381,x12382,f2(x12381))+P11(x12381,f2(x12381),f20(x12381,x12382,x12383))
% 1.14/1.27 [1239]~P14(x12391)+~P11(x12391,x12392,f2(x12391))+~P12(x12391,x12393,f2(x12391))+P11(x12391,f2(x12391),f20(x12391,x12392,x12393))
% 1.14/1.27 [1240]~P49(x12401)+~P12(x12401,x12403,f2(x12401))+~P12(x12401,x12402,f2(x12401))+P12(x12401,f2(x12401),f10(x12401,x12402,x12403))
% 1.14/1.27 [1241]~P13(x12411)+~P12(x12411,x12413,f2(x12411))+~P12(x12411,x12412,f2(x12411))+P12(x12411,f2(x12411),f20(x12411,x12412,x12413))
% 1.14/1.27 [1242]~P14(x12421)+~P12(x12421,x12423,f2(x12421))+~P12(x12421,x12422,f2(x12421))+P12(x12421,f2(x12421),f20(x12421,x12422,x12423))
% 1.14/1.27 [1243]~P49(x12431)+~P11(x12431,f2(x12431),x12433)+~P11(x12431,f2(x12431),x12432)+P11(x12431,f2(x12431),f10(x12431,x12432,x12433))
% 1.14/1.27 [1244]~P57(x12441)+~P11(x12441,f2(x12441),x12443)+~P11(x12441,f2(x12441),x12442)+P11(x12441,f2(x12441),f10(x12441,x12442,x12443))
% 1.14/1.27 [1245]~P58(x12451)+~P11(x12451,f2(x12451),x12453)+~P11(x12451,f2(x12451),x12452)+P11(x12451,f2(x12451),f10(x12451,x12452,x12453))
% 1.14/1.27 [1247]~P13(x12471)+~P11(x12471,f2(x12471),x12473)+~P11(x12471,f2(x12471),x12472)+P11(x12471,f2(x12471),f20(x12471,x12472,x12473))
% 1.14/1.27 [1248]~P14(x12481)+~P11(x12481,f2(x12481),x12482)+~P12(x12481,f2(x12481),x12483)+P11(x12481,f2(x12481),f20(x12481,x12482,x12483))
% 1.14/1.27 [1249]~P51(x12491)+~P12(x12491,f2(x12491),x12493)+~P12(x12491,f2(x12491),x12492)+P12(x12491,f2(x12491),f10(x12491,x12492,x12493))
% 1.14/1.27 [1252]~P20(x12521)+~P12(x12521,f2(x12521),x12523)+~P12(x12521,f2(x12521),x12522)+P12(x12521,f2(x12521),f9(x12521,x12522,x12523))
% 1.14/1.27 [1253]~P13(x12531)+~P12(x12531,f2(x12531),x12533)+~P12(x12531,f2(x12531),x12532)+P12(x12531,f2(x12531),f20(x12531,x12532,x12533))
% 1.14/1.27 [1254]~P14(x12541)+~P12(x12541,f2(x12541),x12543)+~P12(x12541,f2(x12541),x12542)+P12(x12541,f2(x12541),f20(x12541,x12542,x12543))
% 1.14/1.27 [1255]~P48(x12551)+~P12(x12551,f3(x12551),x12553)+~P12(x12551,f3(x12551),x12552)+P12(x12551,f3(x12551),f10(x12551,x12552,x12553))
% 1.14/1.27 [1256]~P20(x12561)+~P11(x12561,x12563,f2(x12561))+~P11(x12561,x12562,f2(x12561))+P11(x12561,f9(x12561,x12562,x12563),f2(x12561))
% 1.14/1.27 [1257]~P20(x12571)+~P11(x12571,x12573,f2(x12571))+~P12(x12571,x12572,f2(x12571))+P12(x12571,f9(x12571,x12572,x12573),f2(x12571))
% 1.14/1.27 [1258]~P20(x12581)+~P11(x12581,x12582,f2(x12581))+~P12(x12581,x12583,f2(x12581))+P12(x12581,f9(x12581,x12582,x12583),f2(x12581))
% 1.14/1.27 [1259]~P20(x12591)+~P12(x12591,x12593,f2(x12591))+~P12(x12591,x12592,f2(x12591))+P12(x12591,f9(x12591,x12592,x12593),f2(x12591))
% 1.14/1.27 [1261]~P49(x12611)+~P11(x12611,x12613,f2(x12611))+~P11(x12611,f2(x12611),x12612)+P11(x12611,f10(x12611,x12612,x12613),f2(x12611))
% 1.14/1.27 [1262]~P49(x12621)+~P11(x12621,x12622,f2(x12621))+~P11(x12621,f2(x12621),x12623)+P11(x12621,f10(x12621,x12622,x12623),f2(x12621))
% 1.14/1.27 [1264]~P57(x12641)+~P11(x12641,x12643,f2(x12641))+~P11(x12641,f2(x12641),x12642)+P11(x12641,f10(x12641,x12642,x12643),f2(x12641))
% 1.14/1.27 [1266]~P57(x12661)+~P11(x12661,x12662,f2(x12661))+~P11(x12661,f2(x12661),x12663)+P11(x12661,f10(x12661,x12662,x12663),f2(x12661))
% 1.14/1.27 [1267]~P13(x12671)+~P11(x12671,x12673,f2(x12671))+~P11(x12671,f2(x12671),x12672)+P11(x12671,f20(x12671,x12672,x12673),f2(x12671))
% 1.14/1.27 [1268]~P13(x12681)+~P11(x12681,x12682,f2(x12681))+~P11(x12681,f2(x12681),x12683)+P11(x12681,f20(x12681,x12682,x12683),f2(x12681))
% 1.14/1.27 [1269]~P14(x12691)+~P11(x12691,x12692,f2(x12691))+~P12(x12691,f2(x12691),x12693)+P11(x12691,f20(x12691,x12692,x12693),f2(x12691))
% 1.14/1.27 [1270]~P14(x12701)+~P12(x12701,x12703,f2(x12701))+~P11(x12701,f2(x12701),x12702)+P11(x12701,f20(x12701,x12702,x12703),f2(x12701))
% 1.14/1.27 [1272]~P51(x12721)+~P12(x12721,x12723,f2(x12721))+~P12(x12721,f2(x12721),x12722)+P12(x12721,f10(x12721,x12722,x12723),f2(x12721))
% 1.14/1.27 [1273]~P51(x12731)+~P12(x12731,x12732,f2(x12731))+~P12(x12731,f2(x12731),x12733)+P12(x12731,f10(x12731,x12732,x12733),f2(x12731))
% 1.14/1.27 [1274]~P13(x12741)+~P12(x12741,x12743,f2(x12741))+~P12(x12741,f2(x12741),x12742)+P12(x12741,f20(x12741,x12742,x12743),f2(x12741))
% 1.14/1.27 [1275]~P13(x12751)+~P12(x12751,x12752,f2(x12751))+~P12(x12751,f2(x12751),x12753)+P12(x12751,f20(x12751,x12752,x12753),f2(x12751))
% 1.14/1.27 [1276]~P14(x12761)+~P12(x12761,x12763,f2(x12761))+~P12(x12761,f2(x12761),x12762)+P12(x12761,f20(x12761,x12762,x12763),f2(x12761))
% 1.14/1.27 [1277]~P14(x12771)+~P12(x12771,x12772,f2(x12771))+~P12(x12771,f2(x12771),x12773)+P12(x12771,f20(x12771,x12772,x12773),f2(x12771))
% 1.14/1.27 [1284]P68(x12842,x12841,x12843)+P12(a1,x12841,f29(x12843,x12841,x12842))+P12(a1,f27(x12843,x12841,x12842),x12841)+E(x12841,f2(a1))
% 1.14/1.27 [1285]P68(x12852,x12851,x12853)+P12(a1,x12851,f29(x12853,x12851,x12852))+E(x12851,f2(a1))+P11(a1,f2(a1),f27(x12853,x12851,x12852))
% 1.14/1.27 [1286]P68(x12862,x12861,x12863)+P12(a1,f27(x12863,x12861,x12862),x12861)+E(x12861,f2(a1))+P11(a1,f29(x12863,x12861,x12862),f2(a1))
% 1.14/1.27 [1287]P68(x12872,x12871,x12873)+E(x12871,f2(a1))+P11(a1,f2(a1),f27(x12873,x12871,x12872))+P11(a1,f29(x12873,x12871,x12872),f2(a1))
% 1.14/1.27 [1292]~P49(x12921)+~P11(x12921,f10(x12921,x12923,x12922),f2(x12921))+P11(x12921,x12922,f2(x12921))+P11(x12921,x12923,f2(x12921))
% 1.14/1.27 [1293]~P13(x12931)+~P11(x12931,f20(x12931,x12933,x12932),f2(x12931))+P11(x12931,x12932,f2(x12931))+P11(x12931,x12933,f2(x12931))
% 1.14/1.27 [1294]~P13(x12941)+~P12(x12941,f20(x12941,x12943,x12942),f2(x12941))+P12(x12941,x12942,f2(x12941))+P12(x12941,x12943,f2(x12941))
% 1.14/1.27 [1295]~P49(x12951)+~P11(x12951,f2(x12951),f10(x12951,x12953,x12952))+P11(x12951,x12952,f2(x12951))+P11(x12951,f2(x12951),x12953)
% 1.14/1.27 [1296]~P49(x12961)+~P11(x12961,f2(x12961),f10(x12961,x12962,x12963))+P11(x12961,x12962,f2(x12961))+P11(x12961,f2(x12961),x12963)
% 1.14/1.27 [1297]~P13(x12971)+~P11(x12971,f2(x12971),f20(x12971,x12973,x12972))+P11(x12971,x12972,f2(x12971))+P11(x12971,f2(x12971),x12973)
% 1.14/1.27 [1298]~P13(x12981)+~P11(x12981,f2(x12981),f20(x12981,x12982,x12983))+P11(x12981,x12982,f2(x12981))+P11(x12981,f2(x12981),x12983)
% 1.14/1.27 [1299]~P49(x12991)+P11(x12991,f2(x12991),x12992)+~P11(x12991,f2(x12991),f10(x12991,x12993,x12992))+P11(x12991,x12992,f2(x12991))
% 1.14/1.27 [1300]~P49(x13001)+P11(x13001,f2(x13001),x13002)+~P11(x13001,f2(x13001),f10(x13001,x13002,x13003))+P11(x13001,x13002,f2(x13001))
% 1.14/1.27 [1301]~P13(x13011)+P11(x13011,f2(x13011),x13012)+~P11(x13011,f2(x13011),f20(x13011,x13013,x13012))+P11(x13011,x13012,f2(x13011))
% 1.14/1.27 [1302]~P13(x13021)+P11(x13021,f2(x13021),x13022)+~P11(x13021,f2(x13021),f20(x13021,x13022,x13023))+P11(x13021,x13022,f2(x13021))
% 1.14/1.27 [1303]~P13(x13031)+~P12(x13031,f2(x13031),f20(x13031,x13033,x13032))+P12(x13031,x13032,f2(x13031))+P12(x13031,f2(x13031),x13033)
% 1.14/1.27 [1304]~P13(x13041)+~P12(x13041,f2(x13041),f20(x13041,x13042,x13043))+P12(x13041,x13042,f2(x13041))+P12(x13041,f2(x13041),x13043)
% 1.14/1.27 [1305]~P13(x13051)+P12(x13051,f2(x13051),x13052)+~P12(x13051,f2(x13051),f20(x13051,x13053,x13052))+P12(x13051,x13052,f2(x13051))
% 1.14/1.27 [1306]~P13(x13061)+P12(x13061,f2(x13061),x13062)+~P12(x13061,f2(x13061),f20(x13061,x13062,x13063))+P12(x13061,x13062,f2(x13061))
% 1.14/1.27 [1307]~P49(x13071)+P11(x13071,f2(x13071),x13072)+~P11(x13071,f10(x13071,x13073,x13072),f2(x13071))+P11(x13071,x13072,f2(x13071))
% 1.14/1.27 [1308]~P49(x13081)+P11(x13081,f2(x13081),x13082)+~P11(x13081,f10(x13081,x13082,x13083),f2(x13081))+P11(x13081,x13082,f2(x13081))
% 1.14/1.27 [1309]~P13(x13091)+P11(x13091,f2(x13091),x13092)+~P11(x13091,f20(x13091,x13093,x13092),f2(x13091))+P11(x13091,x13092,f2(x13091))
% 1.14/1.27 [1310]~P13(x13101)+P11(x13101,f2(x13101),x13102)+~P11(x13101,f20(x13101,x13102,x13103),f2(x13101))+P11(x13101,x13102,f2(x13101))
% 1.14/1.27 [1311]~P13(x13111)+P12(x13111,f2(x13111),x13112)+~P12(x13111,f20(x13111,x13113,x13112),f2(x13111))+P12(x13111,x13112,f2(x13111))
% 1.14/1.27 [1312]~P13(x13121)+P12(x13121,f2(x13121),x13122)+~P12(x13121,f20(x13121,x13122,x13123),f2(x13121))+P12(x13121,x13122,f2(x13121))
% 1.14/1.27 [1313]~P49(x13131)+~P11(x13131,f10(x13131,x13132,x13133),f2(x13131))+P11(x13131,f2(x13131),x13132)+P11(x13131,f2(x13131),x13133)
% 1.14/1.27 [1314]~P13(x13141)+~P11(x13141,f20(x13141,x13142,x13143),f2(x13141))+P11(x13141,f2(x13141),x13142)+P11(x13141,f2(x13141),x13143)
% 1.14/1.27 [1315]~P13(x13151)+~P12(x13151,f20(x13151,x13152,x13153),f2(x13151))+P12(x13151,f2(x13151),x13152)+P12(x13151,f2(x13151),x13153)
% 1.14/1.27 [1326]P68(x13261,x13262,x13263)+P12(a1,x13262,f29(x13263,x13262,x13261))+P12(a1,f27(x13263,x13262,x13261),x13262)+~P67(f21(x13261,x13263))
% 1.14/1.27 [1327]P68(x13271,x13272,x13273)+P12(a1,x13272,f29(x13273,x13272,x13271))+P11(a1,f2(a1),f27(x13273,x13272,x13271))+~P67(f21(x13271,x13273))
% 1.14/1.27 [1328]P68(x13281,x13282,x13283)+P12(a1,f27(x13283,x13282,x13281),x13282)+P11(a1,f29(x13283,x13282,x13281),f2(a1))+~P67(f21(x13281,x13283))
% 1.14/1.27 [1334]~P51(x13341)+~P12(x13341,f2(x13341),f10(x13341,x13343,x13342))+P12(x13341,f2(x13341),x13342)+~P12(x13341,f2(x13341),x13343)
% 1.14/1.27 [1335]~P51(x13351)+~P12(x13351,f2(x13351),f10(x13351,x13352,x13353))+P12(x13351,f2(x13351),x13352)+~P12(x13351,f2(x13351),x13353)
% 1.14/1.27 [1341]P68(x13411,x13412,x13413)+P11(a1,f2(a1),f27(x13413,x13412,x13411))+P11(a1,f29(x13413,x13412,x13411),f2(a1))+~P67(f21(x13411,x13413))
% 1.14/1.27 [1081]~P49(x10811)+~E(x10813,f2(x10811))+~E(x10812,f2(x10811))+E(f9(x10811,f10(x10811,x10812,x10812),f10(x10811,x10813,x10813)),f2(x10811))
% 1.14/1.27 [1329]~P61(x13291)+~P11(x13291,x13292,f2(x13291))+~P11(x13291,x13293,f2(x13291))+E(f10(x13291,f4(x13291,x13292),f4(x13291,x13293)),f4(x13291,f10(x13291,x13292,x13293)))
% 1.14/1.27 [1330]~P61(x13301)+~P11(x13301,x13302,f2(x13301))+~P11(x13301,f2(x13301),x13303)+E(f10(x13301,f4(x13301,x13302),f4(x13301,x13303)),f4(x13301,f10(x13301,x13302,x13303)))
% 1.14/1.27 [1331]~P61(x13311)+~P11(x13311,x13313,f2(x13311))+~P11(x13311,f2(x13311),x13312)+E(f10(x13311,f4(x13311,x13312),f4(x13311,x13313)),f4(x13311,f10(x13311,x13312,x13313)))
% 1.14/1.27 [1332]~P61(x13321)+~P11(x13321,f2(x13321),x13322)+~P11(x13321,f2(x13321),x13323)+E(f10(x13321,f4(x13321,x13322),f4(x13321,x13323)),f4(x13321,f10(x13321,x13322,x13323)))
% 1.14/1.27 [1445]~P12(a1,x14452,x14453)+~P12(a1,f2(a1),x14453)+P11(a1,f3(a1),x14451)+~E(f9(a1,x14452,f10(a1,x14453,x14451)),x14453)
% 1.14/1.27 [1446]~P11(a1,f2(a1),x14462)+~P12(a1,f2(a1),x14463)+P11(a1,x14461,f3(a1))+~E(f9(a1,x14462,f10(a1,x14463,x14461)),x14463)
% 1.14/1.27 [1464]P68(x14642,x14641,x14643)+E(x14641,f2(a1))+P12(a1,x14641,f2(a1))+~P67(f21(x14642,f27(x14643,x14641,x14642)))
% 1.14/1.27 [1465]P68(x14652,x14651,x14653)+E(x14651,f2(a1))+P12(a1,f2(a1),x14651)+~P67(f21(x14652,f29(x14653,x14651,x14652)))
% 1.14/1.27 [1514]P68(x15141,x15142,x15143)+P12(a1,x15142,f2(a1))+~P67(f21(x15141,x15143))+~P67(f21(x15141,f27(x15143,x15142,x15141)))
% 1.14/1.27 [1515]P68(x15151,x15152,x15153)+P12(a1,f2(a1),x15152)+~P67(f21(x15151,x15153))+~P67(f21(x15151,f29(x15153,x15152,x15151)))
% 1.14/1.27 [1599]P68(x15993,x15991,x15992)+E(x15991,f2(a1))+P12(a1,x15991,f2(a1))+E(f9(a1,f10(a1,x15991,f28(x15992,x15991,x15993)),f27(x15992,x15991,x15993)),x15992)
% 1.14/1.27 [1600]P68(x16003,x16001,x16002)+E(x16001,f2(a1))+P12(a1,f2(a1),x16001)+E(f9(a1,f10(a1,x16001,f30(x16002,x16001,x16003)),f29(x16002,x16001,x16003)),x16002)
% 1.14/1.27 [1605]P68(x16052,x16051,x16053)+P12(a1,x16051,f29(x16053,x16051,x16052))+E(x16051,f2(a1))+~P67(f21(x16052,f27(x16053,x16051,x16052)))
% 1.14/1.27 [1606]P68(x16062,x16061,x16063)+P12(a1,f27(x16063,x16061,x16062),x16061)+E(x16061,f2(a1))+~P67(f21(x16062,f29(x16063,x16061,x16062)))
% 1.14/1.27 [1607]P68(x16072,x16071,x16073)+E(x16071,f2(a1))+P11(a1,f2(a1),f27(x16073,x16071,x16072))+~P67(f21(x16072,f29(x16073,x16071,x16072)))
% 1.14/1.27 [1608]P68(x16082,x16081,x16083)+E(x16081,f2(a1))+P11(a1,f29(x16083,x16081,x16082),f2(a1))+~P67(f21(x16082,f27(x16083,x16081,x16082)))
% 1.14/1.27 [1615]~P49(x16151)+~E(x16153,f2(x16151))+~E(x16152,f2(x16151))+P11(x16151,f9(x16151,f10(x16151,x16152,x16152),f10(x16151,x16153,x16153)),f2(x16151))
% 1.14/1.27 [1624]P68(x16243,x16241,x16242)+P12(a1,x16241,f2(a1))+~P67(f21(x16243,x16242))+E(f9(a1,f10(a1,x16241,f28(x16242,x16241,x16243)),f27(x16242,x16241,x16243)),x16242)
% 1.14/1.27 [1625]P68(x16253,x16251,x16252)+P12(a1,f2(a1),x16251)+~P67(f21(x16253,x16252))+E(f9(a1,f10(a1,x16251,f30(x16252,x16251,x16253)),f29(x16252,x16251,x16253)),x16252)
% 1.14/1.27 [1643]P68(x16431,x16432,x16433)+P12(a1,x16432,f29(x16433,x16432,x16431))+~P67(f21(x16431,x16433))+~P67(f21(x16431,f27(x16433,x16432,x16431)))
% 1.14/1.27 [1644]P68(x16441,x16442,x16443)+P12(a1,f27(x16443,x16442,x16441),x16442)+~P67(f21(x16441,x16443))+~P67(f21(x16441,f29(x16443,x16442,x16441)))
% 1.14/1.27 [1645]P68(x16451,x16452,x16453)+P11(a1,f2(a1),f27(x16453,x16452,x16451))+~P67(f21(x16451,x16453))+~P67(f21(x16451,f29(x16453,x16452,x16451)))
% 1.14/1.27 [1646]P68(x16461,x16462,x16463)+P11(a1,f29(x16463,x16462,x16461),f2(a1))+~P67(f21(x16461,x16463))+~P67(f21(x16461,f27(x16463,x16462,x16461)))
% 1.14/1.27 [1664]~P48(x16641)+~P12(x16641,x16642,f3(x16641))+~P12(x16641,f2(x16641),x16642)+P12(x16641,f10(x16641,x16642,f18(x16641,x16642,x16643)),f18(x16641,x16642,x16643))
% 1.14/1.27 [1672]P68(x16723,x16721,x16722)+P12(a1,x16721,f29(x16722,x16721,x16723))+E(x16721,f2(a1))+E(f9(a1,f10(a1,x16721,f28(x16722,x16721,x16723)),f27(x16722,x16721,x16723)),x16722)
% 1.14/1.27 [1673]P68(x16733,x16731,x16732)+P12(a1,f27(x16732,x16731,x16733),x16731)+E(x16731,f2(a1))+E(f9(a1,f10(a1,x16731,f30(x16732,x16731,x16733)),f29(x16732,x16731,x16733)),x16732)
% 1.14/1.27 [1674]P68(x16743,x16741,x16742)+E(x16741,f2(a1))+P11(a1,f2(a1),f27(x16742,x16741,x16743))+E(f9(a1,f10(a1,x16741,f30(x16742,x16741,x16743)),f29(x16742,x16741,x16743)),x16742)
% 1.14/1.27 [1675]P68(x16753,x16751,x16752)+E(x16751,f2(a1))+P11(a1,f29(x16752,x16751,x16753),f2(a1))+E(f9(a1,f10(a1,x16751,f28(x16752,x16751,x16753)),f27(x16752,x16751,x16753)),x16752)
% 1.14/1.27 [1703]P68(x17033,x17031,x17032)+P12(a1,x17031,f29(x17032,x17031,x17033))+~P67(f21(x17033,x17032))+E(f9(a1,f10(a1,x17031,f28(x17032,x17031,x17033)),f27(x17032,x17031,x17033)),x17032)
% 1.14/1.27 [1704]P68(x17043,x17041,x17042)+P12(a1,f27(x17042,x17041,x17043),x17041)+~P67(f21(x17043,x17042))+E(f9(a1,f10(a1,x17041,f30(x17042,x17041,x17043)),f29(x17042,x17041,x17043)),x17042)
% 1.14/1.27 [1705]P68(x17053,x17051,x17052)+P11(a1,f2(a1),f27(x17052,x17051,x17053))+~P67(f21(x17053,x17052))+E(f9(a1,f10(a1,x17051,f30(x17052,x17051,x17053)),f29(x17052,x17051,x17053)),x17052)
% 1.14/1.27 [1706]P68(x17063,x17061,x17062)+P11(a1,f29(x17062,x17061,x17063),f2(a1))+~P67(f21(x17063,x17062))+E(f9(a1,f10(a1,x17061,f28(x17062,x17061,x17063)),f27(x17062,x17061,x17063)),x17062)
% 1.14/1.27 [1741]~P12(a1,x17412,x17413)+~P12(a1,f2(a1),x17413)+P11(a1,f2(a1),x17411)+~P11(a1,f2(a1),f9(a1,f10(a1,x17413,x17411),x17412))
% 1.14/1.27 [1750]P11(a1,x17501,f2(a1))+~P11(a1,f2(a1),x17502)+~P12(a1,f2(a1),x17503)+~P12(a1,f9(a1,f10(a1,x17503,x17501),x17502),f2(a1))
% 1.14/1.27 [1751]P68(x17512,x17511,x17513)+E(x17511,f2(a1))+~P67(f21(x17512,f27(x17513,x17511,x17512)))+~P67(f21(x17512,f29(x17513,x17511,x17512)))
% 1.14/1.27 [1759]P68(x17591,x17592,x17593)+~P67(f21(x17591,x17593))+~P67(f21(x17591,f27(x17593,x17592,x17591)))+~P67(f21(x17591,f29(x17593,x17592,x17591)))
% 1.14/1.27 [1760]P68(x17603,x17601,x17602)+E(x17601,f2(a1))+E(f9(a1,f10(a1,x17601,f28(x17602,x17601,x17603)),f27(x17602,x17601,x17603)),x17602)+~P67(f21(x17603,f29(x17602,x17601,x17603)))
% 1.14/1.27 [1761]P68(x17613,x17611,x17612)+E(x17611,f2(a1))+E(f9(a1,f10(a1,x17611,f30(x17612,x17611,x17613)),f29(x17612,x17611,x17613)),x17612)+~P67(f21(x17613,f27(x17612,x17611,x17613)))
% 1.14/1.27 [1765]~P49(x17652)+~E(x17651,f2(x17652))+~E(x17653,f2(x17652))+~P12(x17652,f2(x17652),f9(x17652,f10(x17652,x17653,x17653),f10(x17652,x17651,x17651)))
% 1.14/1.27 [1766]P68(x17663,x17661,x17662)+~P67(f21(x17663,x17662))+E(f9(a1,f10(a1,x17661,f28(x17662,x17661,x17663)),f27(x17662,x17661,x17663)),x17662)+~P67(f21(x17663,f29(x17662,x17661,x17663)))
% 1.14/1.27 [1767]P68(x17673,x17671,x17672)+~P67(f21(x17673,x17672))+E(f9(a1,f10(a1,x17671,f30(x17672,x17671,x17673)),f29(x17672,x17671,x17673)),x17672)+~P67(f21(x17673,f27(x17672,x17671,x17673)))
% 1.14/1.27 [1781]P68(x17813,x17811,x17812)+E(x17811,f2(a1))+E(f9(a1,f10(a1,x17811,f30(x17812,x17811,x17813)),f29(x17812,x17811,x17813)),x17812)+E(f9(a1,f10(a1,x17811,f28(x17812,x17811,x17813)),f27(x17812,x17811,x17813)),x17812)
% 1.14/1.27 [1790]P68(x17903,x17901,x17902)+~P67(f21(x17903,x17902))+E(f9(a1,f10(a1,x17901,f30(x17902,x17901,x17903)),f29(x17902,x17901,x17903)),x17902)+E(f9(a1,f10(a1,x17901,f28(x17902,x17901,x17903)),f27(x17902,x17901,x17903)),x17902)
% 1.14/1.27 [1592]~P48(x15921)+~P11(x15921,x15922,f3(x15921))+~P11(x15921,f2(x15921),x15922)+P11(x15921,f18(x15921,x15922,f9(a41,x15923,f3(a41))),x15922)
% 1.14/1.27 [1598]~P48(x15981)+~P12(x15981,x15982,f3(x15981))+~P12(x15981,f2(x15981),x15982)+P12(x15981,f18(x15981,x15982,f9(a41,x15983,f3(a41))),f3(x15981))
% 1.14/1.27 [1864]~P48(x18641)+P11(x18641,x18642,x18643)+~P11(x18641,f2(x18641),x18643)+~P11(x18641,f18(x18641,x18642,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18641,x18643,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1854]~P44(x18541)+~E(x18543,f2(x18541))+~E(x18542,f2(x18541))+E(f9(x18541,f18(x18541,x18542,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18541,x18543,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(x18541))
% 1.14/1.27 [1870]~P44(x18701)+~E(x18703,f2(x18701))+~E(x18702,f2(x18701))+P11(x18701,f9(x18701,f18(x18701,x18702,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18701,x18703,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))),f2(x18701))
% 1.14/1.27 [1879]~P44(x18792)+~E(x18791,f2(x18792))+~E(x18793,f2(x18792))+~P12(x18792,f2(x18792),f9(x18792,f18(x18792,x18793,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18792,x18791,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11))))))
% 1.14/1.27 [963]~P33(x9631)+~P11(x9631,x9634,x9633)+P11(x9631,x9632,x9633)+~P11(x9631,x9632,x9634)
% 1.14/1.27 [964]~P31(x9641)+~P11(x9641,x9642,x9644)+P11(x9641,x9642,x9643)+~P11(x9641,x9644,x9643)
% 1.14/1.27 [965]~P33(x9651)+~P12(x9651,x9654,x9653)+P12(x9651,x9652,x9653)+~P11(x9651,x9652,x9654)
% 1.14/1.27 [966]~P33(x9661)+~P12(x9661,x9662,x9664)+P12(x9661,x9662,x9663)+~P11(x9661,x9664,x9663)
% 1.14/1.27 [967]~P33(x9671)+~P12(x9671,x9674,x9673)+P12(x9671,x9672,x9673)+~P12(x9671,x9672,x9674)
% 1.14/1.27 [968]~P31(x9681)+~P12(x9681,x9682,x9684)+P12(x9681,x9682,x9683)+~P11(x9681,x9684,x9683)
% 1.14/1.27 [969]~P31(x9691)+~P12(x9691,x9694,x9693)+P12(x9691,x9692,x9693)+~P11(x9691,x9692,x9694)
% 1.14/1.27 [970]~P31(x9701)+~P12(x9701,x9702,x9704)+P12(x9701,x9702,x9703)+~P12(x9701,x9704,x9703)
% 1.14/1.27 [616]~P7(x6162)+~E(x6164,f2(x6162))+~E(x6161,f2(x6162))+E(x6161,f20(x6162,x6163,x6164))
% 1.14/1.27 [617]~P7(x6171)+~E(x6173,f2(x6171))+~E(x6174,f2(x6171))+E(f20(x6171,x6172,x6173),x6174)
% 1.14/1.27 [680]~P7(x6802)+E(x6801,f2(x6802))+~E(x6801,f20(x6802,x6804,x6803))+~E(x6803,f2(x6802))
% 1.14/1.27 [681]~P7(x6812)+E(x6811,f2(x6812))+~E(f20(x6812,x6814,x6813),x6811)+~E(x6813,f2(x6812))
% 1.14/1.27 [800]~P46(x8002)+~E(f20(x8002,x8003,x8001),x8004)+E(x8001,f2(x8002))+E(x8003,f10(x8002,x8004,x8001))
% 1.14/1.27 [802]~P46(x8022)+~E(f10(x8022,x8023,x8021),x8024)+E(x8021,f2(x8022))+E(x8023,f20(x8022,x8024,x8021))
% 1.14/1.27 [803]~P7(x8032)+~E(f20(x8032,x8033,x8031),x8034)+E(x8031,f2(x8032))+E(x8033,f10(x8032,x8034,x8031))
% 1.14/1.27 [804]~P7(x8042)+~E(f10(x8042,x8043,x8041),x8044)+E(x8041,f2(x8042))+E(x8043,f20(x8042,x8044,x8041))
% 1.14/1.27 [805]~P46(x8052)+~E(x8053,f20(x8052,x8054,x8051))+E(x8051,f2(x8052))+E(f10(x8052,x8053,x8051),x8054)
% 1.14/1.27 [807]~P46(x8072)+~E(x8073,f10(x8072,x8074,x8071))+E(x8071,f2(x8072))+E(f20(x8072,x8073,x8071),x8074)
% 1.14/1.27 [808]~P7(x8082)+~E(x8083,f20(x8082,x8084,x8081))+E(x8081,f2(x8082))+E(f10(x8082,x8083,x8081),x8084)
% 1.14/1.27 [809]~P7(x8092)+~E(x8093,f10(x8092,x8094,x8091))+E(x8091,f2(x8092))+E(f20(x8092,x8093,x8091),x8094)
% 1.14/1.27 [816]~P7(x8162)+~E(x8161,f2(x8162))+~E(f10(x8162,x8161,x8164),x8163)+E(x8161,f20(x8162,x8163,x8164))
% 1.14/1.27 [817]~P7(x8171)+~E(x8174,f2(x8171))+~E(x8172,f10(x8171,x8174,x8173))+E(f20(x8171,x8172,x8173),x8174)
% 1.14/1.27 [1066]~P48(x10663)+E(x10661,x10662)+~P12(x10663,f3(x10663),x10664)+~E(f18(x10663,x10664,x10661),f18(x10663,x10664,x10662))
% 1.14/1.27 [1080]~P32(x10802)+P12(f43(x10801,x10802),x10804,x10803)+~P11(f43(x10801,x10802),x10804,x10803)+P11(f43(x10801,x10802),x10803,x10804)
% 1.14/1.27 [1212]~P20(x12121)+~P11(x12121,x12122,x12123)+~P11(x12121,f2(x12121),x12124)+P11(x12121,x12122,f9(x12121,x12123,x12124))
% 1.14/1.27 [1213]~P20(x12131)+~P11(x12131,x12132,x12134)+~P11(x12131,f2(x12131),x12133)+P11(x12131,x12132,f9(x12131,x12133,x12134))
% 1.14/1.27 [1214]~P48(x12141)+~P12(x12141,x12142,x12144)+~P12(x12141,f2(x12141),x12143)+P12(x12141,x12142,f9(x12141,x12143,x12144))
% 1.14/1.27 [1215]~P20(x12151)+~P11(x12151,x12152,x12154)+~P12(x12151,f2(x12151),x12153)+P12(x12151,x12152,f9(x12151,x12153,x12154))
% 1.14/1.27 [1216]~P20(x12161)+~P12(x12161,x12162,x12164)+~P11(x12161,f2(x12161),x12163)+P12(x12161,x12162,f9(x12161,x12163,x12164))
% 1.14/1.27 [1282]~P44(x12822)+~P11(x12822,x12823,x12824)+P11(x12822,f18(x12822,x12823,x12821),f18(x12822,x12824,x12821))+P10(a41,x12821)
% 1.14/1.27 [1388]~P48(x13881)+~P11(a41,x13883,x13884)+~P12(x13881,f3(x13881),x13882)+P11(x13881,f18(x13881,x13882,x13883),f18(x13881,x13882,x13884))
% 1.14/1.27 [1389]~P48(x13891)+~P11(a41,x13893,x13894)+~P11(x13891,f3(x13891),x13892)+P11(x13891,f18(x13891,x13892,x13893),f18(x13891,x13892,x13894))
% 1.14/1.27 [1391]~P48(x13911)+~P12(a41,x13913,x13914)+~P12(x13911,f3(x13911),x13912)+P12(x13911,f18(x13911,x13912,x13913),f18(x13911,x13912,x13914))
% 1.14/1.27 [1403]~P49(x14031)+~P11(x14031,x14034,x14033)+~P12(x14031,x14032,f2(x14031))+P11(x14031,f10(x14031,x14032,x14033),f10(x14031,x14032,x14034))
% 1.14/1.27 [1404]~P58(x14041)+~P11(x14041,x14044,x14043)+~P11(x14041,x14042,f2(x14041))+P11(x14041,f10(x14041,x14042,x14043),f10(x14041,x14042,x14044))
% 1.14/1.27 [1405]~P58(x14051)+~P11(x14051,x14054,x14052)+~P11(x14051,x14053,f2(x14051))+P11(x14051,f10(x14051,x14052,x14053),f10(x14051,x14054,x14053))
% 1.14/1.27 [1406]~P13(x14061)+~P11(x14061,x14064,x14062)+~P11(x14061,x14063,f2(x14061))+P11(x14061,f20(x14061,x14062,x14063),f20(x14061,x14064,x14063))
% 1.14/1.27 [1410]~P49(x14101)+~P12(x14101,x14104,x14102)+~P12(x14101,x14103,f2(x14101))+P12(x14101,f10(x14101,x14102,x14103),f10(x14101,x14104,x14103))
% 1.14/1.27 [1411]~P49(x14111)+~P12(x14111,x14114,x14113)+~P12(x14111,x14112,f2(x14111))+P12(x14111,f10(x14111,x14112,x14113),f10(x14111,x14112,x14114))
% 1.14/1.27 [1412]~P14(x14121)+~P12(x14121,x14124,x14122)+~P12(x14121,x14123,f2(x14121))+P12(x14121,f20(x14121,x14122,x14123),f20(x14121,x14124,x14123))
% 1.14/1.27 [1413]~P49(x14131)+~P11(x14131,x14133,x14134)+~P12(x14131,f2(x14131),x14132)+P11(x14131,f10(x14131,x14132,x14133),f10(x14131,x14132,x14134))
% 1.14/1.27 [1414]~P60(x14141)+~P11(x14141,x14143,x14144)+~P11(x14141,f2(x14141),x14142)+P11(x14141,f10(x14141,x14142,x14143),f10(x14141,x14142,x14144))
% 1.14/1.27 [1415]~P59(x14151)+~P11(x14151,x14153,x14154)+~P11(x14151,f2(x14151),x14152)+P11(x14151,f10(x14151,x14152,x14153),f10(x14151,x14152,x14154))
% 1.14/1.27 [1416]~P60(x14161)+~P11(x14161,x14162,x14164)+~P11(x14161,f2(x14161),x14163)+P11(x14161,f10(x14161,x14162,x14163),f10(x14161,x14164,x14163))
% 1.14/1.27 [1417]~P48(x14171)+~P11(x14171,x14172,x14174)+~P11(x14171,f2(x14171),x14172)+P11(x14171,f18(x14171,x14172,x14173),f18(x14171,x14174,x14173))
% 1.14/1.27 [1418]~P13(x14181)+~P11(x14181,x14182,x14184)+~P11(x14181,f2(x14181),x14183)+P11(x14181,f20(x14181,x14182,x14183),f20(x14181,x14184,x14183))
% 1.14/1.27 [1420]~P51(x14201)+~P12(x14201,x14203,x14204)+~P12(x14201,f2(x14201),x14202)+P12(x14201,f10(x14201,x14202,x14203),f10(x14201,x14202,x14204))
% 1.14/1.27 [1421]~P45(x14211)+~P12(x14211,x14213,x14214)+~P12(x14211,f2(x14211),x14212)+P12(x14211,f10(x14211,x14212,x14213),f10(x14211,x14212,x14214))
% 1.14/1.27 [1422]~P49(x14221)+~P12(x14221,x14222,x14224)+~P12(x14221,f2(x14221),x14223)+P12(x14221,f10(x14221,x14222,x14223),f10(x14221,x14224,x14223))
% 1.14/1.27 [1423]~P51(x14231)+~P12(x14231,x14232,x14234)+~P12(x14231,f2(x14231),x14233)+P12(x14231,f10(x14231,x14232,x14233),f10(x14231,x14234,x14233))
% 1.14/1.27 [1424]~P49(x14241)+~P12(x14241,x14243,x14244)+~P12(x14241,f2(x14241),x14242)+P12(x14241,f10(x14241,x14242,x14243),f10(x14241,x14242,x14244))
% 1.14/1.27 [1425]~P14(x14251)+~P12(x14251,x14252,x14254)+~P12(x14251,f2(x14251),x14253)+P12(x14251,f20(x14251,x14252,x14253),f20(x14251,x14254,x14253))
% 1.14/1.27 [1439]~P44(x14391)+~P11(x14391,f4(x14391,x14392),f4(x14391,x14394))+P11(x14391,f18(x14391,x14392,x14393),f18(x14391,x14394,x14393))+~P10(a41,x14393)
% 1.14/1.27 [1479]~P14(x14791)+~P12(x14791,x14794,f2(x14791))+~P11(x14791,x14793,f20(x14791,x14792,x14794))+P11(x14791,x14792,f10(x14791,x14793,x14794))
% 1.14/1.27 [1480]~P14(x14801)+~P12(x14801,x14804,f2(x14801))+~P11(x14801,x14803,f10(x14801,x14802,x14804))+P11(x14801,x14802,f20(x14801,x14803,x14804))
% 1.14/1.27 [1481]~P14(x14811)+~P12(x14811,x14814,f2(x14811))+~P12(x14811,x14813,f20(x14811,x14812,x14814))+P12(x14811,x14812,f10(x14811,x14813,x14814))
% 1.14/1.27 [1482]~P14(x14821)+~P12(x14821,x14824,f2(x14821))+~P12(x14821,x14823,f10(x14821,x14822,x14824))+P12(x14821,x14822,f20(x14821,x14823,x14824))
% 1.14/1.27 [1483]~P13(x14831)+~P12(x14831,f2(x14831),x14834)+~P11(x14831,f20(x14831,x14832,x14834),x14833)+P11(x14831,x14832,f10(x14831,x14833,x14834))
% 1.14/1.27 [1484]~P13(x14841)+~P12(x14841,f2(x14841),x14844)+~P11(x14841,f10(x14841,x14842,x14844),x14843)+P11(x14841,x14842,f20(x14841,x14843,x14844))
% 1.14/1.27 [1486]~P14(x14861)+~P12(x14861,f2(x14861),x14864)+~P11(x14861,f20(x14861,x14862,x14864),x14863)+P11(x14861,x14862,f10(x14861,x14863,x14864))
% 1.14/1.27 [1487]~P14(x14871)+~P12(x14871,f2(x14871),x14874)+~P11(x14871,f10(x14871,x14872,x14874),x14873)+P11(x14871,x14872,f20(x14871,x14873,x14874))
% 1.14/1.27 [1488]~P13(x14881)+~P12(x14881,f2(x14881),x14884)+~P12(x14881,f20(x14881,x14882,x14884),x14883)+P12(x14881,x14882,f10(x14881,x14883,x14884))
% 1.14/1.27 [1489]~P13(x14891)+~P12(x14891,f2(x14891),x14894)+~P12(x14891,f10(x14891,x14892,x14894),x14893)+P12(x14891,x14892,f20(x14891,x14893,x14894))
% 1.14/1.27 [1491]~P14(x14911)+~P12(x14911,f2(x14911),x14914)+~P12(x14911,f20(x14911,x14912,x14914),x14913)+P12(x14911,x14912,f10(x14911,x14913,x14914))
% 1.14/1.27 [1492]~P14(x14921)+~P12(x14921,f2(x14921),x14924)+~P12(x14921,f10(x14921,x14922,x14924),x14923)+P12(x14921,x14922,f20(x14921,x14923,x14924))
% 1.14/1.27 [1493]~P14(x14931)+~P12(x14931,x14933,f2(x14931))+~P11(x14931,f20(x14931,x14934,x14933),x14932)+P11(x14931,f10(x14931,x14932,x14933),x14934)
% 1.14/1.27 [1494]~P14(x14941)+~P12(x14941,x14943,f2(x14941))+~P11(x14941,f10(x14941,x14944,x14943),x14942)+P11(x14941,f20(x14941,x14942,x14943),x14944)
% 1.14/1.27 [1495]~P14(x14951)+~P12(x14951,x14953,f2(x14951))+~P12(x14951,f20(x14951,x14954,x14953),x14952)+P12(x14951,f10(x14951,x14952,x14953),x14954)
% 1.14/1.27 [1496]~P14(x14961)+~P12(x14961,x14963,f2(x14961))+~P12(x14961,f10(x14961,x14964,x14963),x14962)+P12(x14961,f20(x14961,x14962,x14963),x14964)
% 1.14/1.27 [1497]~P13(x14971)+~P12(x14971,f2(x14971),x14973)+~P11(x14971,x14972,f20(x14971,x14974,x14973))+P11(x14971,f10(x14971,x14972,x14973),x14974)
% 1.14/1.27 [1498]~P14(x14981)+~P12(x14981,f2(x14981),x14983)+~P11(x14981,x14982,f20(x14981,x14984,x14983))+P11(x14981,f10(x14981,x14982,x14983),x14984)
% 1.14/1.27 [1499]~P13(x14991)+~P12(x14991,f2(x14991),x14993)+~P11(x14991,x14992,f10(x14991,x14994,x14993))+P11(x14991,f20(x14991,x14992,x14993),x14994)
% 1.14/1.27 [1501]~P14(x15011)+~P12(x15011,f2(x15011),x15013)+~P11(x15011,x15012,f10(x15011,x15014,x15013))+P11(x15011,f20(x15011,x15012,x15013),x15014)
% 1.14/1.27 [1502]~P13(x15021)+~P12(x15021,f2(x15021),x15023)+~P12(x15021,x15022,f20(x15021,x15024,x15023))+P12(x15021,f10(x15021,x15022,x15023),x15024)
% 1.14/1.27 [1503]~P14(x15031)+~P12(x15031,f2(x15031),x15033)+~P12(x15031,x15032,f20(x15031,x15034,x15033))+P12(x15031,f10(x15031,x15032,x15033),x15034)
% 1.14/1.27 [1504]~P13(x15041)+~P12(x15041,f2(x15041),x15043)+~P12(x15041,x15042,f10(x15041,x15044,x15043))+P12(x15041,f20(x15041,x15042,x15043),x15044)
% 1.14/1.27 [1506]~P14(x15061)+~P12(x15061,f2(x15061),x15063)+~P12(x15061,x15062,f10(x15061,x15064,x15063))+P12(x15061,f20(x15061,x15062,x15063),x15064)
% 1.14/1.27 [1511]P12(x15111,x15113,x15112)+~P49(x15111)+P12(x15111,x15112,x15113)+~P12(x15111,f10(x15111,x15114,x15112),f10(x15111,x15114,x15113))
% 1.14/1.27 [1512]P12(x15121,x15123,x15122)+~P49(x15121)+P12(x15121,x15122,x15123)+~P12(x15121,f10(x15121,x15122,x15124),f10(x15121,x15123,x15124))
% 1.14/1.27 [1526]~P49(x15261)+P12(x15261,x15262,x15263)+~P12(x15261,f10(x15261,x15262,x15264),f10(x15261,x15263,x15264))+P12(x15261,x15264,f2(x15261))
% 1.14/1.27 [1527]~P49(x15271)+P12(x15271,x15272,x15273)+~P12(x15271,f10(x15271,x15274,x15272),f10(x15271,x15274,x15273))+P12(x15271,x15274,f2(x15271))
% 1.14/1.27 [1528]~P49(x15281)+P12(x15281,x15282,x15283)+~P12(x15281,f10(x15281,x15284,x15283),f10(x15281,x15284,x15282))+P12(x15281,f2(x15281),x15284)
% 1.14/1.27 [1529]~P49(x15291)+P12(x15291,x15292,x15293)+~P12(x15291,f10(x15291,x15293,x15294),f10(x15291,x15292,x15294))+P12(x15291,f2(x15291),x15294)
% 1.14/1.27 [1537]~P49(x15371)+P12(x15371,f2(x15371),x15372)+~P12(x15371,f10(x15371,x15373,x15372),f10(x15371,x15374,x15372))+P12(x15371,x15372,f2(x15371))
% 1.14/1.27 [1538]~P49(x15381)+P12(x15381,f2(x15381),x15382)+~P12(x15381,f10(x15381,x15382,x15383),f10(x15381,x15382,x15384))+P12(x15381,x15382,f2(x15381))
% 1.14/1.27 [1562]~P48(x15623)+~P11(x15623,f18(x15623,x15624,x15621),f18(x15623,x15624,x15622))+P11(a41,x15621,x15622)+~P12(x15623,f3(x15623),x15624)
% 1.14/1.27 [1564]~P48(x15643)+~P12(x15643,f18(x15643,x15644,x15641),f18(x15643,x15644,x15642))+P12(a41,x15641,x15642)+~P12(x15643,f3(x15643),x15644)
% 1.14/1.27 [1565]~P49(x15651)+P11(x15651,x15652,x15653)+~P11(x15651,f10(x15651,x15654,x15653),f10(x15651,x15654,x15652))+~P12(x15651,x15654,f2(x15651))
% 1.14/1.27 [1566]~P49(x15661)+P12(x15661,x15662,x15663)+~P12(x15661,f10(x15661,x15664,x15663),f10(x15661,x15664,x15662))+~P12(x15661,x15664,f2(x15661))
% 1.14/1.27 [1567]~P49(x15671)+P11(x15671,x15672,x15673)+~P11(x15671,f10(x15671,x15674,x15672),f10(x15671,x15674,x15673))+~P12(x15671,f2(x15671),x15674)
% 1.14/1.27 [1568]~P51(x15681)+P11(x15681,x15682,x15683)+~P11(x15681,f10(x15681,x15684,x15682),f10(x15681,x15684,x15683))+~P12(x15681,f2(x15681),x15684)
% 1.14/1.27 [1569]~P51(x15691)+P11(x15691,x15692,x15693)+~P11(x15691,f10(x15691,x15692,x15694),f10(x15691,x15693,x15694))+~P12(x15691,f2(x15691),x15694)
% 1.14/1.27 [1570]~P49(x15701)+P12(x15701,x15702,x15703)+~P12(x15701,f10(x15701,x15704,x15702),f10(x15701,x15704,x15703))+~P12(x15701,f2(x15701),x15704)
% 1.14/1.27 [1571]~P51(x15711)+P12(x15711,x15712,x15713)+~P12(x15711,f10(x15711,x15714,x15712),f10(x15711,x15714,x15713))+~P11(x15711,f2(x15711),x15714)
% 1.14/1.27 [1572]~P52(x15721)+P12(x15721,x15722,x15723)+~P12(x15721,f10(x15721,x15724,x15722),f10(x15721,x15724,x15723))+~P11(x15721,f2(x15721),x15724)
% 1.14/1.27 [1573]~P48(x15731)+P12(x15731,x15732,x15733)+~P11(x15731,f2(x15731),x15733)+~P12(x15731,f18(x15731,x15732,x15734),f18(x15731,x15733,x15734))
% 1.14/1.27 [1574]~P51(x15741)+P12(x15741,x15742,x15743)+~P12(x15741,f10(x15741,x15742,x15744),f10(x15741,x15743,x15744))+~P11(x15741,f2(x15741),x15744)
% 1.14/1.27 [1575]~P52(x15751)+P12(x15751,x15752,x15753)+~P12(x15751,f10(x15751,x15752,x15754),f10(x15751,x15753,x15754))+~P11(x15751,f2(x15751),x15754)
% 1.14/1.27 [1444]~P43(x14442)+E(x14441,f2(x14442))+~P11(a40,x14443,f2(a40))+~P11(a40,f17(x14442,x14441),f10(a40,x14443,f17(x14442,x14444)))
% 1.14/1.27 [1786]~P12(a1,x17864,x17861)+~P11(a1,f2(a1),x17864)+~P12(a1,f2(a1),x17863)+P11(a1,f2(a1),f9(a1,f10(a1,x17861,f5(a1,x17862,x17863)),x17864))
% 1.14/1.27 [1787]~P12(a1,x17871,x17874)+~P11(a1,x17874,f2(a1))+~P12(a1,f2(a1),x17873)+P11(a1,f9(a1,f10(a1,x17871,f5(a1,x17872,x17873)),x17874),f2(a1))
% 1.14/1.27 [1791]~P12(a1,x17911,x17914)+~P11(a1,x17914,f2(a1))+~P12(a1,f2(a1),x17912)+P12(a1,f10(a1,x17911,x17912),f9(a1,f10(a1,x17911,f5(a1,x17913,x17912)),x17914))
% 1.14/1.27 [1792]~P12(a1,x17924,x17921)+~P11(a1,f2(a1),x17924)+~P12(a1,f2(a1),x17923)+P12(a1,f9(a1,f10(a1,x17921,f5(a1,x17922,x17923)),x17924),f10(a1,x17921,x17923))
% 1.14/1.27 [1799]~P48(x17991)+P11(x17991,x17992,x17993)+~P11(x17991,f2(x17991),x17993)+~P11(x17991,f18(x17991,x17992,f9(a41,x17994,f3(a41))),f18(x17991,x17993,f9(a41,x17994,f3(a41))))
% 1.14/1.27 [1383]~P22(x13831)+~P11(x13831,x13833,x13835)+~P11(x13831,x13832,x13834)+P11(x13831,f9(x13831,x13832,x13833),f9(x13831,x13834,x13835))
% 1.14/1.27 [1384]~P25(x13841)+~P11(x13841,x13843,x13845)+~P12(x13841,x13842,x13844)+P12(x13841,f9(x13841,x13842,x13843),f9(x13841,x13844,x13845))
% 1.14/1.27 [1385]~P25(x13851)+~P11(x13851,x13852,x13854)+~P12(x13851,x13853,x13855)+P12(x13851,f9(x13851,x13852,x13853),f9(x13851,x13854,x13855))
% 1.14/1.27 [1386]~P25(x13861)+~P12(x13861,x13863,x13865)+~P12(x13861,x13862,x13864)+P12(x13861,f9(x13861,x13862,x13863),f9(x13861,x13864,x13865))
% 1.14/1.27 [1618]~P44(x16181)+~P12(x16181,f4(x16181,x16182),x16184)+~P12(x16181,f4(x16181,x16183),x16185)+P12(x16181,f10(x16181,f4(x16181,x16182),f4(x16181,x16183)),f10(x16181,x16184,x16185))
% 1.14/1.27 [1650]~P36(x16501)+~P12(a40,f17(x16501,x16503),x16505)+~P12(a40,f17(x16501,x16502),x16504)+P12(a40,f17(x16501,f10(x16501,x16502,x16503)),f10(a40,x16504,x16505))
% 1.14/1.27 [1651]~P43(x16511)+~P12(a40,f17(x16511,x16513),x16515)+~P12(a40,f17(x16511,x16512),x16514)+P12(a40,f17(x16511,f9(x16511,x16512,x16513)),f9(a40,x16514,x16515))
% 1.14/1.27 [1756]~P66(x17565)+E(x17561,x17562)+E(x17563,x17564)+~E(f9(x17565,f10(x17565,x17563,x17561),f10(x17565,x17564,x17562)),f9(x17565,f10(x17565,x17563,x17562),f10(x17565,x17564,x17561)))
% 1.14/1.27 [1772]~P8(x17722)+E(x17721,f2(x17722))+E(x17723,f2(x17722))+E(f20(x17722,f9(x17722,f10(x17722,x17724,x17721),f10(x17722,x17725,x17723)),f10(x17722,x17723,x17721)),f9(x17722,f20(x17722,x17724,x17723),f20(x17722,x17725,x17721)))
% 1.14/1.27 [1654]~P9(x16541)+~E(f5(x16541,x16543,x16544),f5(x16541,x16546,x16544))+~E(f5(x16541,x16542,x16544),f5(x16541,x16545,x16544))+E(f5(x16541,f10(x16541,x16542,x16543),x16544),f5(x16541,f10(x16541,x16545,x16546),x16544))
% 1.14/1.27 [1655]~P9(x16551)+~E(f5(x16551,x16553,x16554),f5(x16551,x16556,x16554))+~E(f5(x16551,x16552,x16554),f5(x16551,x16555,x16554))+E(f5(x16551,f9(x16551,x16552,x16553),x16554),f5(x16551,f9(x16551,x16555,x16556),x16554))
% 1.14/1.27 [912]~P44(x9122)+P11(x9122,f18(x9122,x9123,x9121),f2(x9122))+~E(x9123,f2(x9122))+~P10(a41,x9121)+E(x9121,f2(a41))
% 1.14/1.27 [1076]~P44(x10762)+~P11(x10762,x10763,f2(x10762))+P11(x10762,f18(x10762,x10763,x10761),f2(x10762))+P10(a41,x10761)+E(x10761,f2(a41))
% 1.14/1.27 [1091]~P20(x10912)+~P11(x10912,f2(x10912),x10913)+~P11(x10912,f2(x10912),x10911)+~E(f9(x10912,x10913,x10911),f2(x10912))+E(x10911,f2(x10912))
% 1.14/1.27 [1092]~P20(x10922)+~P11(x10922,f2(x10922),x10923)+~P11(x10922,f2(x10922),x10921)+~E(f9(x10922,x10921,x10923),f2(x10922))+E(x10921,f2(x10922))
% 1.14/1.27 [1105]~P44(x11053)+~P12(x11053,f2(x11053),f18(x11053,x11052,x11051))+~P10(a41,x11051)+~E(x11052,f2(x11053))+E(x11051,f2(a41))
% 1.14/1.27 [1189]~P44(x11892)+~P12(x11892,f2(x11892),f18(x11892,x11893,x11891))+P12(x11892,f2(x11892),x11893)+~E(x11893,f2(x11892))+E(x11891,f2(a41))
% 1.14/1.27 [1210]~P44(x12102)+~P12(x12102,f2(x12102),f18(x12102,x12103,x12101))+P12(x12102,f2(x12102),x12103)+P10(a41,x12101)+E(x12101,f2(a41))
% 1.14/1.27 [1393]~P44(x13931)+~P11(x13931,x13932,f3(x13931))+~P11(x13931,f2(x13931),x13932)+~P11(x13931,f2(x13931),x13933)+P11(x13931,f10(x13931,x13932,x13933),x13933)
% 1.14/1.27 [1394]~P44(x13941)+~P11(x13941,x13943,f3(x13941))+~P11(x13941,f2(x13941),x13943)+~P11(x13941,f2(x13941),x13942)+P11(x13941,f10(x13941,x13942,x13943),x13942)
% 1.14/1.27 [1850]~P48(x18503)+E(x18501,x18502)+~P11(x18503,f2(x18503),x18502)+~P11(x18503,f2(x18503),x18501)+~E(f18(x18503,x18501,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(x18503,x18502,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))
% 1.14/1.27 [1288]~P13(x12881)+P12(x12881,f2(x12881),x12882)+~P11(x12881,x12883,f2(x12881))+P12(x12881,x12882,f2(x12881))+P11(x12881,x12883,f20(x12881,x12884,x12882))
% 1.14/1.27 [1289]~P13(x12891)+P12(x12891,f2(x12891),x12892)+~P12(x12891,x12893,f2(x12891))+P12(x12891,x12892,f2(x12891))+P12(x12891,x12893,f20(x12891,x12894,x12892))
% 1.14/1.27 [1290]~P13(x12901)+P12(x12901,f2(x12901),x12902)+~P11(x12901,f2(x12901),x12904)+P12(x12901,x12902,f2(x12901))+P11(x12901,f20(x12901,x12903,x12902),x12904)
% 1.14/1.27 [1291]~P13(x12911)+P12(x12911,f2(x12911),x12912)+~P12(x12911,f2(x12911),x12914)+P12(x12911,x12912,f2(x12911))+P12(x12911,f20(x12911,x12913,x12912),x12914)
% 1.14/1.27 [1377]~P13(x13771)+P12(x13771,f2(x13771),x13773)+P11(x13771,x13772,f2(x13771))+~P11(x13771,x13772,f20(x13771,x13774,x13773))+P12(x13771,x13773,f2(x13771))
% 1.14/1.27 [1378]~P13(x13781)+P12(x13781,f2(x13781),x13783)+P12(x13781,x13782,f2(x13781))+~P12(x13781,x13782,f20(x13781,x13784,x13783))+P12(x13781,x13783,f2(x13781))
% 1.14/1.27 [1379]~P13(x13791)+P12(x13791,f2(x13791),x13792)+P12(x13791,x13792,f2(x13791))+~P11(x13791,f20(x13791,x13794,x13792),x13793)+P11(x13791,f2(x13791),x13793)
% 1.14/1.27 [1380]~P13(x13801)+P12(x13801,f2(x13801),x13802)+P12(x13801,x13802,f2(x13801))+~P12(x13801,f20(x13801,x13804,x13802),x13803)+P12(x13801,f2(x13801),x13803)
% 1.14/1.27 [1530]~P48(x15301)+~P12(x15301,x15302,x15304)+~P11(x15301,f2(x15301),x15302)+P12(x15301,f18(x15301,x15302,x15303),f18(x15301,x15304,x15303))+~P12(a41,f2(a41),x15303)
% 1.14/1.27 [1539]~P48(x15391)+~P11(a41,x15394,x15393)+~P11(x15391,x15392,f3(x15391))+~P11(x15391,f2(x15391),x15392)+P11(x15391,f18(x15391,x15392,x15393),f18(x15391,x15392,x15394))
% 1.14/1.27 [1540]~P48(x15401)+~P12(a41,x15404,x15403)+~P12(x15401,x15402,f3(x15401))+~P12(x15401,f2(x15401),x15402)+P12(x15401,f18(x15401,x15402,x15403),f18(x15401,x15402,x15404))
% 1.14/1.27 [1576]~P13(x15761)+~P11(x15761,x15763,f2(x15761))+~P11(x15761,f10(x15761,x15763,x15762),x15764)+P12(x15761,x15762,f2(x15761))+P11(x15761,x15763,f20(x15761,x15764,x15762))
% 1.14/1.27 [1577]~P13(x15771)+~P12(x15771,x15773,f2(x15771))+~P12(x15771,f10(x15771,x15773,x15772),x15774)+P12(x15771,x15772,f2(x15771))+P12(x15771,x15773,f20(x15771,x15774,x15772))
% 1.14/1.27 [1578]~P13(x15781)+~P11(x15781,f2(x15781),x15784)+~P11(x15781,x15783,f10(x15781,x15784,x15782))+P12(x15781,x15782,f2(x15781))+P11(x15781,f20(x15781,x15783,x15782),x15784)
% 1.14/1.27 [1579]~P13(x15791)+~P12(x15791,f2(x15791),x15794)+~P12(x15791,x15793,f10(x15791,x15794,x15792))+P12(x15791,x15792,f2(x15791))+P12(x15791,f20(x15791,x15793,x15792),x15794)
% 1.14/1.27 [1580]~P13(x15801)+~P11(x15801,x15803,f2(x15801))+~P11(x15801,x15804,f10(x15801,x15803,x15802))+P12(x15801,f2(x15801),x15802)+P11(x15801,x15803,f20(x15801,x15804,x15802))
% 1.14/1.27 [1581]~P13(x15811)+~P12(x15811,x15813,f2(x15811))+~P12(x15811,x15814,f10(x15811,x15813,x15812))+P12(x15811,f2(x15811),x15812)+P12(x15811,x15813,f20(x15811,x15814,x15812))
% 1.14/1.27 [1582]~P13(x15821)+~P12(x15821,x15822,f2(x15821))+~P11(x15821,x15824,f10(x15821,x15823,x15822))+P12(x15821,f2(x15821),x15822)+P11(x15821,x15823,f20(x15821,x15824,x15822))
% 1.14/1.27 [1583]~P13(x15831)+~P12(x15831,x15832,f2(x15831))+~P11(x15831,x15834,f20(x15831,x15833,x15832))+P12(x15831,f2(x15831),x15832)+P11(x15831,x15833,f10(x15831,x15834,x15832))
% 1.14/1.27 [1584]~P13(x15841)+~P12(x15841,x15842,f2(x15841))+~P12(x15841,x15844,f10(x15841,x15843,x15842))+P12(x15841,f2(x15841),x15842)+P12(x15841,x15843,f20(x15841,x15844,x15842))
% 1.14/1.27 [1585]~P13(x15851)+~P12(x15851,x15852,f2(x15851))+~P12(x15851,x15854,f20(x15851,x15853,x15852))+P12(x15851,f2(x15851),x15852)+P12(x15851,x15853,f10(x15851,x15854,x15852))
% 1.14/1.27 [1586]~P13(x15861)+~P12(x15861,x15862,f2(x15861))+~P11(x15861,f20(x15861,x15864,x15862),x15863)+P12(x15861,f2(x15861),x15862)+P11(x15861,f10(x15861,x15863,x15862),x15864)
% 1.14/1.27 [1587]~P13(x15871)+~P12(x15871,x15872,f2(x15871))+~P11(x15871,f10(x15871,x15874,x15872),x15873)+P12(x15871,f2(x15871),x15872)+P11(x15871,f20(x15871,x15873,x15872),x15874)
% 1.14/1.27 [1588]~P13(x15881)+~P12(x15881,x15882,f2(x15881))+~P12(x15881,f20(x15881,x15884,x15882),x15883)+P12(x15881,f2(x15881),x15882)+P12(x15881,f10(x15881,x15883,x15882),x15884)
% 1.14/1.27 [1589]~P13(x15891)+~P12(x15891,x15892,f2(x15891))+~P12(x15891,f10(x15891,x15894,x15892),x15893)+P12(x15891,f2(x15891),x15892)+P12(x15891,f20(x15891,x15893,x15892),x15894)
% 1.14/1.27 [1590]~P13(x15901)+~P11(x15901,f2(x15901),x15904)+~P11(x15901,f10(x15901,x15904,x15902),x15903)+P12(x15901,f2(x15901),x15902)+P11(x15901,f20(x15901,x15903,x15902),x15904)
% 1.14/1.27 [1591]~P13(x15911)+~P12(x15911,f2(x15911),x15914)+~P12(x15911,f10(x15911,x15914,x15912),x15913)+P12(x15911,f2(x15911),x15912)+P12(x15911,f20(x15911,x15913,x15912),x15914)
% 1.14/1.27 [1687]~P13(x16871)+~P11(x16871,x16873,x16874)+~P11(x16871,x16872,f2(x16871))+~P12(x16871,f2(x16871),f10(x16871,x16873,x16874))+P11(x16871,f20(x16871,x16872,x16873),f20(x16871,x16872,x16874))
% 1.14/1.27 [1688]~P14(x16881)+~P12(x16881,x16883,x16884)+~P12(x16881,x16882,f2(x16881))+~P12(x16881,f2(x16881),f10(x16881,x16883,x16884))+P12(x16881,f20(x16881,x16882,x16883),f20(x16881,x16882,x16884))
% 1.14/1.27 [1689]~P14(x16891)+~P11(x16891,x16894,x16893)+~P11(x16891,f2(x16891),x16892)+~P12(x16891,f2(x16891),f10(x16891,x16893,x16894))+P11(x16891,f20(x16891,x16892,x16893),f20(x16891,x16892,x16894))
% 1.14/1.27 [1690]~P14(x16901)+~P12(x16901,x16904,x16903)+~P12(x16901,f2(x16901),x16902)+~P12(x16901,f2(x16901),f10(x16901,x16903,x16904))+P12(x16901,f20(x16901,x16902,x16903),f20(x16901,x16902,x16904))
% 1.14/1.27 [1717]~P13(x17171)+~P12(x17171,x17174,f2(x17171))+~P11(x17171,x17173,f10(x17171,x17172,x17174))+~P11(x17171,f10(x17171,x17172,x17174),x17173)+P11(x17171,x17172,f20(x17171,x17173,x17174))
% 1.14/1.27 [1718]~P13(x17181)+~P11(x17181,x17182,f2(x17181))+~P11(x17181,x17183,f10(x17181,x17182,x17184))+~P11(x17181,f10(x17181,x17182,x17184),x17183)+P11(x17181,x17182,f20(x17181,x17183,x17184))
% 1.14/1.27 [1719]~P13(x17191)+~P12(x17191,x17194,f2(x17191))+~P12(x17191,x17193,f10(x17191,x17192,x17194))+~P12(x17191,f10(x17191,x17192,x17194),x17193)+P12(x17191,x17192,f20(x17191,x17193,x17194))
% 1.14/1.27 [1720]~P13(x17201)+~P12(x17201,x17202,f2(x17201))+~P12(x17201,x17203,f10(x17201,x17202,x17204))+~P12(x17201,f10(x17201,x17202,x17204),x17203)+P12(x17201,x17202,f20(x17201,x17203,x17204))
% 1.14/1.27 [1721]~P13(x17211)+~P12(x17211,x17213,f2(x17211))+~P11(x17211,x17212,f10(x17211,x17214,x17213))+~P11(x17211,f10(x17211,x17214,x17213),x17212)+P11(x17211,f20(x17211,x17212,x17213),x17214)
% 1.14/1.27 [1722]~P13(x17221)+~P12(x17221,x17223,f2(x17221))+~P12(x17221,x17222,f10(x17221,x17224,x17223))+~P12(x17221,f10(x17221,x17224,x17223),x17222)+P12(x17221,f20(x17221,x17222,x17223),x17224)
% 1.14/1.27 [1723]~P13(x17231)+~P11(x17231,f2(x17231),x17234)+~P11(x17231,x17232,f10(x17231,x17234,x17233))+~P11(x17231,f10(x17231,x17234,x17233),x17232)+P11(x17231,f20(x17231,x17232,x17233),x17234)
% 1.14/1.27 [1724]~P13(x17241)+~P12(x17241,f2(x17241),x17244)+~P12(x17241,x17242,f10(x17241,x17244,x17243))+~P12(x17241,f10(x17241,x17244,x17243),x17242)+P12(x17241,f20(x17241,x17242,x17243),x17244)
% 1.14/1.27 [1686]~P48(x16863)+E(x16861,x16862)+~P11(x16863,f2(x16863),x16862)+~P11(x16863,f2(x16863),x16861)+~E(f18(x16863,x16861,f9(a41,x16864,f3(a41))),f18(x16863,x16862,f9(a41,x16864,f3(a41))))
% 1.14/1.27 [1096]~P8(x10962)+~E(f20(x10962,x10964,x10963),f20(x10962,x10965,x10961))+E(f10(x10962,x10964,x10961),f10(x10962,x10965,x10963))+E(x10961,f2(x10962))+E(x10963,f2(x10962))
% 1.14/1.27 [1097]~P8(x10972)+~E(f10(x10972,x10974,x10973),f10(x10972,x10975,x10971))+E(f20(x10972,x10974,x10971),f20(x10972,x10975,x10973))+E(x10971,f2(x10972))+E(x10973,f2(x10972))
% 1.14/1.27 [1801]P11(a1,x18011,x18012)+~P12(a1,x18013,x18014)+~P12(a1,x18013,x18015)+~P11(a1,x18014,f2(a1))+~P11(a1,f9(a1,f10(a1,x18013,x18012),x18015),f9(a1,f10(a1,x18013,x18011),x18014))
% 1.14/1.27 [1802]P11(a1,x18021,x18022)+~P12(a1,x18023,x18024)+~P12(a1,x18025,x18024)+~P11(a1,f2(a1),x18025)+~P11(a1,f9(a1,f10(a1,x18024,x18021),x18025),f9(a1,f10(a1,x18024,x18022),x18023))
% 1.14/1.27 [1507]~P66(x15074)+E(x15071,x15072)+~E(x15075,x15076)+E(x15073,f2(x15074))+~E(f9(x15074,x15075,f10(x15074,x15073,x15071)),f9(x15074,x15076,f10(x15074,x15073,x15072)))
% 1.14/1.27 [722]~P28(x7222)+~P29(x7222)+~P34(x7222)+~P62(x7222)+~E(f18(x7222,x7221,x7223),f2(x7222))+E(x7221,f2(x7222))
% 1.14/1.27 [723]~P28(x7232)+~P29(x7232)+~P34(x7232)+~P62(x7232)+~E(f18(x7232,x7233,x7231),f2(x7232))+~E(x7231,f2(a41))
% 1.14/1.27 [1062]~P20(x10621)+~P11(x10621,f2(x10621),x10623)+~P11(x10621,f2(x10621),x10622)+~E(x10623,f2(x10621))+~E(x10622,f2(x10621))+E(f9(x10621,x10622,x10623),f2(x10621))
% 1.14/1.27 [1882]~P11(a40,f2(a40),x18822)+~P11(a40,f2(a40),x18821)+~P12(a40,f2(a40),x18823)+~P12(a40,x18821,f20(a40,x18823,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))+~P12(a40,x18822,f20(a40,x18823,f15(a40,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))+P12(a40,f14(f9(a40,f18(a40,x18821,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))),f18(a40,x18822,f15(a41,f9(a1,f9(a1,f9(a1,f3(a1),a11),a11),f9(a1,f9(a1,f3(a1),a11),a11)))))),x18823)
% 1.14/1.27 [1430]~P48(x14303)+E(x14301,x14302)+~P11(x14303,f2(x14303),x14302)+~P11(x14303,f2(x14303),x14301)+~E(f18(x14303,x14301,x14304),f18(x14303,x14302,x14304))+~P12(a41,f2(a41),x14304)
% 1.14/1.27 [1510]~P12(a1,x15101,x15103)+E(f5(a1,x15102,x15101),x15103)+E(x15101,f2(a1))+P12(a1,f2(a1),x15101)+~P11(a1,x15103,f2(a1))+~E(x15102,f9(a1,f10(a1,x15101,x15104),x15103))
% 1.14/1.27 [1558]~P12(a1,x15583,x15581)+E(f5(a1,x15582,x15581),x15583)+E(x15581,f2(a1))+~P11(a1,f2(a1),x15583)+~P12(a1,f2(a1),x15581)+~E(x15582,f9(a1,f10(a1,x15581,x15584),x15583))
% 1.14/1.27 [1626]~P60(x16261)+~P11(x16261,x16263,x16265)+~P11(x16261,x16262,x16264)+~P11(x16261,f2(x16261),x16263)+~P11(x16261,f2(x16261),x16264)+P11(x16261,f10(x16261,x16262,x16263),f10(x16261,x16264,x16265))
% 1.14/1.27 [1627]~P60(x16271)+~P11(x16271,x16273,x16275)+~P11(x16271,x16272,x16274)+~P11(x16271,f2(x16271),x16273)+~P11(x16271,f2(x16271),x16272)+P11(x16271,f10(x16271,x16272,x16273),f10(x16271,x16274,x16275))
% 1.14/1.27 [1628]~P14(x16281)+~P11(x16281,x16285,x16283)+~P11(x16281,x16282,x16284)+~P11(x16281,f2(x16281),x16282)+~P12(x16281,f2(x16281),x16285)+P11(x16281,f20(x16281,x16282,x16283),f20(x16281,x16284,x16285))
% 1.14/1.27 [1629]~P51(x16291)+~P11(x16291,x16293,x16295)+~P12(x16291,x16292,x16294)+~P11(x16291,f2(x16291),x16292)+~P12(x16291,f2(x16291),x16293)+P12(x16291,f10(x16291,x16292,x16293),f10(x16291,x16294,x16295))
% 1.14/1.27 [1630]~P51(x16301)+~P11(x16301,x16302,x16304)+~P12(x16301,x16303,x16305)+~P11(x16301,f2(x16301),x16303)+~P12(x16301,f2(x16301),x16302)+P12(x16301,f10(x16301,x16302,x16303),f10(x16301,x16304,x16305))
% 1.14/1.27 [1631]~P51(x16311)+~P12(x16311,x16313,x16315)+~P12(x16311,x16312,x16314)+~P11(x16311,f2(x16311),x16313)+~P11(x16311,f2(x16311),x16312)+P12(x16311,f10(x16311,x16312,x16313),f10(x16311,x16314,x16315))
% 1.14/1.27 [1632]~P51(x16321)+~P12(x16321,x16323,x16325)+~P12(x16321,x16322,x16324)+~P11(x16321,f2(x16321),x16323)+~P12(x16321,f2(x16321),x16324)+P12(x16321,f10(x16321,x16322,x16323),f10(x16321,x16324,x16325))
% 1.14/1.27 [1633]~P14(x16331)+~P11(x16331,x16335,x16333)+~P12(x16331,x16332,x16334)+~P11(x16331,f2(x16331),x16332)+~P12(x16331,f2(x16331),x16335)+P12(x16331,f20(x16331,x16332,x16333),f20(x16331,x16334,x16335))
% 1.14/1.27 [1634]~P14(x16341)+~P11(x16341,x16342,x16344)+~P12(x16341,x16345,x16343)+~P12(x16341,f2(x16341),x16345)+~P12(x16341,f2(x16341),x16342)+P12(x16341,f20(x16341,x16342,x16343),f20(x16341,x16344,x16345))
% 1.14/1.27 [1616]~P68(x16161,x16164,x16163)+~P12(a1,x16164,x16162)+~P11(a1,x16162,f2(a1))+~P12(a1,x16164,f2(a1))+P67(f21(x16161,x16162))+~E(x16163,f9(a1,f10(a1,x16164,x16165),x16162))
% 1.14/1.27 [1617]~P68(x16171,x16174,x16173)+~P12(a1,x16172,x16174)+~P11(a1,f2(a1),x16172)+~P12(a1,f2(a1),x16174)+P67(f21(x16171,x16172))+~E(x16173,f9(a1,f10(a1,x16174,x16175),x16172))
% 1.14/1.27 [664]~P28(x6642)+~P29(x6642)+~P34(x6642)+~P62(x6642)+~E(x6643,f2(x6642))+E(f18(x6642,x6643,x6641),f2(x6642))+E(x6641,f2(a41))
% 1.14/1.27 [1649]~P12(a1,x16493,x16491)+~P12(a1,x16491,x16493)+E(f5(a1,x16492,x16491),x16493)+E(x16491,f2(a1))+~P11(a1,x16493,f2(a1))+~P11(a1,f2(a1),x16493)+~E(x16492,f9(a1,f10(a1,x16491,x16494),x16493))
% 1.14/1.27 [1788]~P53(x17881)+~P11(x17881,x17885,x17886)+~P11(x17881,x17883,x17886)+~P11(x17881,f2(x17881),x17884)+~P11(x17881,f2(x17881),x17882)+~E(f9(x17881,x17882,x17884),f3(x17881))+P11(x17881,f9(x17881,f10(x17881,x17882,x17883),f10(x17881,x17884,x17885)),x17886)
% 1.14/1.27 [1789]~P54(x17891)+~P12(x17891,x17895,x17896)+~P12(x17891,x17893,x17896)+~P11(x17891,f2(x17891),x17894)+~P11(x17891,f2(x17891),x17892)+~E(f9(x17891,x17892,x17894),f3(x17891))+P12(x17891,f9(x17891,f10(x17891,x17892,x17893),f10(x17891,x17894,x17895)),x17896)
% 1.14/1.27 [1804]~P11(a1,x18045,x18043)+~P12(a1,x18046,x18045)+P11(a1,x18041,x18042)+~P11(a1,f2(a1),x18044)+~P12(a1,f2(a1),x18045)+~P11(a1,f2(a1),f9(a1,f10(a1,x18045,x18042),x18046))+~E(f9(a1,f10(a1,x18043,x18041),x18044),f9(a1,f10(a1,x18045,x18042),x18046))
% 1.14/1.27 [1805]~P11(a1,x18055,x18053)+~P12(a1,x18054,x18053)+P11(a1,x18051,x18052)+~P11(a1,f2(a1),x18056)+~P12(a1,f2(a1),x18055)+~P12(a1,f9(a1,f10(a1,x18055,x18051),x18056),f2(a1))+~E(f9(a1,f10(a1,x18053,x18052),x18054),f9(a1,f10(a1,x18055,x18051),x18056))
% 1.14/1.27 %EqnAxiom
% 1.14/1.27 [1]E(x11,x11)
% 1.14/1.27 [2]E(x22,x21)+~E(x21,x22)
% 1.14/1.27 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.14/1.27 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 1.14/1.27 [5]~E(x51,x52)+E(f20(x51,x53,x54),f20(x52,x53,x54))
% 1.14/1.27 [6]~E(x61,x62)+E(f20(x63,x61,x64),f20(x63,x62,x64))
% 1.14/1.27 [7]~E(x71,x72)+E(f20(x73,x74,x71),f20(x73,x74,x72))
% 1.14/1.27 [8]~E(x81,x82)+E(f14(x81),f14(x82))
% 1.14/1.27 [9]~E(x91,x92)+E(f9(x91,x93,x94),f9(x92,x93,x94))
% 1.14/1.27 [10]~E(x101,x102)+E(f9(x103,x101,x104),f9(x103,x102,x104))
% 1.14/1.27 [11]~E(x111,x112)+E(f9(x113,x114,x111),f9(x113,x114,x112))
% 1.14/1.27 [12]~E(x121,x122)+E(f3(x121),f3(x122))
% 1.14/1.27 [13]~E(x131,x132)+E(f10(x131,x133,x134),f10(x132,x133,x134))
% 1.14/1.27 [14]~E(x141,x142)+E(f10(x143,x141,x144),f10(x143,x142,x144))
% 1.14/1.27 [15]~E(x151,x152)+E(f10(x153,x154,x151),f10(x153,x154,x152))
% 1.14/1.27 [16]~E(x161,x162)+E(f29(x161,x163,x164),f29(x162,x163,x164))
% 1.14/1.27 [17]~E(x171,x172)+E(f29(x173,x171,x174),f29(x173,x172,x174))
% 1.14/1.27 [18]~E(x181,x182)+E(f29(x183,x184,x181),f29(x183,x184,x182))
% 1.14/1.27 [19]~E(x191,x192)+E(f15(x191,x193),f15(x192,x193))
% 1.14/1.27 [20]~E(x201,x202)+E(f15(x203,x201),f15(x203,x202))
% 1.14/1.27 [21]~E(x211,x212)+E(f16(x211),f16(x212))
% 1.14/1.27 [22]~E(x221,x222)+E(f18(x221,x223,x224),f18(x222,x223,x224))
% 1.14/1.27 [23]~E(x231,x232)+E(f18(x233,x231,x234),f18(x233,x232,x234))
% 1.14/1.27 [24]~E(x241,x242)+E(f18(x243,x244,x241),f18(x243,x244,x242))
% 1.14/1.27 [25]~E(x251,x252)+E(f4(x251,x253),f4(x252,x253))
% 1.14/1.27 [26]~E(x261,x262)+E(f4(x263,x261),f4(x263,x262))
% 1.14/1.27 [27]~E(x271,x272)+E(f27(x271,x273,x274),f27(x272,x273,x274))
% 1.14/1.27 [28]~E(x281,x282)+E(f27(x283,x281,x284),f27(x283,x282,x284))
% 1.14/1.27 [29]~E(x291,x292)+E(f27(x293,x294,x291),f27(x293,x294,x292))
% 1.14/1.27 [30]~E(x301,x302)+E(f21(x301,x303),f21(x302,x303))
% 1.14/1.27 [31]~E(x311,x312)+E(f21(x313,x311),f21(x313,x312))
% 1.14/1.27 [32]~E(x321,x322)+E(f19(x321,x323),f19(x322,x323))
% 1.14/1.27 [33]~E(x331,x332)+E(f19(x333,x331),f19(x333,x332))
% 1.14/1.27 [34]~E(x341,x342)+E(f5(x341,x343,x344),f5(x342,x343,x344))
% 1.14/1.27 [35]~E(x351,x352)+E(f5(x353,x351,x354),f5(x353,x352,x354))
% 1.14/1.27 [36]~E(x361,x362)+E(f5(x363,x364,x361),f5(x363,x364,x362))
% 1.14/1.27 [37]~E(x371,x372)+E(f8(x371,x373,x374),f8(x372,x373,x374))
% 1.14/1.27 [38]~E(x381,x382)+E(f8(x383,x381,x384),f8(x383,x382,x384))
% 1.14/1.27 [39]~E(x391,x392)+E(f8(x393,x394,x391),f8(x393,x394,x392))
% 1.14/1.27 [40]~E(x401,x402)+E(f28(x401,x403,x404),f28(x402,x403,x404))
% 1.14/1.27 [41]~E(x411,x412)+E(f28(x413,x411,x414),f28(x413,x412,x414))
% 1.14/1.27 [42]~E(x421,x422)+E(f28(x423,x424,x421),f28(x423,x424,x422))
% 1.14/1.27 [43]~E(x431,x432)+E(f30(x431,x433,x434),f30(x432,x433,x434))
% 1.14/1.27 [44]~E(x441,x442)+E(f30(x443,x441,x444),f30(x443,x442,x444))
% 1.14/1.27 [45]~E(x451,x452)+E(f30(x453,x454,x451),f30(x453,x454,x452))
% 1.14/1.27 [46]~E(x461,x462)+E(f17(x461,x463),f17(x462,x463))
% 1.14/1.27 [47]~E(x471,x472)+E(f17(x473,x471),f17(x473,x472))
% 1.14/1.27 [48]~E(x481,x482)+E(f43(x481,x483),f43(x482,x483))
% 1.14/1.27 [49]~E(x491,x492)+E(f43(x493,x491),f43(x493,x492))
% 1.14/1.27 [50]~E(x501,x502)+E(f32(x501),f32(x502))
% 1.14/1.27 [51]~E(x511,x512)+E(f35(x511),f35(x512))
% 1.14/1.27 [52]~E(x521,x522)+E(f22(x521),f22(x522))
% 1.14/1.27 [53]~E(x531,x532)+E(f7(x531),f7(x532))
% 1.14/1.27 [54]~E(x541,x542)+E(f33(x541),f33(x542))
% 1.14/1.27 [55]~E(x551,x552)+E(f34(x551),f34(x552))
% 1.14/1.27 [56]~E(x561,x562)+E(f38(x561,x563,x564,x565),f38(x562,x563,x564,x565))
% 1.14/1.27 [57]~E(x571,x572)+E(f38(x573,x571,x574,x575),f38(x573,x572,x574,x575))
% 1.14/1.27 [58]~E(x581,x582)+E(f38(x583,x584,x581,x585),f38(x583,x584,x582,x585))
% 1.14/1.27 [59]~E(x591,x592)+E(f38(x593,x594,x595,x591),f38(x593,x594,x595,x592))
% 1.14/1.27 [60]~E(x601,x602)+E(f36(x601,x603),f36(x602,x603))
% 1.14/1.27 [61]~E(x611,x612)+E(f36(x613,x611),f36(x613,x612))
% 1.14/1.27 [62]~E(x621,x622)+E(f24(x621,x623),f24(x622,x623))
% 1.14/1.27 [63]~E(x631,x632)+E(f24(x633,x631),f24(x633,x632))
% 1.14/1.27 [64]~E(x641,x642)+E(f37(x641,x643),f37(x642,x643))
% 1.14/1.27 [65]~E(x651,x652)+E(f37(x653,x651),f37(x653,x652))
% 1.14/1.27 [66]~E(x661,x662)+E(f31(x661,x663),f31(x662,x663))
% 1.14/1.27 [67]~E(x671,x672)+E(f31(x673,x671),f31(x673,x672))
% 1.14/1.27 [68]~E(x681,x682)+E(f26(x681),f26(x682))
% 1.14/1.27 [69]~E(x691,x692)+E(f23(x691,x693),f23(x692,x693))
% 1.14/1.27 [70]~E(x701,x702)+E(f23(x703,x701),f23(x703,x702))
% 1.14/1.27 [71]~P1(x711)+P1(x712)+~E(x711,x712)
% 1.14/1.27 [72]P12(x722,x723,x724)+~E(x721,x722)+~P12(x721,x723,x724)
% 1.14/1.27 [73]P12(x733,x732,x734)+~E(x731,x732)+~P12(x733,x731,x734)
% 1.14/1.27 [74]P12(x743,x744,x742)+~E(x741,x742)+~P12(x743,x744,x741)
% 1.14/1.27 [75]P10(x752,x753)+~E(x751,x752)+~P10(x751,x753)
% 1.14/1.27 [76]P10(x763,x762)+~E(x761,x762)+~P10(x763,x761)
% 1.14/1.28 [77]~P27(x771)+P27(x772)+~E(x771,x772)
% 1.14/1.28 [78]P11(x782,x783,x784)+~E(x781,x782)+~P11(x781,x783,x784)
% 1.14/1.28 [79]P11(x793,x792,x794)+~E(x791,x792)+~P11(x793,x791,x794)
% 1.14/1.28 [80]P11(x803,x804,x802)+~E(x801,x802)+~P11(x803,x804,x801)
% 1.14/1.28 [81]~P14(x811)+P14(x812)+~E(x811,x812)
% 1.14/1.28 [82]~P2(x821)+P2(x822)+~E(x821,x822)
% 1.14/1.28 [83]~P20(x831)+P20(x832)+~E(x831,x832)
% 1.14/1.28 [84]~P8(x841)+P8(x842)+~E(x841,x842)
% 1.14/1.28 [85]~P50(x851)+P50(x852)+~E(x851,x852)
% 1.14/1.28 [86]~P3(x861)+P3(x862)+~E(x861,x862)
% 1.14/1.28 [87]~P7(x871)+P7(x872)+~E(x871,x872)
% 1.14/1.28 [88]~P35(x881)+P35(x882)+~E(x881,x882)
% 1.14/1.28 [89]~P44(x891)+P44(x892)+~E(x891,x892)
% 1.14/1.28 [90]~P28(x901)+P28(x902)+~E(x901,x902)
% 1.14/1.28 [91]~P48(x911)+P48(x912)+~E(x911,x912)
% 1.14/1.28 [92]~P67(x921)+P67(x922)+~E(x921,x922)
% 1.14/1.28 [93]P68(x932,x933,x934)+~E(x931,x932)+~P68(x931,x933,x934)
% 1.14/1.28 [94]P68(x943,x942,x944)+~E(x941,x942)+~P68(x943,x941,x944)
% 1.14/1.28 [95]P68(x953,x954,x952)+~E(x951,x952)+~P68(x953,x954,x951)
% 1.14/1.28 [96]~P55(x961)+P55(x962)+~E(x961,x962)
% 1.14/1.28 [97]~P51(x971)+P51(x972)+~E(x971,x972)
% 1.14/1.28 [98]~P13(x981)+P13(x982)+~E(x981,x982)
% 1.14/1.28 [99]~P29(x991)+P29(x992)+~E(x991,x992)
% 1.14/1.28 [100]~P37(x1001)+P37(x1002)+~E(x1001,x1002)
% 1.14/1.28 [101]~P62(x1011)+P62(x1012)+~E(x1011,x1012)
% 1.14/1.28 [102]~P34(x1021)+P34(x1022)+~E(x1021,x1022)
% 1.14/1.28 [103]~P9(x1031)+P9(x1032)+~E(x1031,x1032)
% 1.14/1.28 [104]~P53(x1041)+P53(x1042)+~E(x1041,x1042)
% 1.14/1.28 [105]~P30(x1051)+P30(x1052)+~E(x1051,x1052)
% 1.14/1.28 [106]~P18(x1061)+P18(x1062)+~E(x1061,x1062)
% 1.14/1.28 [107]~P21(x1071)+P21(x1072)+~E(x1071,x1072)
% 1.14/1.28 [108]~P49(x1081)+P49(x1082)+~E(x1081,x1082)
% 1.14/1.28 [109]~P43(x1091)+P43(x1092)+~E(x1091,x1092)
% 1.14/1.28 [110]~P38(x1101)+P38(x1102)+~E(x1101,x1102)
% 1.14/1.28 [111]~P63(x1111)+P63(x1112)+~E(x1111,x1112)
% 1.14/1.28 [112]~P33(x1121)+P33(x1122)+~E(x1121,x1122)
% 1.14/1.28 [113]~P46(x1131)+P46(x1132)+~E(x1131,x1132)
% 1.14/1.28 [114]~P17(x1141)+P17(x1142)+~E(x1141,x1142)
% 1.14/1.28 [115]~P56(x1151)+P56(x1152)+~E(x1151,x1152)
% 1.14/1.28 [116]~P31(x1161)+P31(x1162)+~E(x1161,x1162)
% 1.14/1.28 [117]~P23(x1171)+P23(x1172)+~E(x1171,x1172)
% 1.14/1.28 [118]~P57(x1181)+P57(x1182)+~E(x1181,x1182)
% 1.14/1.28 [119]~P47(x1191)+P47(x1192)+~E(x1191,x1192)
% 1.14/1.28 [120]~P4(x1201)+P4(x1202)+~E(x1201,x1202)
% 1.14/1.28 [121]~P60(x1211)+P60(x1212)+~E(x1211,x1212)
% 1.14/1.28 [122]~P42(x1221)+P42(x1222)+~E(x1221,x1222)
% 1.14/1.28 [123]~P66(x1231)+P66(x1232)+~E(x1231,x1232)
% 1.14/1.28 [124]~P64(x1241)+P64(x1242)+~E(x1241,x1242)
% 1.14/1.28 [125]~P16(x1251)+P16(x1252)+~E(x1251,x1252)
% 1.14/1.28 [126]~P22(x1261)+P22(x1262)+~E(x1261,x1262)
% 1.14/1.28 [127]~P36(x1271)+P36(x1272)+~E(x1271,x1272)
% 1.14/1.28 [128]~P41(x1281)+P41(x1282)+~E(x1281,x1282)
% 1.14/1.28 [129]~P58(x1291)+P58(x1292)+~E(x1291,x1292)
% 1.14/1.28 [130]~P15(x1301)+P15(x1302)+~E(x1301,x1302)
% 1.14/1.28 [131]~P61(x1311)+P61(x1312)+~E(x1311,x1312)
% 1.14/1.28 [132]~P32(x1321)+P32(x1322)+~E(x1321,x1322)
% 1.14/1.28 [133]~P40(x1331)+P40(x1332)+~E(x1331,x1332)
% 1.14/1.28 [134]~P54(x1341)+P54(x1342)+~E(x1341,x1342)
% 1.14/1.28 [135]~P5(x1351)+P5(x1352)+~E(x1351,x1352)
% 1.14/1.28 [136]~P59(x1361)+P59(x1362)+~E(x1361,x1362)
% 1.14/1.28 [137]~P25(x1371)+P25(x1372)+~E(x1371,x1372)
% 1.14/1.28 [138]~P26(x1381)+P26(x1382)+~E(x1381,x1382)
% 1.14/1.28 [139]~P65(x1391)+P65(x1392)+~E(x1391,x1392)
% 1.14/1.28 [140]~P24(x1401)+P24(x1402)+~E(x1401,x1402)
% 1.14/1.28 [141]~P52(x1411)+P52(x1412)+~E(x1411,x1412)
% 1.14/1.28 [142]~P6(x1421)+P6(x1422)+~E(x1421,x1422)
% 1.14/1.28 [143]~P19(x1431)+P19(x1432)+~E(x1431,x1432)
% 1.14/1.28 [144]~P45(x1441)+P45(x1442)+~E(x1441,x1442)
% 1.14/1.28 [145]~P39(x1451)+P39(x1452)+~E(x1451,x1452)
% 1.14/1.28
% 1.14/1.28 %-------------------------------------------
% 1.14/1.28 cnf(1884,plain,
% 1.14/1.28 ($false),
% 1.14/1.28 inference(scs_inference,[],[483,516,1831]),
% 1.14/1.28 ['proof']).
% 1.14/1.28 % SZS output end Proof
% 1.14/1.28 % Total time :0.090000s
%------------------------------------------------------------------------------