TSTP Solution File: SWW196+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW196+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 : n018.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 00:13:04 EDT 2023
% Result : Theorem 1.03s 1.22s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW196+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 22:19:46 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.99/1.14 %-------------------------------------------
% 0.99/1.14 % File :CSE---1.6
% 0.99/1.14 % Problem :theBenchmark
% 0.99/1.14 % Transform :cnf
% 0.99/1.14 % Format :tptp:raw
% 0.99/1.14 % Command :java -jar mcs_scs.jar %d %s
% 0.99/1.14
% 0.99/1.14 % Result :Theorem 0.080000s
% 0.99/1.14 % Output :CNFRefutation 0.080000s
% 0.99/1.14 %-------------------------------------------
% 0.99/1.14 %------------------------------------------------------------------------------
% 0.99/1.14 % File : SWW196+1 : TPTP v8.1.2. Released v5.2.0.
% 0.99/1.14 % Domain : Software Verification
% 0.99/1.14 % Problem : Fundamental Theorem of Algebra 436457, 1000 axioms selected
% 0.99/1.14 % Version : Especial.
% 0.99/1.14 % English :
% 0.99/1.14
% 0.99/1.14 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.99/1.14 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.99/1.14 % Source : [Bla11]
% 0.99/1.14 % Names : fta_436457.1000.p [Bla11]
% 0.99/1.14
% 0.99/1.14 % Status : Theorem
% 0.99/1.14 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 0.13 v7.3.0, 0.17 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.30 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0, 0.48 v5.2.0
% 0.99/1.15 % Syntax : Number of formulae : 1172 ( 371 unt; 0 def)
% 0.99/1.15 % Number of atoms : 2753 ( 716 equ)
% 0.99/1.15 % Maximal formula atoms : 13 ( 2 avg)
% 0.99/1.15 % Number of connectives : 1791 ( 210 ~; 66 |; 164 &)
% 0.99/1.15 % ( 277 <=>;1074 =>; 0 <=; 0 <~>)
% 0.99/1.15 % Maximal formula depth : 13 ( 5 avg)
% 0.99/1.15 % Maximal term depth : 7 ( 1 avg)
% 0.99/1.15 % Number of predicates : 64 ( 63 usr; 1 prp; 0-3 aty)
% 0.99/1.15 % Number of functors : 22 ( 22 usr; 8 con; 0-3 aty)
% 0.99/1.15 % Number of variables : 2477 (2460 !; 17 ?)
% 0.99/1.15 % SPC : FOF_THM_RFO_SEQ
% 0.99/1.15
% 0.99/1.15 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.99/1.15 % 2011-03-01 11:24:47
% 0.99/1.15 %------------------------------------------------------------------------------
% 0.99/1.15 %----Relevant facts (992)
% 0.99/1.15 fof(fact__096EX_Am_O_An_A_061_A2_A_K_Am_096,axiom,
% 0.99/1.15 ? [B_m] : v_na____ = 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) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_n,axiom,
% 0.99/1.15 v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_e,axiom,
% 0.99/1.15 c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_assms_I2_J,axiom,
% 0.99/1.15 v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__numeral__1__right,axiom,
% 0.99/1.15 ! [V_a,T_a] :
% 0.99/1.15 ( class_Int_Onumber__ring(T_a)
% 0.99/1.15 => 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 ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__numeral__1,axiom,
% 0.99/1.15 ! [V_a,T_a] :
% 0.99/1.15 ( class_Int_Onumber__ring(T_a)
% 0.99/1.15 => 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 ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_Bit0__Pls,axiom,
% 0.99/1.15 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 0.99/1.15
% 0.99/1.15 fof(fact_rel__simps_I38_J,axiom,
% 0.99/1.15 ! [V_l_2] :
% 0.99/1.15 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 0.99/1.15 <=> c_Int_OPls = V_l_2 ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_rel__simps_I44_J,axiom,
% 0.99/1.15 ! [V_k_2] :
% 0.99/1.15 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 0.99/1.15 <=> V_k_2 = c_Int_OPls ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_rel__simps_I49_J,axiom,
% 0.99/1.15 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_rel__simps_I50_J,axiom,
% 0.99/1.15 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_rel__simps_I39_J,axiom,
% 0.99/1.15 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_rel__simps_I46_J,axiom,
% 0.99/1.15 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 0.99/1.15
% 0.99/1.15 fof(fact_number__of__mult,axiom,
% 0.99/1.15 ! [V_w,V_v,T_a] :
% 0.99/1.15 ( class_Int_Onumber__ring(T_a)
% 0.99/1.15 => 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)) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_arith__simps_I32_J,axiom,
% 0.99/1.15 ! [V_w,V_v,T_a] :
% 0.99/1.15 ( class_Int_Onumber__ring(T_a)
% 0.99/1.15 => 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)) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_zmult__commute,axiom,
% 0.99/1.15 ! [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) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_times__numeral__code_I5_J,axiom,
% 0.99/1.15 ! [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)) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_zmult__assoc,axiom,
% 0.99/1.15 ! [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)) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__Pls,axiom,
% 0.99/1.15 ! [V_w] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,V_w) = c_Int_OPls ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__Bit0,axiom,
% 0.99/1.15 ! [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)) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_number__of__Pls,axiom,
% 0.99/1.15 ! [T_a] :
% 0.99/1.15 ( class_Int_Onumber__ring(T_a)
% 0.99/1.15 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_eq__number__of,axiom,
% 0.99/1.15 ! [V_y_2,V_x_2,T_a] :
% 0.99/1.15 ( ( class_Int_Onumber__ring(T_a)
% 0.99/1.15 & class_Int_Oring__char__0(T_a) )
% 0.99/1.15 => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
% 0.99/1.15 <=> V_x_2 = V_y_2 ) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_number__of__reorient,axiom,
% 0.99/1.15 ! [V_x_2,V_w_2,T_a] :
% 0.99/1.15 ( class_Int_Onumber(T_a)
% 0.99/1.15 => ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = V_x_2
% 0.99/1.15 <=> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_w_2) ) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_rel__simps_I51_J,axiom,
% 0.99/1.15 ! [V_l_2,V_k_2] :
% 0.99/1.15 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 0.99/1.15 <=> V_k_2 = V_l_2 ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_rel__simps_I48_J,axiom,
% 0.99/1.15 ! [V_l_2,V_k_2] :
% 0.99/1.15 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 0.99/1.15 <=> V_k_2 = V_l_2 ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__number__of__left,axiom,
% 0.99/1.15 ! [V_z,V_w,V_v,T_a] :
% 0.99/1.15 ( class_Int_Onumber__ring(T_a)
% 0.99/1.15 => 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) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_even__mult__two__ex,axiom,
% 0.99/1.15 ! [V_nb_2] :
% 0.99/1.15 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 0.99/1.15 <=> ? [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) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_nat__number__of__Pls,axiom,
% 0.99/1.15 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_semiring__norm_I113_J,axiom,
% 0.99/1.15 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_semiring__norm_I112_J,axiom,
% 0.99/1.15 ! [T_a] :
% 0.99/1.15 ( class_Int_Onumber__ring(T_a)
% 0.99/1.15 => c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_even__product__nat,axiom,
% 0.99/1.15 ! [V_y_2,V_x_2] :
% 0.99/1.15 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_x_2,V_y_2))
% 0.99/1.15 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 0.99/1.15 | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_y_2) ) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_even__zero__nat,axiom,
% 0.99/1.15 c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__cancel2,axiom,
% 0.99/1.15 ! [V_nb_2,V_k_2,V_m_2] :
% 0.99/1.15 ( 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)
% 0.99/1.15 <=> ( V_m_2 = V_nb_2
% 0.99/1.15 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__cancel1,axiom,
% 0.99/1.15 ! [V_nb_2,V_m_2,V_k_2] :
% 0.99/1.15 ( 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)
% 0.99/1.15 <=> ( V_m_2 = V_nb_2
% 0.99/1.15 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 0.99/1.15 ! [V_nb_2,V_m_2,V_k_2] :
% 0.99/1.15 ( 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)
% 0.99/1.15 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.99/1.15 | V_m_2 = V_nb_2 ) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__is__0,axiom,
% 0.99/1.15 ! [V_nb_2,V_m_2] :
% 0.99/1.15 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.99/1.15 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.99/1.15 | V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__0__right,axiom,
% 0.99/1.15 ! [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) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__0,axiom,
% 0.99/1.15 ! [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) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_number__of__is__id,axiom,
% 0.99/1.15 ! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k ).
% 0.99/1.15
% 0.99/1.15 fof(fact_Pls__def,axiom,
% 0.99/1.15 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_zero__is__num__zero,axiom,
% 0.99/1.15 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_nat__mult__commute,axiom,
% 0.99/1.15 ! [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) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_nat__mult__assoc,axiom,
% 0.99/1.15 ! [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)) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult__zero__left,axiom,
% 0.99/1.15 ! [V_a,T_a] :
% 0.99/1.15 ( class_Rings_Omult__zero(T_a)
% 0.99/1.15 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 0.99/1.15 ! [V_a,T_a] :
% 0.99/1.15 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.15 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.15
% 0.99/1.15 fof(fact_mult_Ozero__left,axiom,
% 0.99/1.16 ! [V_b,T_a] :
% 0.99/1.16 ( class_RealVector_Oreal__normed__algebra(T_a)
% 0.99/1.16 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_mult__left_Ozero,axiom,
% 0.99/1.16 ! [V_y,T_a] :
% 0.99/1.16 ( class_RealVector_Oreal__normed__algebra(T_a)
% 0.99/1.16 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_mult__zero__right,axiom,
% 0.99/1.16 ! [V_a,T_a] :
% 0.99/1.16 ( class_Rings_Omult__zero(T_a)
% 0.99/1.16 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 0.99/1.16 ! [V_a,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_mult_Ozero__right,axiom,
% 0.99/1.16 ! [V_a,T_a] :
% 0.99/1.16 ( class_RealVector_Oreal__normed__algebra(T_a)
% 0.99/1.16 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_mult__right_Ozero,axiom,
% 0.99/1.16 ! [V_x,T_a] :
% 0.99/1.16 ( class_RealVector_Oreal__normed__algebra(T_a)
% 0.99/1.16 => c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_mult__eq__0__iff,axiom,
% 0.99/1.16 ! [V_ba_2,V_a_2,T_a] :
% 0.99/1.16 ( class_Rings_Oring__no__zero__divisors(T_a)
% 0.99/1.16 => ( c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_ba_2) = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.16 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.16 | V_ba_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_no__zero__divisors,axiom,
% 0.99/1.16 ! [V_b,V_a,T_a] :
% 0.99/1.16 ( class_Rings_Ono__zero__divisors(T_a)
% 0.99/1.16 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.16 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.16 => c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_divisors__zero,axiom,
% 0.99/1.16 ! [V_b,V_a,T_a] :
% 0.99/1.16 ( class_Rings_Ono__zero__divisors(T_a)
% 0.99/1.16 => ( c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.16 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 0.99/1.16 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.99/1.16 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => 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)) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.99/1.16 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => 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)) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.99/1.16 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => 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))) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.99/1.16 ! [V_rx,V_ly,V_lx,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => 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) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.99/1.16 ! [V_rx,V_ly,V_lx,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => 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)) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.99/1.16 ! [V_ry,V_rx,V_lx,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => 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) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.99/1.16 ! [V_ry,V_rx,V_lx,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => 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)) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.99/1.16 ! [V_b,V_a,T_a] :
% 0.99/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.99/1.16 => c_Groups_Otimes__class_Otimes(T_a,V_a,V_b) = c_Groups_Otimes__class_Otimes(T_a,V_b,V_a) ) ).
% 0.99/1.16
% 0.99/1.16 fof(fact_odd__Suc__mult__two__ex,axiom,
% 0.99/1.16 ! [V_nb_2] :
% 0.99/1.16 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.16 <=> ? [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)) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 1.03/1.16 ! [V_n,V_x,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => 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)) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_power2__eq__square__number__of,axiom,
% 1.03/1.16 ! [V_w,T_b] :
% 1.03/1.16 ( ( class_Groups_Omonoid__mult(T_b)
% 1.03/1.16 & class_Int_Onumber(T_b) )
% 1.03/1.16 => 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)) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_even__equiv__def,axiom,
% 1.03/1.16 ! [V_x_2] :
% 1.03/1.16 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.16 <=> ? [B_y] : V_x_2 = 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))),B_y) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_nat__number__of__mult__left,axiom,
% 1.03/1.16 ! [V_k,V_v_H,V_v] :
% 1.03/1.16 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.03/1.16 => 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) )
% 1.03/1.16 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.03/1.16 => 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) ) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_mult__nat__number__of,axiom,
% 1.03/1.16 ! [V_v_H,V_v] :
% 1.03/1.16 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.03/1.16 => 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) )
% 1.03/1.16 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.03/1.16 => 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)) ) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_nat__mult__2,axiom,
% 1.03/1.16 ! [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) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_nat__mult__2__right,axiom,
% 1.03/1.16 ! [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) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_not__iszero__Numeral1,axiom,
% 1.03/1.16 ! [T_a] :
% 1.03/1.16 ( class_Int_Onumber__ring(T_a)
% 1.03/1.16 => ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_nat__even__iff__2__dvd,axiom,
% 1.03/1.16 ! [V_x_2] :
% 1.03/1.16 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.16 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_x_2) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_numeral__2__eq__2,axiom,
% 1.03/1.16 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_dvd_Oorder__refl,axiom,
% 1.03/1.16 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_dvd__0__right,axiom,
% 1.03/1.16 ! [V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_dvd__1__left,axiom,
% 1.03/1.16 ! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_pos__add__strict,axiom,
% 1.03/1.16 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.16 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.16 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.03/1.16 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_dvd__refl,axiom,
% 1.03/1.16 ! [V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_a) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 1.03/1.16 ! [V_c,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 1.03/1.16 ! [V_d,V_c,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 1.03/1.16 ! [V_d,V_c,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 1.03/1.16 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => 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)) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 1.03/1.16 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 1.03/1.16 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_linorder__neqE__linordered__idom,axiom,
% 1.03/1.16 ! [V_y,V_x,T_a] :
% 1.03/1.16 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.16 => ( V_x != V_y
% 1.03/1.16 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.03/1.16 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_dvd__trans,axiom,
% 1.03/1.16 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.03/1.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
% 1.03/1.16 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_dvd__add,axiom,
% 1.03/1.16 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.03/1.16 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 1.03/1.16 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ) ).
% 1.03/1.16
% 1.03/1.16 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 1.03/1.16 ! [V_q,V_x,T_a] :
% 1.03/1.16 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.16 => 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)) ) ).
% 1.03/1.16
% 1.03/1.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 1.03/1.17 ! [V_q,V_x,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => 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)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 1.03/1.17 ! [V_q,V_x,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => 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)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_even__less__0__iff,axiom,
% 1.03/1.17 ! [V_a_2,T_a] :
% 1.03/1.17 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.17 => ( 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))
% 1.03/1.17 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_zless__linear,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 1.03/1.17 | V_x = V_y
% 1.03/1.17 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_n__not__Suc__n,axiom,
% 1.03/1.17 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_Suc__n__not__n,axiom,
% 1.03/1.17 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 1.03/1.17
% 1.03/1.17 fof(fact_nat__add__commute,axiom,
% 1.03/1.17 ! [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) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oeq__iff,axiom,
% 1.03/1.17 ! [V_y_2,V_x_2] :
% 1.03/1.17 ( V_x_2 = V_y_2
% 1.03/1.17 <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 1.03/1.17 & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Ole__less,axiom,
% 1.03/1.17 ! [V_y_2,V_x_2] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 1.03/1.17 <=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) )
% 1.03/1.17 | V_x_2 = V_y_2 ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_add__Suc__right,axiom,
% 1.03/1.17 ! [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)) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__reduce,axiom,
% 1.03/1.17 ! [V_nb_2,V_k_2] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2))
% 1.03/1.17 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_nb_2) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_nat__add__left__commute,axiom,
% 1.03/1.17 ! [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)) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_add__Suc,axiom,
% 1.03/1.17 ! [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)) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_add__Suc__shift,axiom,
% 1.03/1.17 ! [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)) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_nat_Oinject,axiom,
% 1.03/1.17 ! [V_nat_H_2,V_nat_2] :
% 1.03/1.17 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 1.03/1.17 <=> V_nat_2 = V_nat_H_2 ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_nat__add__assoc,axiom,
% 1.03/1.17 ! [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)) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__le,axiom,
% 1.03/1.17 ! [V_y_2,V_x_2] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) )
% 1.03/1.17 <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 1.03/1.17 & V_x_2 != V_y_2 ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_nat__add__left__cancel,axiom,
% 1.03/1.17 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.17 ( 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)
% 1.03/1.17 <=> V_m_2 = V_nb_2 ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_nat__add__right__cancel,axiom,
% 1.03/1.17 ! [V_nb_2,V_k_2,V_m_2] :
% 1.03/1.17 ( 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)
% 1.03/1.17 <=> V_m_2 = V_nb_2 ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oneq__le__trans,axiom,
% 1.03/1.17 ! [V_b,V_a] :
% 1.03/1.17 ( V_a != V_b
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oeq__refl,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( V_x = V_y
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oantisym__conv,axiom,
% 1.03/1.17 ! [V_x_2,V_y_2] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 1.03/1.17 <=> V_x_2 = V_y_2 ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 | V_x = V_y ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Ole__neq__trans,axiom,
% 1.03/1.17 ! [V_b,V_a] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 1.03/1.17 => ( V_a != V_b
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 1.03/1.17 ! [V_c,V_b,V_a] :
% 1.03/1.17 ( V_a = V_b
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 1.03/1.17 ! [V_c,V_b,V_a] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 1.03/1.17 => ( V_b = V_c
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__antisym,axiom,
% 1.03/1.17 ! [V_n,V_m] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)
% 1.03/1.17 => V_m = V_n ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oantisym,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 1.03/1.17 => V_x = V_y ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oorder__trans,axiom,
% 1.03/1.17 ! [V_z,V_y,V_x] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 1.03/1.17 ! [V_c,V_b,V_a] :
% 1.03/1.17 ( V_a = V_b
% 1.03/1.17 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b) )
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Ole__less__trans,axiom,
% 1.03/1.17 ! [V_z,V_y,V_x] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) )
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_Suc__inject,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 1.03/1.17 => V_x = V_y ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__imp__neq,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => V_x != V_y ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__not__sym,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__imp__le,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__imp__not__less,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => V_x != V_y ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => V_y != V_x ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 1.03/1.17 ! [V_c,V_b,V_a] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) )
% 1.03/1.17 => ( V_b = V_c
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__le__trans,axiom,
% 1.03/1.17 ! [V_z,V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__asym_H,axiom,
% 1.03/1.17 ! [V_b,V_a] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) )
% 1.03/1.17 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__trans,axiom,
% 1.03/1.17 ! [V_z,V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) )
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd_Oless__asym,axiom,
% 1.03/1.17 ! [V_y,V_x] :
% 1.03/1.17 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 1.03/1.17 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 1.03/1.17 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_odd__pow,axiom,
% 1.03/1.17 ! [V_n,V_x] :
% 1.03/1.17 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x)
% 1.03/1.17 => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 1.03/1.17 ! [V_q,V_p,V_x,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => 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)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_add__number__of__left,axiom,
% 1.03/1.17 ! [V_z,V_w,V_v,T_a] :
% 1.03/1.17 ( class_Int_Onumber__ring(T_a)
% 1.03/1.17 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_add__number__of__eq,axiom,
% 1.03/1.17 ! [V_w,V_v,T_a] :
% 1.03/1.17 ( class_Int_Onumber__ring(T_a)
% 1.03/1.17 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_number__of__add,axiom,
% 1.03/1.17 ! [V_w,V_v,T_a] :
% 1.03/1.17 ( class_Int_Onumber__ring(T_a)
% 1.03/1.17 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__1__iff__1,axiom,
% 1.03/1.17 ! [V_m_2] :
% 1.03/1.17 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 1.03/1.17 <=> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_less__number__of,axiom,
% 1.03/1.17 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.17 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.17 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.17 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.03/1.17 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_one__is__add,axiom,
% 1.03/1.17 ! [V_nb_2,V_m_2] :
% 1.03/1.17 ( 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)
% 1.03/1.17 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.03/1.17 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.03/1.17 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.17 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_add__is__1,axiom,
% 1.03/1.17 ! [V_nb_2,V_m_2] :
% 1.03/1.17 ( 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))
% 1.03/1.17 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.03/1.17 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.03/1.17 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.17 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_zpower__zadd__distrib,axiom,
% 1.03/1.17 ! [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)) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_mult__Suc__right,axiom,
% 1.03/1.17 ! [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)) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_mult__Suc,axiom,
% 1.03/1.17 ! [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)) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_even__power,axiom,
% 1.03/1.17 ! [V_nb_2,V_x_2] :
% 1.03/1.17 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x_2,V_nb_2))
% 1.03/1.17 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.17 & V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_sum__squares__gt__zero__iff,axiom,
% 1.03/1.17 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.17 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.17 => ( 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)))
% 1.03/1.17 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.17 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_not__sum__squares__lt__zero,axiom,
% 1.03/1.17 ! [V_y,V_x,T_a] :
% 1.03/1.17 ( class_Rings_Olinordered__ring(T_a)
% 1.03/1.17 => ~ 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)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_power__less__zero__eq,axiom,
% 1.03/1.17 ! [V_nb_2,V_x_2,T_a] :
% 1.03/1.17 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.17 => ( 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))
% 1.03/1.17 <=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.17 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__0__left,axiom,
% 1.03/1.17 ! [V_a,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.17 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__triv__left,axiom,
% 1.03/1.17 ! [V_b,V_a,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__triv__right,axiom,
% 1.03/1.17 ! [V_b,V_a,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__mult2,axiom,
% 1.03/1.17 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__mult,axiom,
% 1.03/1.17 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_mult__dvd__mono,axiom,
% 1.03/1.17 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.17 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.03/1.17 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)) ) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvdI,axiom,
% 1.03/1.17 ! [V_k,V_b,V_a,T_a] :
% 1.03/1.17 ( class_Rings_Odvd(T_a)
% 1.03/1.17 => ( V_a = c_Groups_Otimes__class_Otimes(T_a,V_b,V_k)
% 1.03/1.17 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_a) ) ) ).
% 1.03/1.17
% 1.03/1.17 fof(fact_dvd__mult__left,axiom,
% 1.03/1.17 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)
% 1.03/1.18 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_dvd__mult__right,axiom,
% 1.03/1.18 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)
% 1.03/1.18 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 1.03/1.18 ! [V_q,V_y,V_x,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_double__eq__0__iff,axiom,
% 1.03/1.18 ! [V_a_2,T_a] :
% 1.03/1.18 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.03/1.18 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.18 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_add__0__iff,axiom,
% 1.03/1.18 ! [V_a_2,V_ba_2,T_a] :
% 1.03/1.18 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.03/1.18 => ( V_ba_2 = c_Groups_Oplus__class_Oplus(T_a,V_ba_2,V_a_2)
% 1.03/1.18 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 1.03/1.18 ! [V_a,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 1.03/1.18 ! [V_a,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult_Oadd__right,axiom,
% 1.03/1.18 ! [V_b_H,V_b,V_a,T_a] :
% 1.03/1.18 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 1.03/1.18 ! [V_z,V_y,V_x,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__right_Oadd,axiom,
% 1.03/1.18 ! [V_y,V_x,V_xa,T_a] :
% 1.03/1.18 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_crossproduct__noteq,axiom,
% 1.03/1.18 ! [V_d_2,V_c_2,V_ba_2,V_a_2,T_a] :
% 1.03/1.18 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.03/1.18 => ( ( V_a_2 != V_ba_2
% 1.03/1.18 & V_c_2 != V_d_2 )
% 1.03/1.18 <=> 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)) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__semiring__class_Odistrib,axiom,
% 1.03/1.18 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 1.03/1.18 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult_Oadd__left,axiom,
% 1.03/1.18 ! [V_b,V_a_H,V_a,T_a] :
% 1.03/1.18 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__left_Oadd,axiom,
% 1.03/1.18 ! [V_ya,V_y,V_x,T_a] :
% 1.03/1.18 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 1.03/1.18 ! [V_b,V_m,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => 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) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_combine__common__factor,axiom,
% 1.03/1.18 ! [V_c,V_b,V_e,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Osemiring(T_a)
% 1.03/1.18 => 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) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_crossproduct__eq,axiom,
% 1.03/1.18 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 1.03/1.18 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.03/1.18 => ( 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))
% 1.03/1.18 <=> ( V_w_2 = V_x_2
% 1.03/1.18 | V_y_2 = V_z_2 ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_Suc__neq__Zero,axiom,
% 1.03/1.18 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_Zero__neq__Suc,axiom,
% 1.03/1.18 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_nat_Osimps_I3_J,axiom,
% 1.03/1.18 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_Suc__not__Zero,axiom,
% 1.03/1.18 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_nat_Osimps_I2_J,axiom,
% 1.03/1.18 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_Zero__not__Suc,axiom,
% 1.03/1.18 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 1.03/1.18 ! [V_q,V_p,V_x,T_a] :
% 1.03/1.18 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_zpower__zpower,axiom,
% 1.03/1.18 ! [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)) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_add__eq__self__zero,axiom,
% 1.03/1.18 ! [V_n,V_m] :
% 1.03/1.18 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 1.03/1.18 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_add__is__0,axiom,
% 1.03/1.18 ! [V_nb_2,V_m_2] :
% 1.03/1.18 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.18 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.18 & V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_Nat_Oadd__0__right,axiom,
% 1.03/1.18 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.03/1.18
% 1.03/1.18 fof(fact_plus__nat_Oadd__0,axiom,
% 1.03/1.18 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 1.03/1.18
% 1.03/1.18 fof(fact_rel__simps_I17_J,axiom,
% 1.03/1.18 ! [V_l_2,V_k_2] :
% 1.03/1.18 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_less__int__code_I16_J,axiom,
% 1.03/1.18 ! [V_k2_2,V_k1_2] :
% 1.03/1.18 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_rel__simps_I2_J,axiom,
% 1.03/1.18 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_rel__simps_I14_J,axiom,
% 1.03/1.18 ! [V_l_2,V_k_2] :
% 1.03/1.18 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_less__int__code_I13_J,axiom,
% 1.03/1.18 ! [V_k2_2,V_k1_2] :
% 1.03/1.18 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_Suc__mult__cancel1,axiom,
% 1.03/1.18 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.18 ( 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)
% 1.03/1.18 <=> V_m_2 = V_nb_2 ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_add__mult__distrib2,axiom,
% 1.03/1.18 ! [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)) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_add__mult__distrib,axiom,
% 1.03/1.18 ! [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)) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_left__add__mult__distrib,axiom,
% 1.03/1.18 ! [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) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_less__number__of__int__code,axiom,
% 1.03/1.18 ! [V_l_2,V_k_2] :
% 1.03/1.18 ( 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))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_even__Suc,axiom,
% 1.03/1.18 ! [V_x_2] :
% 1.03/1.18 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(V_x_2))
% 1.03/1.18 <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_even__sum__nat,axiom,
% 1.03/1.18 ! [V_y_2,V_x_2] :
% 1.03/1.18 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x_2,V_y_2))
% 1.03/1.18 <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.18 & c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_y_2) )
% 1.03/1.18 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.18 & ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_y_2) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_even__add,axiom,
% 1.03/1.18 ! [V_nb_2,V_m_2] :
% 1.03/1.18 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2))
% 1.03/1.18 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_m_2)
% 1.03/1.18 <=> c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_odd__add,axiom,
% 1.03/1.18 ! [V_nb_2,V_m_2] :
% 1.03/1.18 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2))
% 1.03/1.18 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_m_2)
% 1.03/1.18 <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_even__zero__int,axiom,
% 1.03/1.18 c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_odd__times__odd,axiom,
% 1.03/1.18 ! [V_y,V_x] :
% 1.03/1.18 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x)
% 1.03/1.18 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y)
% 1.03/1.18 => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_anything__times__even,axiom,
% 1.03/1.18 ! [V_x,V_y] :
% 1.03/1.18 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y)
% 1.03/1.18 => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x,V_y)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_even__times__anything,axiom,
% 1.03/1.18 ! [V_y,V_x] :
% 1.03/1.18 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x)
% 1.03/1.18 => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x,V_y)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_even__product,axiom,
% 1.03/1.18 ! [V_y_2,V_x_2] :
% 1.03/1.18 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x_2,V_y_2))
% 1.03/1.18 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.18 | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y_2) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_less__special_I1_J,axiom,
% 1.03/1.18 ! [V_y_2,T_a] :
% 1.03/1.18 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.18 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.18 => ( 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))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_less__special_I3_J,axiom,
% 1.03/1.18 ! [V_x_2,T_a] :
% 1.03/1.18 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.18 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.18 => ( 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))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_zero__less__power__eq,axiom,
% 1.03/1.18 ! [V_nb_2,V_x_2,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.18 => ( 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))
% 1.03/1.18 <=> ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.18 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.18 & V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
% 1.03/1.18 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.18 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_power__less__zero__eq__number__of,axiom,
% 1.03/1.18 ! [V_w_2,V_x_2,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.18 => ( 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))
% 1.03/1.18 <=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.03/1.18 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_Suc3__eq__add__3,axiom,
% 1.03/1.18 ! [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) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_not__sum__power2__lt__zero,axiom,
% 1.03/1.18 ! [V_y,V_x,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.18 => ~ 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_sum__power2__gt__zero__iff,axiom,
% 1.03/1.18 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.18 => ( 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))))))
% 1.03/1.18 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.18 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_dvd__mult__cancel__left,axiom,
% 1.03/1.18 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.03/1.18 ( class_Rings_Oidom(T_a)
% 1.03/1.18 => ( c_Rings_Odvd__class_Odvd(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))
% 1.03/1.18 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.18 | c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_ba_2) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_dvd__mult__cancel__right,axiom,
% 1.03/1.18 ! [V_ba_2,V_c_2,V_a_2,T_a] :
% 1.03/1.18 ( class_Rings_Oidom(T_a)
% 1.03/1.18 => ( c_Rings_Odvd__class_Odvd(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))
% 1.03/1.18 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.18 | c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_ba_2) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_odd__power__less__zero,axiom,
% 1.03/1.18 ! [V_n,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => 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)) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_iszero__def,axiom,
% 1.03/1.18 ! [V_z_2,T_a] :
% 1.03/1.18 ( class_Rings_Osemiring__1(T_a)
% 1.03/1.18 => ( c_Int_Oiszero(T_a,V_z_2)
% 1.03/1.18 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_iszero__0,axiom,
% 1.03/1.18 ! [T_a] :
% 1.03/1.18 ( class_Rings_Osemiring__1(T_a)
% 1.03/1.18 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_zero__less__power__eq__number__of,axiom,
% 1.03/1.18 ! [V_w_2,V_x_2,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.18 => ( 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)))
% 1.03/1.18 <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.18 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.03/1.18 & V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
% 1.03/1.18 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.03/1.18 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_add__2__eq__Suc_H,axiom,
% 1.03/1.18 ! [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)) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_add__2__eq__Suc,axiom,
% 1.03/1.18 ! [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)) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_sum__squares__eq__zero__iff,axiom,
% 1.03/1.18 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.18 => ( 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)
% 1.03/1.18 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.18 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_add__scale__eq__noteq,axiom,
% 1.03/1.18 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 1.03/1.18 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.03/1.18 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.18 => ( ( V_a = V_b
% 1.03/1.18 & V_c != V_d )
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_right__distrib__number__of,axiom,
% 1.03/1.18 ! [V_c,V_b,V_v,T_b] :
% 1.03/1.18 ( ( class_Int_Onumber(T_b)
% 1.03/1.18 & class_Rings_Osemiring(T_b) )
% 1.03/1.18 => 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)) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_left__distrib__number__of,axiom,
% 1.03/1.18 ! [V_v,V_b,V_a,T_b] :
% 1.03/1.18 ( ( class_Int_Onumber(T_b)
% 1.03/1.18 & class_Rings_Osemiring(T_b) )
% 1.03/1.18 => 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))) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__strict__left__mono__neg,axiom,
% 1.03/1.18 ! [V_c,V_a,V_b,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__strict__right__mono__neg,axiom,
% 1.03/1.18 ! [V_c,V_a,V_b,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_comm__mult__strict__left__mono,axiom,
% 1.03/1.18 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__strict__left__mono,axiom,
% 1.03/1.18 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__strict__right__mono,axiom,
% 1.03/1.18 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__neg__neg,axiom,
% 1.03/1.18 ! [V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__neg__pos,axiom,
% 1.03/1.18 ! [V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__less__cancel__left__neg,axiom,
% 1.03/1.18 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => ( 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))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(T_a,V_ba_2,V_a_2) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_zero__less__mult__pos2,axiom,
% 1.03/1.18 ! [V_a,V_b,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.18 => ( 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))
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.18 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_zero__less__mult__pos,axiom,
% 1.03/1.18 ! [V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.18 => ( 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))
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.18 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__pos__neg2,axiom,
% 1.03/1.18 ! [V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__pos__neg,axiom,
% 1.03/1.18 ! [V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__pos__pos,axiom,
% 1.03/1.18 ! [V_b,V_a,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.18 => 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)) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__less__cancel__left__pos,axiom,
% 1.03/1.18 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.18 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.03/1.18 => ( 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))
% 1.03/1.18 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) ) ) ) ).
% 1.03/1.18
% 1.03/1.18 fof(fact_mult__less__cancel__left__disj,axiom,
% 1.03/1.18 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.03/1.18 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.18 => ( 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))
% 1.03/1.18 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.03/1.18 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) )
% 1.03/1.18 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.18 & c_Orderings_Oord__class_Oless(T_a,V_ba_2,V_a_2) ) ) ) ) ).
% 1.03/1.18
% 1.03/1.19 fof(fact_mult__less__cancel__right__disj,axiom,
% 1.03/1.19 ! [V_ba_2,V_c_2,V_a_2,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.19 => ( 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))
% 1.03/1.19 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.03/1.19 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) )
% 1.03/1.19 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.19 & c_Orderings_Oord__class_Oless(T_a,V_ba_2,V_a_2) ) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_not__square__less__zero,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__ring(T_a)
% 1.03/1.19 => ~ 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__numeral__0__right,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__numeral__0,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.19 ( c_Rings_Odvd__class_Odvd(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))
% 1.03/1.19 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_mult__eq__1__iff,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.03/1.19 & V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_bin__less__0__simps_I4_J,axiom,
% 1.03/1.19 ! [V_w_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_rel__simps_I12_J,axiom,
% 1.03/1.19 ! [V_k_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_bin__less__0__simps_I1_J,axiom,
% 1.03/1.19 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_rel__simps_I16_J,axiom,
% 1.03/1.19 ! [V_l_2,V_k_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__int__code_I15_J,axiom,
% 1.03/1.19 ! [V_k2_2,V_k1_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_bin__less__0__simps_I3_J,axiom,
% 1.03/1.19 ! [V_w_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_rel__simps_I4_J,axiom,
% 1.03/1.19 ! [V_k_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_rel__simps_I10_J,axiom,
% 1.03/1.19 ! [V_k_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zmult__zless__mono2,axiom,
% 1.03/1.19 ! [V_k,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 1.03/1.19 => 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)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_sum__power2__eq__zero__iff,axiom,
% 1.03/1.19 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.19 => ( 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)
% 1.03/1.19 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.19 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power2__less__0,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.19 => ~ 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__less__power2,axiom,
% 1.03/1.19 ! [V_a_2,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.19 => ( 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)))))
% 1.03/1.19 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power2__sum,axiom,
% 1.03/1.19 ! [V_y,V_x,T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__odd__eq,axiom,
% 1.03/1.19 ! [V_n,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.19 => 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))))) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 1.03/1.19 ! [V_n,V_x,T_a] :
% 1.03/1.19 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.19 => 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))) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__eq__0__iff__number__of,axiom,
% 1.03/1.19 ! [V_w_2,V_a_2,T_a] :
% 1.03/1.19 ( ( class_Power_Opower(T_a)
% 1.03/1.19 & class_Rings_Omult__zero(T_a)
% 1.03/1.19 & class_Rings_Ono__zero__divisors(T_a)
% 1.03/1.19 & class_Rings_Ozero__neq__one(T_a) )
% 1.03/1.19 => ( 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)
% 1.03/1.19 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.19 & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_number__of__Bit0,axiom,
% 1.03/1.19 ! [V_w,T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_odd__nat__equiv__def2,axiom,
% 1.03/1.19 ! [V_x_2] :
% 1.03/1.19 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.19 <=> ? [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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_even__nat__equiv__def2,axiom,
% 1.03/1.19 ! [V_x_2] :
% 1.03/1.19 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.19 <=> ? [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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_iszero__number__of__Bit1,axiom,
% 1.03/1.19 ! [V_w,T_a] :
% 1.03/1.19 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 & class_Int_Oring__char__0(T_a) )
% 1.03/1.19 => ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w))) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_iszero__Numeral0,axiom,
% 1.03/1.19 ! [T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_iszero__number__of__Bit0,axiom,
% 1.03/1.19 ! [V_w_2,T_a] :
% 1.03/1.19 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 & class_Int_Oring__char__0(T_a) )
% 1.03/1.19 => ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w_2)))
% 1.03/1.19 <=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power3__eq__cube,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.19 => 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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_numeral__1__eq__Suc__0,axiom,
% 1.03/1.19 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_numeral__3__eq__3,axiom,
% 1.03/1.19 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__power2,axiom,
% 1.03/1.19 ! [T_a] :
% 1.03/1.19 ( class_Rings_Osemiring__1(T_a)
% 1.03/1.19 => 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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__eq__power2,axiom,
% 1.03/1.19 ! [V_a_2,T_a] :
% 1.03/1.19 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.03/1.19 => ( 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)
% 1.03/1.19 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power2__eq__square,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.19 => 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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 1.03/1.19 ! [V_x,T_a] :
% 1.03/1.19 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.19 => 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)))) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_mult__2__right,axiom,
% 1.03/1.19 ! [V_z,T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => 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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_mult__2,axiom,
% 1.03/1.19 ! [V_z,T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => 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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__even__eq,axiom,
% 1.03/1.19 ! [V_n,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.19 => 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)))) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_semiring__norm_I115_J,axiom,
% 1.03/1.19 c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_csqrt,axiom,
% 1.03/1.19 ! [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 ).
% 1.03/1.19
% 1.03/1.19 fof(fact_four__x__squared,axiom,
% 1.03/1.19 ! [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)))) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_unity__coeff__ex,axiom,
% 1.03/1.19 ! [V_l_2,V_P_2,T_a] :
% 1.03/1.19 ( ( class_Rings_Odvd(T_a)
% 1.03/1.19 & class_Rings_Osemiring__0(T_a) )
% 1.03/1.19 => ( ? [B_x] : hBOOL(hAPP(V_P_2,c_Groups_Otimes__class_Otimes(T_a,V_l_2,B_x)))
% 1.03/1.19 <=> ? [B_x] :
% 1.03/1.19 ( c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))
% 1.03/1.19 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__add,axiom,
% 1.03/1.19 ! [V_n,V_m,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__Suc,axiom,
% 1.03/1.19 ! [V_n,V_a,T_a] :
% 1.03/1.19 ( class_Power_Opower(T_a)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__Suc2,axiom,
% 1.03/1.19 ! [V_n,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.19 => 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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__0__Suc,axiom,
% 1.03/1.19 ! [V_n,T_a] :
% 1.03/1.19 ( ( class_Power_Opower(T_a)
% 1.03/1.19 & class_Rings_Osemiring__0(T_a) )
% 1.03/1.19 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__eq__0__iff,axiom,
% 1.03/1.19 ! [V_nb_2,V_a_2,T_a] :
% 1.03/1.19 ( ( class_Power_Opower(T_a)
% 1.03/1.19 & class_Rings_Omult__zero(T_a)
% 1.03/1.19 & class_Rings_Ono__zero__divisors(T_a)
% 1.03/1.19 & class_Rings_Ozero__neq__one(T_a) )
% 1.03/1.19 => ( c_Power_Opower__class_Opower(T_a,V_a_2,V_nb_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.19 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.19 & V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__less__power,axiom,
% 1.03/1.19 ! [V_n,V_a,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.19 => 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)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.03/1.19 ! [V_a_2,T_a] :
% 1.03/1.19 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.03/1.19 => ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__zeroE,axiom,
% 1.03/1.19 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_Suc__mono,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_lessI,axiom,
% 1.03/1.19 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__less__Suc,axiom,
% 1.03/1.19 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_not__real__square__gt__zero,axiom,
% 1.03/1.19 ! [V_x_2] :
% 1.03/1.19 ( ~ 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))
% 1.03/1.19 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zadd__commute,axiom,
% 1.03/1.19 ! [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) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zadd__left__commute,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zadd__assoc,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zdvd__period,axiom,
% 1.03/1.19 ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
% 1.03/1.19 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)
% 1.03/1.19 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))
% 1.03/1.19 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_c_2,V_d_2)),V_t_2)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zdvd__reduce,axiom,
% 1.03/1.19 ! [V_m_2,V_nb_2,V_k_2] :
% 1.03/1.19 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_nb_2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2,V_m_2)))
% 1.03/1.19 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_nb_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__power__less__imp__less,axiom,
% 1.03/1.19 ! [V_n,V_m,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 1.03/1.19 => ( 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))
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__zero__less__power__iff,axiom,
% 1.03/1.19 ! [V_nb_2,V_x_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 1.03/1.19 | V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zadd__0,axiom,
% 1.03/1.19 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zadd__0__right,axiom,
% 1.03/1.19 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__Pls__right,axiom,
% 1.03/1.19 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__Pls,axiom,
% 1.03/1.19 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__Bit0__Bit0,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_Bit0__def,axiom,
% 1.03/1.19 ! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_not__less0,axiom,
% 1.03/1.19 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_neq0__conv,axiom,
% 1.03/1.19 ! [V_nb_2] :
% 1.03/1.19 ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__nat__zero__code,axiom,
% 1.03/1.19 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_gr__implies__not0,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.19 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_gr0I,axiom,
% 1.03/1.19 ! [V_n] :
% 1.03/1.19 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__less__power__nat__eq,axiom,
% 1.03/1.19 ! [V_nb_2,V_x_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zadd__strict__right__mono,axiom,
% 1.03/1.19 ! [V_k,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_Suc__less__SucD,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_Suc__lessD,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__SucE,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 1.03/1.19 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.19 => V_m = V_n ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__trans__Suc,axiom,
% 1.03/1.19 ! [V_k,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_Suc__lessI,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.19 => ( c_Nat_OSuc(V_m) != V_n
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__SucI,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__antisym,axiom,
% 1.03/1.19 ! [V_m,V_n] :
% 1.03/1.19 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 1.03/1.19 => V_m = V_n ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_not__less__less__Suc__eq,axiom,
% 1.03/1.19 ! [V_m_2,V_nb_2] :
% 1.03/1.19 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
% 1.03/1.19 <=> V_nb_2 = V_m_2 ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_Suc__less__eq,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_nb_2))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__Suc__eq,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 1.03/1.19 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.19 | V_m_2 = V_nb_2 ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_not__less__eq,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2] :
% 1.03/1.19 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_plus__numeral__code_I9_J,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__lessD1,axiom,
% 1.03/1.19 ! [V_k,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__add__eq__less,axiom,
% 1.03/1.19 ! [V_n,V_m,V_l,V_k] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.03/1.19 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__less__mono,axiom,
% 1.03/1.19 ! [V_l,V_k,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.03/1.19 => 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)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__less__mono1,axiom,
% 1.03/1.19 ! [V_k,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_trans__less__add2,axiom,
% 1.03/1.19 ! [V_m,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_trans__less__add1,axiom,
% 1.03/1.19 ! [V_m,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__add__left__cancel__less,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_not__add__less2,axiom,
% 1.03/1.19 ! [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) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_not__add__less1,axiom,
% 1.03/1.19 ! [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) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zadd__zmult__distrib2,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zadd__zmult__distrib,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zdvd__mono,axiom,
% 1.03/1.19 ! [V_t_2,V_m_2,V_k_2] :
% 1.03/1.19 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.19 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2)
% 1.03/1.19 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2,V_t_2)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_even__sum,axiom,
% 1.03/1.19 ! [V_y_2,V_x_2] :
% 1.03/1.19 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_y_2))
% 1.03/1.19 <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.19 & c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y_2) )
% 1.03/1.19 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.19 & ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y_2) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_even__plus__even,axiom,
% 1.03/1.19 ! [V_y,V_x] :
% 1.03/1.19 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x)
% 1.03/1.19 => ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y)
% 1.03/1.19 => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_even__plus__odd,axiom,
% 1.03/1.19 ! [V_y,V_x] :
% 1.03/1.19 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x)
% 1.03/1.19 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y)
% 1.03/1.19 => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_odd__plus__even,axiom,
% 1.03/1.19 ! [V_y,V_x] :
% 1.03/1.19 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x)
% 1.03/1.19 => ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y)
% 1.03/1.19 => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_odd__plus__odd,axiom,
% 1.03/1.19 ! [V_y,V_x] :
% 1.03/1.19 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x)
% 1.03/1.19 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y)
% 1.03/1.19 => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zdvd__not__zless,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
% 1.03/1.19 => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zdvd__mult__cancel,axiom,
% 1.03/1.19 ! [V_n,V_m,V_k] :
% 1.03/1.19 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_n))
% 1.03/1.19 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.19 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__Bit1__Bit0,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__Bit0__Bit1,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 1.03/1.19 ! [V_x] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 1.03/1.19 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__Suc__eq__0__disj,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 1.03/1.19 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 | ? [B_j] :
% 1.03/1.19 ( V_m_2 = c_Nat_OSuc(B_j)
% 1.03/1.19 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_nb_2) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__Suc0,axiom,
% 1.03/1.19 ! [V_nb_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 1.03/1.19 <=> V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_gr0__conv__Suc,axiom,
% 1.03/1.19 ! [V_nb_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
% 1.03/1.19 <=> ? [B_m] : V_nb_2 = c_Nat_OSuc(B_m) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__dvd__not__less,axiom,
% 1.03/1.19 ! [V_n,V_m] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.19 => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__less__power__nat__eq__number__of,axiom,
% 1.03/1.19 ! [V_w_2,V_x_2] :
% 1.03/1.19 ( 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)))
% 1.03/1.19 <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__gr__0,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.03/1.19 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__iff__Suc__add,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.19 <=> ? [B_k] : V_nb_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__add__Suc2,axiom,
% 1.03/1.19 ! [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))) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__add__Suc1,axiom,
% 1.03/1.19 ! [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))) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__0__less__mult__iff,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.03/1.19 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_mult__less__cancel1,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.03/1.19 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_mult__less__cancel2,axiom,
% 1.03/1.19 ! [V_nb_2,V_k_2,V_m_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.03/1.19 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__mult__eq__cancel1,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.03/1.19 => ( 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)
% 1.03/1.19 <=> V_m_2 = V_nb_2 ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__mult__less__cancel1,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.03/1.19 => ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_mult__less__mono1,axiom,
% 1.03/1.19 ! [V_k,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.03/1.19 => 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)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_mult__less__mono2,axiom,
% 1.03/1.19 ! [V_k,V_j,V_i] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.03/1.19 => 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)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_Suc__mult__less__cancel1,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_odd__pos,axiom,
% 1.03/1.19 ! [V_n] :
% 1.03/1.19 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_n)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_even__power__nat,axiom,
% 1.03/1.19 ! [V_y_2,V_x_2] :
% 1.03/1.19 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_y_2))
% 1.03/1.19 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.19 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_y_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_mult__Bit1,axiom,
% 1.03/1.19 ! [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) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zero__reorient,axiom,
% 1.03/1.19 ! [V_x_2,T_a] :
% 1.03/1.19 ( class_Groups_Ozero(T_a)
% 1.03/1.19 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 1.03/1.19 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_n__less__m__mult__n,axiom,
% 1.03/1.19 ! [V_m,V_n] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_n__less__n__mult__m,axiom,
% 1.03/1.19 ! [V_m,V_n] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_one__less__mult,axiom,
% 1.03/1.19 ! [V_m,V_n] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 1.03/1.19 => 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)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__mult__dvd__cancel1,axiom,
% 1.03/1.19 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.03/1.19 => ( c_Rings_Odvd__class_Odvd(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))
% 1.03/1.19 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_dvd__mult__cancel,axiom,
% 1.03/1.19 ! [V_n,V_m,V_k] :
% 1.03/1.19 ( c_Rings_Odvd__class_Odvd(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))
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.03/1.19 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__nat__number__of,axiom,
% 1.03/1.19 ! [V_v_H_2,V_v_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
% 1.03/1.19 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) )
% 1.03/1.19 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 1.03/1.19 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Oab__semigroup__mult(T_a)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.03/1.19 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Oab__semigroup__add(T_a)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__left__cancel,axiom,
% 1.03/1.19 ! [V_c_2,V_ba_2,V_a_2,T_a] :
% 1.03/1.19 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.03/1.19 => ( 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)
% 1.03/1.19 <=> V_ba_2 = V_c_2 ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__right__cancel,axiom,
% 1.03/1.19 ! [V_c_2,V_a_2,V_ba_2,T_a] :
% 1.03/1.19 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.03/1.19 => ( 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)
% 1.03/1.19 <=> V_ba_2 = V_c_2 ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__left__imp__eq,axiom,
% 1.03/1.19 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.03/1.19 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.03/1.19 => V_b = V_c ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__imp__eq,axiom,
% 1.03/1.19 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 1.03/1.19 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.03/1.19 => V_b = V_c ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__right__imp__eq,axiom,
% 1.03/1.19 ! [V_c,V_a,V_b,T_a] :
% 1.03/1.19 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.03/1.19 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 1.03/1.19 => V_b = V_c ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_pos2,axiom,
% 1.03/1.19 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)))) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__nat__number__of,axiom,
% 1.03/1.19 ! [V_v_H,V_v] :
% 1.03/1.19 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.03/1.19 => 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) )
% 1.03/1.19 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.03/1.19 => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 1.03/1.19 => 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) )
% 1.03/1.19 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 1.03/1.19 => 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)) ) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__0__number__of,axiom,
% 1.03/1.19 ! [V_v_2] :
% 1.03/1.19 ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_int__even__iff__2__dvd,axiom,
% 1.03/1.19 ! [V_x_2] :
% 1.03/1.19 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.19 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_x_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_less__2__cases,axiom,
% 1.03/1.19 ! [V_n] :
% 1.03/1.19 ( 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))))
% 1.03/1.19 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 | V_n = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__0__left,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__add(T_a)
% 1.03/1.19 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__0,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.03/1.19 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_double__zero__sym,axiom,
% 1.03/1.19 ! [V_a_2,T_a] :
% 1.03/1.19 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.03/1.19 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 1.03/1.19 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__0__right,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__add(T_a)
% 1.03/1.19 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add_Ocomm__neutral,axiom,
% 1.03/1.19 ! [V_a,T_a] :
% 1.03/1.19 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.03/1.19 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__less__cancel__right,axiom,
% 1.03/1.19 ! [V_ba_2,V_c_2,V_a_2,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.03/1.19 => ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__less__cancel__left,axiom,
% 1.03/1.19 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.03/1.19 => ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__strict__right__mono,axiom,
% 1.03/1.19 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.19 => 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)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__strict__left__mono,axiom,
% 1.03/1.19 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.19 => 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)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__strict__mono,axiom,
% 1.03/1.19 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.03/1.19 => 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)) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__less__imp__less__right,axiom,
% 1.03/1.19 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.03/1.19 => ( 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))
% 1.03/1.19 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__less__imp__less__left,axiom,
% 1.03/1.19 ! [V_b,V_a,V_c,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.03/1.19 => ( 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))
% 1.03/1.19 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_field__power__not__zero,axiom,
% 1.03/1.19 ! [V_n,V_a,T_a] :
% 1.03/1.19 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.03/1.19 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.19 => c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__mult__distrib,axiom,
% 1.03/1.19 ! [V_n,V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__commutes,axiom,
% 1.03/1.19 ! [V_n,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 1.03/1.19 ! [V_m_2,V_x_2] :
% 1.03/1.19 ( c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.03/1.19 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.19 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__Suc__0,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_dvd__power__same,axiom,
% 1.03/1.19 ! [V_n,V_y,V_x,T_a] :
% 1.03/1.19 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.19 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 1.03/1.19 => c_Rings_Odvd__class_Odvd(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_y,V_n)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__mult,axiom,
% 1.03/1.19 ! [V_n,V_m,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.19 => 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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__neg__neg,axiom,
% 1.03/1.19 ! [V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.19 => 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)) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_add__pos__pos,axiom,
% 1.03/1.19 ! [V_b,V_a,T_a] :
% 1.03/1.19 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.19 => 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)) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.03/1.19 ! [V_a_2,T_a] :
% 1.03/1.19 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.03/1.19 => ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_real__sum__squared__expand,axiom,
% 1.03/1.19 ! [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)) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_realpow__two__sum__zero__iff,axiom,
% 1.03/1.19 ! [V_y_2,V_x_2] :
% 1.03/1.19 ( 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)
% 1.03/1.19 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.03/1.19 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 1.03/1.19 ! [V_n,V_a,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.19 => ( 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))))
% 1.03/1.19 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__m1__odd,axiom,
% 1.03/1.19 ! [V_n,T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => 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) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power2__diff,axiom,
% 1.03/1.19 ! [V_y,V_x,T_a] :
% 1.03/1.19 ( class_Int_Onumber__ring(T_a)
% 1.03/1.19 => c_Power_Opower__class_Opower(T_a,c_Groups_Ominus__class_Ominus(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_Ominus__class_Ominus(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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_odd__equiv__def,axiom,
% 1.03/1.19 ! [V_x_2] :
% 1.03/1.19 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.19 <=> ? [B_y] : V_x_2 = 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))),B_y),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_le0,axiom,
% 1.03/1.19 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_real__mult__le__cancel__iff1,axiom,
% 1.03/1.19 ! [V_y_2,V_x_2,V_z_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.03/1.19 => ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_real__mult__le__cancel__iff2,axiom,
% 1.03/1.19 ! [V_y_2,V_x_2,V_z_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.03/1.19 => ( 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))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__decreasing,axiom,
% 1.03/1.19 ! [V_a,V_N,V_n,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.03/1.19 => 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)) ) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zle__diff1__eq,axiom,
% 1.03/1.19 ! [V_z_2,V_w_2] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.03/1.19 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_zdvd__zdiffD,axiom,
% 1.03/1.19 ! [V_n,V_m,V_k] :
% 1.03/1.19 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))
% 1.03/1.19 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)
% 1.03/1.19 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__increasing,axiom,
% 1.03/1.19 ! [V_a,V_N,V_n,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.19 => 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)) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_real__add__left__mono,axiom,
% 1.03/1.19 ! [V_z,V_y,V_x] :
% 1.03/1.19 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.03/1.19 => 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)) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__le__imp__le__exp,axiom,
% 1.03/1.19 ! [V_n,V_m,V_a,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.19 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.19 => ( 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))
% 1.03/1.19 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.03/1.19
% 1.03/1.19 fof(fact_power__increasing__iff,axiom,
% 1.03/1.19 ! [V_y_2,V_x_2,V_ba_2,T_a] :
% 1.03/1.19 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_ba_2)
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_one__le__power,axiom,
% 1.03/1.20 ! [V_n,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.20 => 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__eq__real__def,axiom,
% 1.03/1.20 ! [V_y_2,V_x_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.03/1.20 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.03/1.20 | V_x_2 = V_y_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_real__less__def,axiom,
% 1.03/1.20 ! [V_y_2,V_x_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.03/1.20 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.03/1.20 & V_x_2 != V_y_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__not__refl,axiom,
% 1.03/1.20 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__neq__iff,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( V_m_2 != V_nb_2
% 1.03/1.20 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__less__le,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 & V_m_2 != V_nb_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__eq__less__or__eq,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 | V_m_2 = V_nb_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_linorder__neqE__nat,axiom,
% 1.03/1.20 ! [V_y,V_x] :
% 1.03/1.20 ( V_x != V_y
% 1.03/1.20 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__irrefl__nat,axiom,
% 1.03/1.20 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__not__refl2,axiom,
% 1.03/1.20 ! [V_m,V_n] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.03/1.20 => V_m != V_n ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__not__refl3,axiom,
% 1.03/1.20 ! [V_t,V_s] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 1.03/1.20 => V_s != V_t ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__imp__le__nat,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__imp__diff__less,axiom,
% 1.03/1.20 ! [V_n,V_k,V_j] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__neq__implies__less,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => ( V_m != V_n
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__less__mono,axiom,
% 1.03/1.20 ! [V_c,V_b,V_a] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__less__mono2,axiom,
% 1.03/1.20 ! [V_l,V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__diff__iff,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_k_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__or__eq__imp__le,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 | V_m = V_n )
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__less__cases,axiom,
% 1.03/1.20 ! [V_P_2,V_nb_2,V_m_2] :
% 1.03/1.20 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 1.03/1.20 => ( ( V_m_2 = V_nb_2
% 1.03/1.20 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 1.03/1.20 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 1.03/1.20 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
% 1.03/1.20 => hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__number__of,axiom,
% 1.03/1.20 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.20 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.20 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_one__reorient,axiom,
% 1.03/1.20 ! [V_x_2,T_a] :
% 1.03/1.20 ( class_Groups_Oone(T_a)
% 1.03/1.20 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 1.03/1.20 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__eq__diff__eq,axiom,
% 1.03/1.20 ! [V_d_2,V_c_2,V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Oab__group__add(T_a)
% 1.03/1.20 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 1.03/1.20 => ( V_a_2 = V_ba_2
% 1.03/1.20 <=> V_c_2 = V_d_2 ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__eq__diff__less__eq,axiom,
% 1.03/1.20 ! [V_d_2,V_c_2,V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.03/1.20 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_ba_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_number__of__diff,axiom,
% 1.03/1.20 ! [V_w,V_v,T_a] :
% 1.03/1.20 ( class_Int_Onumber__ring(T_a)
% 1.03/1.20 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__iff__diff__le__0,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_ba_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_dvd__diffD,axiom,
% 1.03/1.20 ! [V_n,V_m,V_k] :
% 1.03/1.20 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
% 1.03/1.20 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.03/1.20 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_dvd__diffD1,axiom,
% 1.03/1.20 ! [V_n,V_m,V_k] :
% 1.03/1.20 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
% 1.03/1.20 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.03/1.20 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__add__assoc2,axiom,
% 1.03/1.20 ! [V_i,V_j,V_k] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__diff__assoc2,axiom,
% 1.03/1.20 ! [V_i,V_j,V_k] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.03/1.20 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__add__assoc,axiom,
% 1.03/1.20 ! [V_i,V_j,V_k] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__imp__diff__is__add,axiom,
% 1.03/1.20 ! [V_k_2,V_j_2,V_i_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.03/1.20 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 1.03/1.20 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__add__diff__inverse2,axiom,
% 1.03/1.20 ! [V_m,V_n] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.03/1.20 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__diff__conv2,axiom,
% 1.03/1.20 ! [V_i_2,V_j_2,V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__diff__assoc,axiom,
% 1.03/1.20 ! [V_i,V_j,V_k] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.03/1.20 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__add__diff__inverse,axiom,
% 1.03/1.20 ! [V_m,V_n] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.03/1.20 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__add__diff,axiom,
% 1.03/1.20 ! [V_m,V_n,V_k] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__diff__conv,axiom,
% 1.03/1.20 ! [V_i_2,V_k_2,V_j_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__diff__right,axiom,
% 1.03/1.20 ! [V_i,V_j,V_k] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_real__squared__diff__one__factored,axiom,
% 1.03/1.20 ! [V_x,T_a] :
% 1.03/1.20 ( class_Rings_Oring__1(T_a)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__special_I4_J,axiom,
% 1.03/1.20 ! [V_x_2,T_a] :
% 1.03/1.20 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.20 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__special_I2_J,axiom,
% 1.03/1.20 ! [V_y_2,T_a] :
% 1.03/1.20 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.20 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__add__iff2,axiom,
% 1.03/1.20 ! [V_d_2,V_ba_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__ring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_e_2),V_d_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ba_2,V_a_2),V_e_2),V_d_2)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__add__iff1,axiom,
% 1.03/1.20 ! [V_d_2,V_ba_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__ring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_e_2),V_d_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2),V_e_2),V_c_2),V_d_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_real__le__eq__diff,axiom,
% 1.03/1.20 ! [V_y_2,V_x_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I24_J,axiom,
% 1.03/1.20 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I28_J,axiom,
% 1.03/1.20 ! [V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I23_J,axiom,
% 1.03/1.20 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I20_J,axiom,
% 1.03/1.20 ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I26_J,axiom,
% 1.03/1.20 ! [V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I30_J,axiom,
% 1.03/1.20 ! [V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__is__0__eq_H,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__is__0__eq,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_not__one__le__zero,axiom,
% 1.03/1.20 ! [T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zero__le__one,axiom,
% 1.03/1.20 ! [T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__diff__le,axiom,
% 1.03/1.20 ! [V_m,V_n] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__left__le__one__le,axiom,
% 1.03/1.20 ! [V_y,V_x,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x),V_x) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__right__le__one__le,axiom,
% 1.03/1.20 ! [V_y,V_x,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_x) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__bin__simps_I4_J,axiom,
% 1.03/1.20 ! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__bin__simps_I5_J,axiom,
% 1.03/1.20 ! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__bin__simps_I6_J,axiom,
% 1.03/1.20 ! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__Suc__diff__eq1,axiom,
% 1.03/1.20 ! [V_m,V_j,V_k] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__Suc__diff__eq2,axiom,
% 1.03/1.20 ! [V_m,V_j,V_k] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I25_J,axiom,
% 1.03/1.20 ! [V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_k_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I11_J,axiom,
% 1.03/1.20 ! [V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__le__add__iff1,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_nb_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_nb_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__diff__add__eq1,axiom,
% 1.03/1.20 ! [V_n,V_m,V_u,V_i,V_j] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_u),V_m),V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__eq__add__iff1,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.03/1.20 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_nb_2)
% 1.03/1.20 <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2) = V_nb_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__le__add__iff2,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_nb_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_nb_2)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__diff__add__eq2,axiom,
% 1.03/1.20 ! [V_n,V_m,V_u,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i),V_u),V_n)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__eq__add__iff2,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.03/1.20 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_nb_2)
% 1.03/1.20 <=> V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_nb_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__less__add__iff1,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_nb_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_nb_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__less__add__iff2,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_nb_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_nb_2)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__nat__number__of,axiom,
% 1.03/1.20 ! [V_v_H_2,V_v_2] :
% 1.03/1.20 ( 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))
% 1.03/1.20 <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_int__one__le__iff__zero__less,axiom,
% 1.03/1.20 ! [V_z_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m,V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.03/1.20 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.03/1.20 | V_m = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zmult__eq__1__iff,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m_2,V_nb_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.03/1.20 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.03/1.20 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 1.03/1.20 | ( V_m_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
% 1.03/1.20 & V_nb_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zless__imp__add1__zle,axiom,
% 1.03/1.20 ! [V_z,V_w] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 1.03/1.20 => 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) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add1__zle__eq,axiom,
% 1.03/1.20 ! [V_z_2,V_w_2] :
% 1.03/1.20 ( 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)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zle__add1__eq__le,axiom,
% 1.03/1.20 ! [V_z_2,V_w_2] :
% 1.03/1.20 ( 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)))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_right__minus__eq,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Ogroup__add(T_a)
% 1.03/1.20 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.20 <=> V_a_2 = V_ba_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_eq__iff__diff__eq__0,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Oab__group__add(T_a)
% 1.03/1.20 => ( V_a_2 = V_ba_2
% 1.03/1.20 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__self,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Groups_Ogroup__add(T_a)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__0__right,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Groups_Ogroup__add(T_a)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__eq__diff__less,axiom,
% 1.03/1.20 ! [V_d_2,V_c_2,V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.03/1.20 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult_Odiff__right,axiom,
% 1.03/1.20 ! [V_b_H,V_b,V_a,T_a] :
% 1.03/1.20 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__right_Odiff,axiom,
% 1.03/1.20 ! [V_y,V_x,V_xa,T_a] :
% 1.03/1.20 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult_Odiff__left,axiom,
% 1.03/1.20 ! [V_b,V_a_H,V_a,T_a] :
% 1.03/1.20 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__left_Odiff,axiom,
% 1.03/1.20 ! [V_ya,V_y,V_x,T_a] :
% 1.03/1.20 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__diff__cancel,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Ogroup__add(T_a)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__add__cancel,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Ogroup__add(T_a)
% 1.03/1.20 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_realpow__Suc__le__self,axiom,
% 1.03/1.20 ! [V_n,V_r,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_r,c_Nat_OSuc(V_n)),V_r) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_dvd__diff,axiom,
% 1.03/1.20 ! [V_z,V_y,V_x,T_a] :
% 1.03/1.20 ( class_Rings_Ocomm__ring__1(T_a)
% 1.03/1.20 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 1.03/1.20 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
% 1.03/1.20 => c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zero__neq__one,axiom,
% 1.03/1.20 ! [T_a] :
% 1.03/1.20 ( class_Rings_Ozero__neq__one(T_a)
% 1.03/1.20 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_one__neq__zero,axiom,
% 1.03/1.20 ! [T_a] :
% 1.03/1.20 ( class_Rings_Ozero__neq__one(T_a)
% 1.03/1.20 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__bin__simps_I1_J,axiom,
% 1.03/1.20 ! [V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__bin__simps_I7_J,axiom,
% 1.03/1.20 ! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diffs0__imp__equal,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.20 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.20 => V_m = V_n ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__self__eq__0,axiom,
% 1.03/1.20 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_minus__nat_Odiff__0,axiom,
% 1.03/1.20 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__0__eq__0,axiom,
% 1.03/1.20 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__less,axiom,
% 1.03/1.20 ! [V_m,V_n] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zero__less__diff,axiom,
% 1.03/1.20 ! [V_m_2,V_nb_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_m_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Bit1__Min,axiom,
% 1.03/1.20 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I43_J,axiom,
% 1.03/1.20 ! [V_l_2] :
% 1.03/1.20 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 1.03/1.20 <=> c_Int_OMin = V_l_2 ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I47_J,axiom,
% 1.03/1.20 ! [V_k_2] :
% 1.03/1.20 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 1.03/1.20 <=> V_k_2 = c_Int_OMin ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I40_J,axiom,
% 1.03/1.20 c_Int_OMin != c_Int_OPls ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I37_J,axiom,
% 1.03/1.20 c_Int_OPls != c_Int_OMin ).
% 1.03/1.20
% 1.03/1.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__1__left,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__1,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__1__right,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult_Ocomm__neutral,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I42_J,axiom,
% 1.03/1.20 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I45_J,axiom,
% 1.03/1.20 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__le__imp__le__left,axiom,
% 1.03/1.20 ! [V_b,V_a,V_c,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__le__imp__le__right,axiom,
% 1.03/1.20 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__mono,axiom,
% 1.03/1.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__left__mono,axiom,
% 1.03/1.20 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__right__mono,axiom,
% 1.03/1.20 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__le__cancel__left,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_ba_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__le__cancel__right,axiom,
% 1.03/1.20 ! [V_ba_2,V_c_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_ba_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__Suc__Suc,axiom,
% 1.03/1.20 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__diff__diff,axiom,
% 1.03/1.20 ! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__less__Suc,axiom,
% 1.03/1.20 ! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_dvd__diff__nat,axiom,
% 1.03/1.20 ! [V_n,V_m,V_k] :
% 1.03/1.20 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
% 1.03/1.20 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 1.03/1.20 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__add__inverse2,axiom,
% 1.03/1.20 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__add__inverse,axiom,
% 1.03/1.20 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__diff__left,axiom,
% 1.03/1.20 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__cancel,axiom,
% 1.03/1.20 ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__cancel2,axiom,
% 1.03/1.20 ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__diff__conv,axiom,
% 1.03/1.20 ! [V_k_2,V_j_2,V_i_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__diff__inverse,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I7_J,axiom,
% 1.03/1.20 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zdiff__zmult__distrib,axiom,
% 1.03/1.20 ! [V_w,V_z2,V_z1] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zdiff__zmult__distrib2,axiom,
% 1.03/1.20 ! [V_z2,V_z1,V_w] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_one__dvd,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.20 => c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_power__one,axiom,
% 1.03/1.20 ! [V_n,T_a] :
% 1.03/1.20 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.20 => c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__mult__distrib2,axiom,
% 1.03/1.20 ! [V_n,V_m,V_k] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__mult__distrib,axiom,
% 1.03/1.20 ! [V_k,V_n,V_m] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__0__eq,axiom,
% 1.03/1.20 ! [V_nb_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.03/1.20 <=> V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 1.03/1.20 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I34_J,axiom,
% 1.03/1.20 ! [V_l_2,V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__eq__int__code_I16_J,axiom,
% 1.03/1.20 ! [V_k2_2,V_k1_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zdvd__antisym__nonneg,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
% 1.03/1.20 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
% 1.03/1.20 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
% 1.03/1.20 => V_m = V_n ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__n__not__le__n,axiom,
% 1.03/1.20 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_not__less__eq__eq,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__Suc__eq,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 1.03/1.20 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 | V_m_2 = c_Nat_OSuc(V_nb_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__le__mono,axiom,
% 1.03/1.20 ! [V_m_2,V_nb_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),c_Nat_OSuc(V_m_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,V_m_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__SucI,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__SucE,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 1.03/1.20 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__leD,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__eq__Suc__le,axiom,
% 1.03/1.20 ! [V_m_2,V_nb_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__Suc__eq__le,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__le__eq,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_nb_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__imp__less__Suc,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__leI,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__less__Suc__eq,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
% 1.03/1.20 <=> V_nb_2 = V_m_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__le__lessD,axiom,
% 1.03/1.20 ! [V_n,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I19_J,axiom,
% 1.03/1.20 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_rel__simps_I31_J,axiom,
% 1.03/1.20 ! [V_l_2,V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__eq__int__code_I13_J,axiom,
% 1.03/1.20 ! [V_k2_2,V_k1_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__add2,axiom,
% 1.03/1.20 ! [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)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__add1,axiom,
% 1.03/1.20 ! [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)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__iff__add,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.20 <=> ? [B_k] : V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__add__left__cancel__le,axiom,
% 1.03/1.20 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.20 ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_trans__le__add1,axiom,
% 1.03/1.20 ! [V_m,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_trans__le__add2,axiom,
% 1.03/1.20 ! [V_m,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__le__mono1,axiom,
% 1.03/1.20 ! [V_k,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.20 => 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)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__le__mono,axiom,
% 1.03/1.20 ! [V_l,V_k,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.03/1.20 => 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__leD2,axiom,
% 1.03/1.20 ! [V_n,V_k,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__leD1,axiom,
% 1.03/1.20 ! [V_n,V_k,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__leE,axiom,
% 1.03/1.20 ! [V_n,V_k,V_m] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.03/1.20 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.20 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zless__le,axiom,
% 1.03/1.20 ! [V_w_2,V_z_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
% 1.03/1.20 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2)
% 1.03/1.20 & V_z_2 != V_w_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_int__0__neq__1,axiom,
% 1.03/1.20 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__square,axiom,
% 1.03/1.20 ! [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)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__cube,axiom,
% 1.03/1.20 ! [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))) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__le__mono1,axiom,
% 1.03/1.20 ! [V_k,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.20 => 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)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__le__mono2,axiom,
% 1.03/1.20 ! [V_k,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.20 => 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)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__le__mono,axiom,
% 1.03/1.20 ! [V_l,V_k,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.03/1.20 => 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zadd__left__mono,axiom,
% 1.03/1.20 ! [V_k,V_j,V_i] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.03/1.20 => 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)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__eq__number__of__int__code,axiom,
% 1.03/1.20 ! [V_l_2,V_k_2] :
% 1.03/1.20 ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_even__difference__nat,axiom,
% 1.03/1.20 ! [V_y_2,V_x_2] :
% 1.03/1.20 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x_2,V_y_2))
% 1.03/1.20 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
% 1.03/1.20 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.20 & c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_y_2) )
% 1.03/1.20 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.20 & ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_y_2) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__diff__mult,axiom,
% 1.03/1.20 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.03/1.20 ( class_Rings_Oring(T_a)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zmult__1__right,axiom,
% 1.03/1.20 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z,c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zmult__1,axiom,
% 1.03/1.20 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z) = V_z ).
% 1.03/1.20
% 1.03/1.20 fof(fact_even__difference,axiom,
% 1.03/1.20 ! [V_y_2,V_x_2] :
% 1.03/1.20 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x_2,V_y_2))
% 1.03/1.20 <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.20 & c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y_2) )
% 1.03/1.20 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.20 & ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_y_2) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_odd__one__int,axiom,
% 1.03/1.20 ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_convex__bound__le,axiom,
% 1.03/1.20 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semiring__1(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.03/1.20 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.03/1.20 => 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) ) ) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__special_I1_J,axiom,
% 1.03/1.20 ! [V_y_2,T_a] :
% 1.03/1.20 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.20 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__special_I3_J,axiom,
% 1.03/1.20 ! [V_x_2,T_a] :
% 1.03/1.20 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.20 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_not__iszero__1,axiom,
% 1.03/1.20 ! [T_a] :
% 1.03/1.20 ( class_Rings_Osemiring__1(T_a)
% 1.03/1.20 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_neg__one__even__power,axiom,
% 1.03/1.20 ! [V_x,T_a] :
% 1.03/1.20 ( class_Int_Onumber__ring(T_a)
% 1.03/1.20 => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.03/1.20 => 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) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_neg__one__even__odd__power,axiom,
% 1.03/1.20 ! [V_x,T_a] :
% 1.03/1.20 ( class_Int_Onumber__ring(T_a)
% 1.03/1.20 => ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.03/1.20 => 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) )
% 1.03/1.20 & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.03/1.20 => 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) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__imp__0__less,axiom,
% 1.03/1.20 ! [V_z] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 1.03/1.20 => 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)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_convex__bound__lt,axiom,
% 1.03/1.20 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.03/1.20 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.03/1.20 => 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) ) ) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__iff__diff__less__0,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_ba_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_eq__add__iff1,axiom,
% 1.03/1.20 ! [V_d_2,V_ba_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Rings_Oring(T_a)
% 1.03/1.20 => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_e_2),V_d_2)
% 1.03/1.20 <=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2),V_e_2),V_c_2) = V_d_2 ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_eq__add__iff2,axiom,
% 1.03/1.20 ! [V_d_2,V_ba_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Rings_Oring(T_a)
% 1.03/1.20 => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_e_2),V_d_2)
% 1.03/1.20 <=> V_c_2 = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ba_2,V_a_2),V_e_2),V_d_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult_Oprod__diff__prod,axiom,
% 1.03/1.20 ! [V_b,V_a,V_y,V_x,T_a] :
% 1.03/1.20 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.03/1.20 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_right__diff__distrib__number__of,axiom,
% 1.03/1.20 ! [V_c,V_b,V_v,T_b] :
% 1.03/1.20 ( ( class_Int_Onumber(T_b)
% 1.03/1.20 & class_Rings_Oring(T_b) )
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_left__diff__distrib__number__of,axiom,
% 1.03/1.20 ! [V_v,V_b,V_a,T_b] :
% 1.03/1.20 ( ( class_Int_Onumber(T_b)
% 1.03/1.20 & class_Rings_Oring(T_b) )
% 1.03/1.20 => c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zero__less__one,axiom,
% 1.03/1.20 ! [T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_not__one__less__zero,axiom,
% 1.03/1.20 ! [T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_split__mult__neg__le,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.03/1.20 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.03/1.20 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 1.03/1.20 => 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_split__mult__pos__le,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__ring(T_a)
% 1.03/1.20 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 1.03/1.20 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.03/1.20 => 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__mono,axiom,
% 1.03/1.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.20 => 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)) ) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__mono_H,axiom,
% 1.03/1.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.20 => 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)) ) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__left__mono__neg,axiom,
% 1.03/1.20 ! [V_c,V_a,V_b,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__ring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__right__mono__neg,axiom,
% 1.03/1.20 ! [V_c,V_a,V_b,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__ring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_comm__mult__left__mono,axiom,
% 1.03/1.20 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__comm__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__left__mono,axiom,
% 1.03/1.20 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__right__mono,axiom,
% 1.03/1.20 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__nonpos__nonpos,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__ring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__nonpos__nonneg,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__nonneg__nonpos2,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__nonneg__nonpos,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__nonneg__nonneg,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_mult__le__0__iff,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.03/1.20 & c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.03/1.20 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ba_2) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zero__le__mult__iff,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.03/1.20 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ba_2) )
% 1.03/1.20 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 & c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zero__le__square,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__ring(T_a)
% 1.03/1.20 => 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)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.03/1.20 ! [V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.03/1.20 ! [V_a_2,T_a] :
% 1.03/1.20 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__nonneg__nonneg,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__nonneg__eq__0__iff,axiom,
% 1.03/1.20 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 1.03/1.20 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.20 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.20 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__increasing,axiom,
% 1.03/1.20 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__increasing2,axiom,
% 1.03/1.20 ! [V_a,V_b,V_c,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.03/1.20 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__nonpos__nonpos,axiom,
% 1.03/1.20 ! [V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__bin__simps_I9_J,axiom,
% 1.03/1.20 ! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__bin__simps_I10_J,axiom,
% 1.03/1.20 ! [V_l,V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,V_l)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__bin__simps_I3_J,axiom,
% 1.03/1.20 ! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,V_l)) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__le__less__mono,axiom,
% 1.03/1.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_add__less__le__mono,axiom,
% 1.03/1.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__1__mult,axiom,
% 1.03/1.20 ! [V_n,V_m,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_le__number__of__eq__not__less,axiom,
% 1.03/1.20 ! [V_w_2,V_v_2,T_a] :
% 1.03/1.20 ( ( class_Int_Onumber(T_a)
% 1.03/1.20 & class_Orderings_Olinorder(T_a) )
% 1.03/1.20 => ( 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))
% 1.03/1.20 <=> ~ 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__add__one,axiom,
% 1.03/1.20 ! [V_a,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => 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))) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_Suc__pred,axiom,
% 1.03/1.20 ! [V_n] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.20 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__Suc__less,axiom,
% 1.03/1.20 ! [V_i,V_n] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 1.03/1.20 ! [V_m,T_a] :
% 1.03/1.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.20 => 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) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 1.03/1.20 ! [V_a,V_m,T_a] :
% 1.03/1.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.20 => 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) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 1.03/1.20 ! [V_m,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.20 => 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) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_less__bin__lemma,axiom,
% 1.03/1.20 ! [V_l_2,V_k_2] :
% 1.03/1.20 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
% 1.03/1.20 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_zero__le__power,axiom,
% 1.03/1.20 ! [V_n,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 => 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)) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_power__mono,axiom,
% 1.03/1.20 ! [V_n,V_b,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_diff__add__0,axiom,
% 1.03/1.20 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__diff__split__asm,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,V_P_2] :
% 1.03/1.20 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_ba_2)))
% 1.03/1.20 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_ba_2)
% 1.03/1.20 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.03/1.20 | ? [B_d] :
% 1.03/1.20 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ba_2,B_d)
% 1.03/1.20 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_nat__diff__split,axiom,
% 1.03/1.20 ! [V_ba_2,V_a_2,V_P_2] :
% 1.03/1.20 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_ba_2)))
% 1.03/1.20 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_ba_2)
% 1.03/1.20 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 1.03/1.20 & ! [B_d] :
% 1.03/1.20 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ba_2,B_d)
% 1.03/1.20 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_power__strict__increasing,axiom,
% 1.03/1.20 ! [V_a,V_N,V_n,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.20 => 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)) ) ) ) ).
% 1.03/1.20
% 1.03/1.20 fof(fact_power__less__imp__less__exp,axiom,
% 1.03/1.20 ! [V_n,V_m,V_a,T_a] :
% 1.03/1.20 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.20 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.20 => ( 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))
% 1.03/1.20 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.03/1.20
% 1.03/1.21 fof(fact_power__strict__increasing__iff,axiom,
% 1.03/1.21 ! [V_y_2,V_x_2,V_ba_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_ba_2)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__inject__exp,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2,V_a_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
% 1.03/1.21 => ( 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)
% 1.03/1.21 <=> V_m_2 = V_nb_2 ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I13_J,axiom,
% 1.03/1.21 ! [V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin)
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I9_J,axiom,
% 1.03/1.21 ! [V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_bin__less__0__simps_I2_J,axiom,
% 1.03/1.21 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I3_J,axiom,
% 1.03/1.21 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I6_J,axiom,
% 1.03/1.21 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I8_J,axiom,
% 1.03/1.21 ! [V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_k_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_eq__number__of__Pls__Min,axiom,
% 1.03/1.21 c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 1.03/1.21 ! [V_x,T_a] :
% 1.03/1.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__0,axiom,
% 1.03/1.21 ! [V_a,T_a] :
% 1.03/1.21 ( class_Power_Opower(T_a)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__one__le__power,axiom,
% 1.03/1.21 ! [V_n,V_i] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__le__dvd,axiom,
% 1.03/1.21 ! [V_m,V_b,V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__power__le,axiom,
% 1.03/1.21 ! [V_m,V_n,V_y,V_x,T_a] :
% 1.03/1.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_y,V_m)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_le__imp__power__dvd,axiom,
% 1.03/1.21 ! [V_a,V_n,V_m,T_a] :
% 1.03/1.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I22_J,axiom,
% 1.03/1.21 ! [V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I32_J,axiom,
% 1.03/1.21 ! [V_l_2,V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_less__eq__int__code_I14_J,axiom,
% 1.03/1.21 ! [V_k2_2,V_k1_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I21_J,axiom,
% 1.03/1.21 ! [V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I27_J,axiom,
% 1.03/1.21 ! [V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__imp__le,axiom,
% 1.03/1.21 ! [V_n,V_k] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__mult__le__cancel1,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__le__cancel2,axiom,
% 1.03/1.21 ! [V_nb_2,V_k_2,V_m_2] :
% 1.03/1.21 ( 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))
% 1.03/1.21 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__le__cancel1,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.21 ( 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))
% 1.03/1.21 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zdvd__imp__le,axiom,
% 1.03/1.21 ! [V_n,V_z] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Suc__mult__le__cancel1,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.21 ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zadd__zless__mono,axiom,
% 1.03/1.21 ! [V_z,V_z_H,V_w,V_w_H] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 1.03/1.21 => 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)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__mono__odd,axiom,
% 1.03/1.21 ! [V_y,V_x,V_n,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_n)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_int__0__less__1,axiom,
% 1.03/1.21 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Bit1__def,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_odd__nonzero,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zless__add1__eq,axiom,
% 1.03/1.21 ! [V_z_2,V_w_2] :
% 1.03/1.21 ( 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)))
% 1.03/1.21 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
% 1.03/1.21 | V_w_2 = V_z_2 ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nonzero__number__of__Min,axiom,
% 1.03/1.21 ! [T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_less__add__iff1,axiom,
% 1.03/1.21 ! [V_d_2,V_ba_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.03/1.21 ( class_Rings_Oordered__ring(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_e_2),V_d_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ba_2),V_e_2),V_c_2),V_d_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_less__add__iff2,axiom,
% 1.03/1.21 ! [V_d_2,V_ba_2,V_c_2,V_e_2,V_a_2,T_a] :
% 1.03/1.21 ( class_Rings_Oordered__ring(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ba_2,V_e_2),V_d_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ba_2,V_a_2),V_e_2),V_d_2)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_inf__period_I4_J,axiom,
% 1.03/1.21 ! [V_t_2,V_D_2,V_d_2,T_a] :
% 1.03/1.21 ( ( class_Rings_Ocomm__ring(T_a)
% 1.03/1.21 & class_Rings_Odvd(T_a) )
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 1.03/1.21 => ! [B_x,B_k] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
% 1.03/1.21 <=> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_inf__period_I3_J,axiom,
% 1.03/1.21 ! [V_t_2,V_D_2,V_d_2,T_a] :
% 1.03/1.21 ( ( class_Rings_Ocomm__ring(T_a)
% 1.03/1.21 & class_Rings_Odvd(T_a) )
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 1.03/1.21 => ! [B_x,B_k] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
% 1.03/1.21 <=> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__number__of__diff1,axiom,
% 1.03/1.21 ! [V_c,V_w,V_v,T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c)) = c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__left__le__imp__le,axiom,
% 1.03/1.21 ! [V_b,V_a,V_c,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__right__le__imp__le,axiom,
% 1.03/1.21 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__less__imp__less__left,axiom,
% 1.03/1.21 ! [V_b,V_a,V_c,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__left__less__imp__less,axiom,
% 1.03/1.21 ! [V_b,V_a,V_c,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__less__imp__less__right,axiom,
% 1.03/1.21 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__right__less__imp__less,axiom,
% 1.03/1.21 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__le__less__imp__less,axiom,
% 1.03/1.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => 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)) ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__less__le__imp__less,axiom,
% 1.03/1.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => 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)) ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__strict__mono_H,axiom,
% 1.03/1.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => 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)) ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__strict__mono,axiom,
% 1.03/1.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.03/1.21 => 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)) ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__le__cancel__left__neg,axiom,
% 1.03/1.21 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2,V_a_2) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__le__cancel__left__pos,axiom,
% 1.03/1.21 ! [V_ba_2,V_a_2,V_c_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_ba_2) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__pos__nonneg,axiom,
% 1.03/1.21 ! [V_b,V_a,T_a] :
% 1.03/1.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__nonneg__pos,axiom,
% 1.03/1.21 ! [V_b,V_a,T_a] :
% 1.03/1.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__strict__increasing,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__strict__increasing2,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__neg__nonpos,axiom,
% 1.03/1.21 ! [V_b,V_a,T_a] :
% 1.03/1.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__nonpos__neg,axiom,
% 1.03/1.21 ! [V_b,V_a,T_a] :
% 1.03/1.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_sum__squares__le__zero__iff,axiom,
% 1.03/1.21 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.21 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_sum__squares__ge__zero,axiom,
% 1.03/1.21 ! [V_y,V_x,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__ring(T_a)
% 1.03/1.21 => 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))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zero__less__two,axiom,
% 1.03/1.21 ! [T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => 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))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
% 1.03/1.21 ! [V_x] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.03/1.21 => ( 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))))
% 1.03/1.21 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.21 | V_x = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__less__imp__less__base,axiom,
% 1.03/1.21 ! [V_b,V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__strict__decreasing,axiom,
% 1.03/1.21 ! [V_a,V_N,V_n,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.03/1.21 => 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)) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__gt1__lemma,axiom,
% 1.03/1.21 ! [V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.21 => 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))) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__less__power__Suc,axiom,
% 1.03/1.21 ! [V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.21 => 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))) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__eq__imp__eq__base,axiom,
% 1.03/1.21 ! [V_b,V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Power_Opower__class_Opower(T_a,V_a,V_n) = c_Power_Opower__class_Opower(T_a,V_b,V_n)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 => V_a = V_b ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__0__left,axiom,
% 1.03/1.21 ! [V_n,T_a] :
% 1.03/1.21 ( ( class_Power_Opower(T_a)
% 1.03/1.21 & class_Rings_Osemiring__0(T_a) )
% 1.03/1.21 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 1.03/1.21 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__le__imp__le__base,axiom,
% 1.03/1.21 ! [V_b,V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( 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)))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__inject__base,axiom,
% 1.03/1.21 ! [V_b,V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.03/1.21 => V_a = V_b ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_one__less__power,axiom,
% 1.03/1.21 ! [V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_number__of__Bit1,axiom,
% 1.03/1.21 ! [V_w,T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__gt1,axiom,
% 1.03/1.21 ! [V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.03/1.21 => 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))) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_semiring__norm_I110_J,axiom,
% 1.03/1.21 ! [T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_numeral__1__eq__1,axiom,
% 1.03/1.21 ! [T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_neg__one__odd__power,axiom,
% 1.03/1.21 ! [V_x,T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.03/1.21 => 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) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__power,axiom,
% 1.03/1.21 ! [V_x,V_n,T_a] :
% 1.03/1.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.21 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_n)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zero__le__odd__power,axiom,
% 1.03/1.21 ! [V_x_2,V_nb_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zero__le__even__power,axiom,
% 1.03/1.21 ! [V_x,V_n,T_a] :
% 1.03/1.21 ( ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.21 & class_Rings_Olinordered__ring(T_a) )
% 1.03/1.21 => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_n)
% 1.03/1.21 => 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)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zero__le__power__iff,axiom,
% 1.03/1.21 ! [V_nb_2,V_a_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.03/1.21 | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zero__le__power__eq,axiom,
% 1.03/1.21 ! [V_nb_2,V_x_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.21 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.21 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_eq__0__number__of,axiom,
% 1.03/1.21 ! [V_v_2] :
% 1.03/1.21 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_eq__number__of__0,axiom,
% 1.03/1.21 ! [V_v_2] :
% 1.03/1.21 ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_one__le__mult__iff,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2] :
% 1.03/1.21 ( 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))
% 1.03/1.21 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
% 1.03/1.21 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_nb_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I5_J,axiom,
% 1.03/1.21 ! [V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I29_J,axiom,
% 1.03/1.21 ! [V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I15_J,axiom,
% 1.03/1.21 ! [V_l_2,V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_less__int__code_I14_J,axiom,
% 1.03/1.21 ! [V_k2_2,V_k1_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_rel__simps_I33_J,axiom,
% 1.03/1.21 ! [V_l_2,V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_less__eq__int__code_I15_J,axiom,
% 1.03/1.21 ! [V_k2_2,V_k1_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_number__of2,axiom,
% 1.03/1.21 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)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_one__is__num__one,axiom,
% 1.03/1.21 c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_odd__less__0,axiom,
% 1.03/1.21 ! [V_z_2] :
% 1.03/1.21 ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pos__zmult__eq__1__iff,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)
% 1.03/1.21 => ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_m_2,V_nb_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.03/1.21 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.03/1.21 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__m1__even,axiom,
% 1.03/1.21 ! [V_n,T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__mult__right__cancel,axiom,
% 1.03/1.21 ! [V_ba_2,V_a_2,V_c_2] :
% 1.03/1.21 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.03/1.21 => ( 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)
% 1.03/1.21 <=> V_a_2 = V_ba_2 ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__mult__left__cancel,axiom,
% 1.03/1.21 ! [V_ba_2,V_a_2,V_c_2] :
% 1.03/1.21 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.03/1.21 => ( 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)
% 1.03/1.21 <=> V_a_2 = V_ba_2 ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__mult__commute,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__mult__assoc,axiom,
% 1.03/1.21 ! [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)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__add__mult__distrib,axiom,
% 1.03/1.21 ! [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)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__mult__less__mono2,axiom,
% 1.03/1.21 ! [V_y,V_x,V_z] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.03/1.21 => 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)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__mult__order,axiom,
% 1.03/1.21 ! [V_y,V_x] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.03/1.21 => 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)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__mult__less__iff1,axiom,
% 1.03/1.21 ! [V_y_2,V_x_2,V_z_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__two__squares__add__zero__iff,axiom,
% 1.03/1.21 ! [V_y_2,V_x_2] :
% 1.03/1.21 ( 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)
% 1.03/1.21 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.03/1.21 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_realpow__two__diff,axiom,
% 1.03/1.21 ! [V_y,V_x,T_a] :
% 1.03/1.21 ( class_Rings_Ocomm__ring__1(T_a)
% 1.03/1.21 => c_Groups_Ominus__class_Ominus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(T_a,V_y,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__Suc__less,axiom,
% 1.03/1.21 ! [V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__strict__mono,axiom,
% 1.03/1.21 ! [V_n,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 => 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)) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__Suc__less__one,axiom,
% 1.03/1.21 ! [V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 1.03/1.21 ! [V_m,V_n] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),V_n)
% 1.03/1.21 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_double__number__of__Bit0,axiom,
% 1.03/1.21 ! [V_w,T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__0__left__number__of,axiom,
% 1.03/1.21 ! [V_w,T_a] :
% 1.03/1.21 ( ( class_Power_Opower(T_a)
% 1.03/1.21 & class_Rings_Osemiring__0(T_a) )
% 1.03/1.21 => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => 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) )
% 1.03/1.21 & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => 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) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__le__zero__eq,axiom,
% 1.03/1.21 ! [V_nb_2,V_x_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 & ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.21 & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.03/1.21 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.21 & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zero__le__power__eq__number__of,axiom,
% 1.03/1.21 ! [V_w_2,V_x_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( 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)))
% 1.03/1.21 <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.03/1.21 | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.03/1.21 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_number__of1,axiom,
% 1.03/1.21 ! [V_n] :
% 1.03/1.21 ( 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))
% 1.03/1.21 => ( 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)))
% 1.03/1.21 & 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))) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_one__add__one__is__two,axiom,
% 1.03/1.21 ! [T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => 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))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_less__special_I2_J,axiom,
% 1.03/1.21 ! [V_y_2,T_a] :
% 1.03/1.21 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_less__special_I4_J,axiom,
% 1.03/1.21 ! [V_x_2,T_a] :
% 1.03/1.21 ( ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 & class_Rings_Olinordered__idom(T_a) )
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__special_I2_J,axiom,
% 1.03/1.21 ! [V_w,T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__special_I3_J,axiom,
% 1.03/1.21 ! [V_v,T_a] :
% 1.03/1.21 ( class_Int_Onumber__ring(T_a)
% 1.03/1.21 => 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))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_one__power2,axiom,
% 1.03/1.21 ! [T_a] :
% 1.03/1.21 ( class_Rings_Osemiring__1(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__le__zero__eq__number__of,axiom,
% 1.03/1.21 ! [V_w_2,V_x_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 & ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.03/1.21 & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.03/1.21 | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2))
% 1.03/1.21 & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zero__le__power2,axiom,
% 1.03/1.21 ! [V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => 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))))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power2__le__imp__le,axiom,
% 1.03/1.21 ! [V_y,V_x,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( 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)))))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power2__eq__imp__eq,axiom,
% 1.03/1.21 ! [V_y,V_x,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( 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))))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.03/1.21 => V_x = V_y ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power2__less__imp__less,axiom,
% 1.03/1.21 ! [V_y,V_x,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__semidom(T_a)
% 1.03/1.21 => ( 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)))))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_sum__power2__ge__zero,axiom,
% 1.03/1.21 ! [V_y,V_x,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => 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)))))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_sum__power2__le__zero__iff,axiom,
% 1.03/1.21 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.21 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zero__le__even__power_H,axiom,
% 1.03/1.21 ! [V_n,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => 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))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_even__power__le__0__imp__0,axiom,
% 1.03/1.21 ! [V_k,V_a,T_a] :
% 1.03/1.21 ( class_Rings_Olinordered__idom(T_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_self__quotient__aux2,axiom,
% 1.03/1.21 ! [V_q,V_r,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.21 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_q))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_self__quotient__aux1,axiom,
% 1.03/1.21 ! [V_q,V_r,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.21 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a,V_q))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 1.03/1.21 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)))) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_q__pos__lemma,axiom,
% 1.03/1.21 ! [V_r_H,V_q_H,V_b_H] :
% 1.03/1.21 ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_q__neg__lemma,axiom,
% 1.03/1.21 ! [V_r_H,V_q_H,V_b_H] :
% 1.03/1.21 ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__mult__1,axiom,
% 1.03/1.21 ! [V_z] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z) = V_z ).
% 1.03/1.21
% 1.03/1.21 fof(fact_diff__Suc__1,axiom,
% 1.03/1.21 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 1.03/1.21
% 1.03/1.21 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 1.03/1.21 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__zero__not__eq__one,axiom,
% 1.03/1.21 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zle__refl,axiom,
% 1.03/1.21 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zle__linear,axiom,
% 1.03/1.21 ! [V_w,V_z] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.03/1.21 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zle__trans,axiom,
% 1.03/1.21 ! [V_k,V_j,V_i] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zle__antisym,axiom,
% 1.03/1.21 ! [V_w,V_z] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 1.03/1.21 => V_z = V_w ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__le__antisym,axiom,
% 1.03/1.21 ! [V_w,V_z] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 1.03/1.21 => V_z = V_w ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__le__trans,axiom,
% 1.03/1.21 ! [V_k,V_j,V_i] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__le__linear,axiom,
% 1.03/1.21 ! [V_w,V_z] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.03/1.21 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_real__le__refl,axiom,
% 1.03/1.21 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_le__refl,axiom,
% 1.03/1.21 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_diff__le__self,axiom,
% 1.03/1.21 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__le__linear,axiom,
% 1.03/1.21 ! [V_n,V_m] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_diff__commute,axiom,
% 1.03/1.21 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_eq__imp__le,axiom,
% 1.03/1.21 ! [V_n,V_m] :
% 1.03/1.21 ( V_m = V_n
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_diff__le__mono2,axiom,
% 1.03/1.21 ! [V_l,V_n,V_m] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_diff__le__mono,axiom,
% 1.03/1.21 ! [V_l,V_n,V_m] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_diff__diff__cancel,axiom,
% 1.03/1.21 ! [V_n,V_i] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 1.03/1.21 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_le__trans,axiom,
% 1.03/1.21 ! [V_k,V_j,V_i] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_le__antisym,axiom,
% 1.03/1.21 ! [V_n,V_m] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.03/1.21 => V_m = V_n ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_eq__diff__iff,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
% 1.03/1.21 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_k_2)
% 1.03/1.21 <=> V_m_2 = V_nb_2 ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Nat_Odiff__diff__eq,axiom,
% 1.03/1.21 ! [V_n,V_m,V_k] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 1.03/1.21 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_le__diff__iff,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2,V_k_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_k_2))
% 1.03/1.21 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 1.03/1.21 ! [V_x,T_a] :
% 1.03/1.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__one__right,axiom,
% 1.03/1.21 ! [V_a,T_a] :
% 1.03/1.21 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__dvd__1__iff__1,axiom,
% 1.03/1.21 ! [V_m_2] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 1.03/1.21 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__mult__1,axiom,
% 1.03/1.21 ! [V_n] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) = V_n ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__1__eq__mult__iff,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2] :
% 1.03/1.21 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2)
% 1.03/1.21 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.03/1.21 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__mult__1__right,axiom,
% 1.03/1.21 ! [V_n] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__mult__eq__1__iff,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2] :
% 1.03/1.21 ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.03/1.21 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.03/1.21 & V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_odd__1__nat,axiom,
% 1.03/1.21 ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_One__nat__def,axiom,
% 1.03/1.21 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Suc__eq__plus1,axiom,
% 1.03/1.21 ! [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)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Suc__eq__plus1__left,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__eq__self__implies__10,axiom,
% 1.03/1.21 ! [V_n,V_m] :
% 1.03/1.21 ( V_m = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.03/1.21 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Suc__diff__1,axiom,
% 1.03/1.21 ! [V_n] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Suc__pred_H,axiom,
% 1.03/1.21 ! [V_n] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_add__eq__if,axiom,
% 1.03/1.21 ! [V_n,V_m] :
% 1.03/1.21 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n )
% 1.03/1.21 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__numeral__1__eq__1,axiom,
% 1.03/1.21 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Numeral1__eq1__nat,axiom,
% 1.03/1.21 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mult__eq__if,axiom,
% 1.03/1.21 ! [V_n,V_m] :
% 1.03/1.21 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.03/1.21 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_even__num__iff,axiom,
% 1.03/1.21 ! [V_nb_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
% 1.03/1.21 => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_nb_2)
% 1.03/1.21 <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 1.03/1.21 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)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__eq__if,axiom,
% 1.03/1.21 ! [V_p,V_m] :
% 1.03/1.21 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Power_Opower__class_Opower(tc_Nat_Onat,V_p,V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 1.03/1.21 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Power_Opower__class_Opower(tc_Nat_Onat,V_p,V_m) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_p,c_Power_Opower__class_Opower(tc_Nat_Onat,V_p,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_power__dvd__imp__le,axiom,
% 1.03/1.21 ! [V_n,V_m,V_i] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_realpow__minus__mult,axiom,
% 1.03/1.21 ! [V_x,V_n,T_a] :
% 1.03/1.21 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 => c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_x) = c_Power_Opower__class_Opower(T_a,V_x,V_n) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_expand__Suc,axiom,
% 1.03/1.21 ! [V_v] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))
% 1.03/1.21 => c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__mult__cancel1,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_nb_2),V_m_2)
% 1.03/1.21 <=> V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__mult__cancel2,axiom,
% 1.03/1.21 ! [V_nb_2,V_m_2] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_nb_2,V_m_2),V_m_2)
% 1.03/1.21 <=> V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_nat__1__add__1,axiom,
% 1.03/1.21 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))) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_two__realpow__ge__one,axiom,
% 1.03/1.21 ! [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)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 1.03/1.21 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)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 1.03/1.21 ! [V_y,V_x] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.03/1.21 => 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)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.03/1.21 ! [V_y,V_x] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.03/1.21 => 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)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 1.03/1.21 ! [V_n,V_x] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 1.03/1.21 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)))) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 1.03/1.21 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.03/1.21 ( 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)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_unique__quotient__lemma__neg,axiom,
% 1.03/1.21 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.03/1.21 ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zdiv__mono2__lemma,axiom,
% 1.03/1.21 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.03/1.21 ( 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)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_unique__quotient__lemma,axiom,
% 1.03/1.21 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.03/1.21 ( 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))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_lemma__realpow__diff,axiom,
% 1.03/1.21 ! [V_y,V_n,V_p,T_a] :
% 1.03/1.21 ( class_Groups_Omonoid__mult(T_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,V_y,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_y,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p)),V_y) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_realpow__num__eq__if,axiom,
% 1.03/1.21 ! [V_m,V_n,T_a] :
% 1.03/1.21 ( class_Power_Opower(T_a)
% 1.03/1.21 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,V_m,V_n) = c_Groups_Oone__class_Oone(T_a) )
% 1.03/1.21 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Power_Opower__class_Opower(T_a,V_m,V_n) = c_Groups_Otimes__class_Otimes(T_a,V_m,c_Power_Opower__class_Opower(T_a,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pow__divides__eq__int,axiom,
% 1.03/1.21 ! [V_ba_2,V_a_2,V_nb_2] :
% 1.03/1.21 ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_a_2,V_nb_2),c_Power_Opower__class_Opower(tc_Int_Oint,V_ba_2,V_nb_2))
% 1.03/1.21 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_ba_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pow__divides__pow__int,axiom,
% 1.03/1.21 ! [V_b,V_n,V_a] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_a,V_n),c_Power_Opower__class_Opower(tc_Int_Oint,V_b,V_n))
% 1.03/1.21 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
% 1.03/1.21 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
% 1.03/1.21 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__pos__nat,axiom,
% 1.03/1.21 ! [V_m,V_n] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pow__divides__pow__nat,axiom,
% 1.03/1.21 ! [V_b,V_n,V_a] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_a,V_n),c_Power_Opower__class_Opower(tc_Nat_Onat,V_b,V_n))
% 1.03/1.21 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pow__divides__eq__nat,axiom,
% 1.03/1.21 ! [V_ba_2,V_a_2,V_nb_2] :
% 1.03/1.21 ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_a_2,V_nb_2),c_Power_Opower__class_Opower(tc_Nat_Onat,V_ba_2,V_nb_2))
% 1.03/1.21 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_ba_2) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__number__of__Bit1,axiom,
% 1.03/1.21 ! [V_v,V_w] :
% 1.03/1.21 ( ( 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))
% 1.03/1.21 => 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)) )
% 1.03/1.21 & ( ~ 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))
% 1.03/1.21 => 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)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_neg__zmod__mult__2,axiom,
% 1.03/1.21 ! [V_b,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zdvd__zmod__imp__zdvd,axiom,
% 1.03/1.21 ! [V_n,V_m,V_k] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zdvd__zmod,axiom,
% 1.03/1.21 ! [V_n,V_m,V_f] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,V_m)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,V_n)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zpower__zmod,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__eq__dvd__iff,axiom,
% 1.03/1.21 ! [V_y_2,V_nb_2,V_x_2] :
% 1.03/1.21 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_nb_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_nb_2)
% 1.03/1.21 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_nb_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__add__self2,axiom,
% 1.03/1.21 ! [V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__add__self1,axiom,
% 1.03/1.21 ! [V_a,V_b,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__add__right__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__add__left__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__add__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__simps_I2_J,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__simps_I1_J,axiom,
% 1.03/1.21 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__add__cong,axiom,
% 1.03/1.21 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 1.03/1.21 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 1.03/1.21 => 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) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__mod__iff,axiom,
% 1.03/1.21 ! [V_m_2,V_nb_2,V_k_2,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_nb_2)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_k_2,c_Divides_Odiv__class_Omod(T_a,V_m_2,V_nb_2))
% 1.03/1.21 <=> c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_m_2) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mod__cancel,axiom,
% 1.03/1.21 ! [V_a,V_b,V_c,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_b)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__mod,axiom,
% 1.03/1.21 ! [V_n,V_m,V_k,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_k,V_m)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_k,V_n)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__mod__imp__dvd,axiom,
% 1.03/1.21 ! [V_n,V_m,V_k,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n))
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_k,V_n)
% 1.03/1.21 => c_Rings_Odvd__class_Odvd(T_a,V_k,V_m) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__zero,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__self,axiom,
% 1.03/1.21 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__le__nonneg__dividend,axiom,
% 1.03/1.21 ! [V_k,V_m] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 1.03/1.21 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k),V_m) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.03/1.21 ! [V_y,V_x] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.03/1.21 => 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)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__diff__cong,axiom,
% 1.03/1.21 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Oring__div(T_a)
% 1.03/1.21 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 1.03/1.21 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_H,V_b_H),V_c) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zdiff__zmod__left,axiom,
% 1.03/1.21 ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(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_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y),V_m) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zdiff__zmod__right,axiom,
% 1.03/1.21 ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y),V_m) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__diff__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Oring__div(T_a)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__diff__left__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Oring__div(T_a)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__diff__right__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Oring__div(T_a)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__0,axiom,
% 1.03/1.21 ! [V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__by__0,axiom,
% 1.03/1.21 ! [V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__self,axiom,
% 1.03/1.21 ! [V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__self1__is__0,axiom,
% 1.03/1.21 ! [V_a,V_b,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__self2__is__0,axiom,
% 1.03/1.21 ! [V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__self2,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__self1,axiom,
% 1.03/1.21 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__eq__mod__eq__0,axiom,
% 1.03/1.21 ! [V_ba_2,V_a_2,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_ba_2)
% 1.03/1.21 <=> c_Divides_Odiv__class_Omod(T_a,V_ba_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__imp__mod__0,axiom,
% 1.03/1.21 ! [V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mod__trivial,axiom,
% 1.03/1.21 ! [V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__simps_I3_J,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__zmult1__eq,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__right__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__left__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__eq,axiom,
% 1.03/1.21 ! [V_c,V_b,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__mult1,axiom,
% 1.03/1.21 ! [V_b,V_a,V_c,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__mult2,axiom,
% 1.03/1.21 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__simps_I4_J,axiom,
% 1.03/1.21 ! [V_b,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__cong,axiom,
% 1.03/1.21 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 1.03/1.21 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 1.03/1.21 => 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) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_neg__mod__bound,axiom,
% 1.03/1.21 ! [V_a,V_b] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pos__mod__bound,axiom,
% 1.03/1.21 ! [V_a,V_b] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.03/1.21 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__eq__0__iff,axiom,
% 1.03/1.21 ! [V_d_2,V_m_2] :
% 1.03/1.21 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.21 <=> ? [B_q] : V_m_2 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_d_2,B_q) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 1.03/1.21 ! [V_y_2,V_x_2,T_a] :
% 1.03/1.21 ( ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 & class_Int_Onumber(T_a) )
% 1.03/1.21 => ( c_Rings_Odvd__class_Odvd(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.03/1.21 <=> c_Divides_Odiv__class_Omod(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_y_2),c_Int_Onumber__class_Onumber__of(T_a,V_x_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__by__1,axiom,
% 1.03/1.21 ! [V_a,T_a] :
% 1.03/1.21 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__neg__neg__trivial,axiom,
% 1.03/1.21 ! [V_b,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_neg__mod__conj,axiom,
% 1.03/1.21 ! [V_a,V_b] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => ( 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))
% 1.03/1.21 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_neg__mod__sign,axiom,
% 1.03/1.21 ! [V_a,V_b] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__pos__pos__trivial,axiom,
% 1.03/1.21 ! [V_b,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pos__mod__conj,axiom,
% 1.03/1.21 ! [V_a,V_b] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.03/1.21 => ( 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))
% 1.03/1.21 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pos__mod__sign,axiom,
% 1.03/1.21 ! [V_a,V_b] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.03/1.21 => 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)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__minus1__right,axiom,
% 1.03/1.21 ! [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) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
% 1.03/1.21 ! [V_y_2,V_x_2] :
% 1.03/1.21 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_y_2))
% 1.03/1.21 <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_y_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__pos__neg__trivial,axiom,
% 1.03/1.21 ! [V_b,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.21 => ( 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))
% 1.03/1.21 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__number__of__Bit0,axiom,
% 1.03/1.21 ! [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))) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_split__zmod,axiom,
% 1.03/1.21 ! [V_k_2,V_nb_2,V_P_2] :
% 1.03/1.21 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_nb_2,V_k_2)))
% 1.03/1.21 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.21 => hBOOL(hAPP(V_P_2,V_nb_2)) )
% 1.03/1.21 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.03/1.21 => ! [B_i,B_j] :
% 1.03/1.21 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)
% 1.03/1.21 & c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
% 1.03/1.21 & 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) )
% 1.03/1.21 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 1.03/1.21 & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => ! [B_i,B_j] :
% 1.03/1.21 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)
% 1.03/1.21 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 & 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) )
% 1.03/1.21 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmult2__lemma__aux3,axiom,
% 1.03/1.21 ! [V_q,V_b,V_r,V_c] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmult2__lemma__aux4,axiom,
% 1.03/1.21 ! [V_q,V_b,V_r,V_c] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmult2__lemma__aux1,axiom,
% 1.03/1.21 ! [V_q,V_r,V_b,V_c] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmult2__lemma__aux2,axiom,
% 1.03/1.21 ! [V_q,V_r,V_b,V_c] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => 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)) ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_divmod__int__rel__mod__eq,axiom,
% 1.03/1.21 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 1.03/1.21 ( 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)
% 1.03/1.21 => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.03/1.21 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_b_1) ) )
% 1.03/1.21 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
% 1.03/1.21 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_y)
% 1.03/1.21 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
% 1.03/1.21 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_neq__one__mod__two,axiom,
% 1.03/1.21 ! [V_x_2] :
% 1.03/1.21 ( 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)
% 1.03/1.21 <=> 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_even__def,axiom,
% 1.03/1.21 ! [V_x_2] :
% 1.03/1.21 ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,V_x_2)
% 1.03/1.21 <=> 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) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_zmod__minus1,axiom,
% 1.03/1.21 ! [V_b] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),V_b) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_b,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pos__zmod__mult__2,axiom,
% 1.03/1.21 ! [V_b,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.21 => 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))) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_neg__zdiv__mult__2,axiom,
% 1.03/1.21 ! [V_b,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.21 => c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_b,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_pos__zdiv__mult__2,axiom,
% 1.03/1.21 ! [V_b,V_a] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.21 => c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_a) ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__mult__self4,axiom,
% 1.03/1.21 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__less,axiom,
% 1.03/1.21 ! [V_n,V_m] :
% 1.03/1.21 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.21 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 1.03/1.21
% 1.03/1.21 fof(fact_mod__geq,axiom,
% 1.03/1.22 ! [V_n,V_m] :
% 1.03/1.22 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zdiv__zadd1__eq,axiom,
% 1.03/1.22 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__if,axiom,
% 1.03/1.22 ! [V_n,V_m] :
% 1.03/1.22 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 1.03/1.22 & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.03/1.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_DIVISION__BY__ZERO,axiom,
% 1.03/1.22 ! [V_a] :
% 1.03/1.22 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.22 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__div__trivial,axiom,
% 1.03/1.22 ! [V_b,V_a,T_a] :
% 1.03/1.22 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.22 => c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zmod__zdiv__trivial,axiom,
% 1.03/1.22 ! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_le__mod__geq,axiom,
% 1.03/1.22 ! [V_m,V_n] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.03/1.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__less__eq__dividend,axiom,
% 1.03/1.22 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_m) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__mult__distrib2,axiom,
% 1.03/1.22 ! [V_n,V_m,V_k] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__mult__distrib,axiom,
% 1.03/1.22 ! [V_k,V_n,V_m] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 1.03/1.22 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__Suc,axiom,
% 1.03/1.22 ! [V_n,V_m] :
% 1.03/1.22 ( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 1.03/1.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.03/1.22 & ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 1.03/1.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__1,axiom,
% 1.03/1.22 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__less__divisor,axiom,
% 1.03/1.22 ! [V_m,V_n] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.22 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__eq__0__iff,axiom,
% 1.03/1.22 ! [V_d_2,V_m_2] :
% 1.03/1.22 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.03/1.22 <=> ? [B_q] : V_m_2 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_d_2,B_q) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__mult__self3,axiom,
% 1.03/1.22 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_mod__le__divisor,axiom,
% 1.03/1.22 ! [V_m,V_n] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.03/1.22 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_odd__nat__mod__two__eq__one,axiom,
% 1.03/1.22 ! [V_x] :
% 1.03/1.22 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.03/1.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_even__nat__mod__two__eq__zero,axiom,
% 1.03/1.22 ! [V_x] :
% 1.03/1.22 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x)
% 1.03/1.22 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_odd__nat__equiv__def,axiom,
% 1.03/1.22 ! [V_x_2] :
% 1.03/1.22 ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.22 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_even__nat__equiv__def,axiom,
% 1.03/1.22 ! [V_x_2] :
% 1.03/1.22 ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
% 1.03/1.22 <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_div__by__1,axiom,
% 1.03/1.22 ! [V_a,T_a] :
% 1.03/1.22 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.22 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zdiv__self,axiom,
% 1.03/1.22 ! [V_a] :
% 1.03/1.22 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.22 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_div__self,axiom,
% 1.03/1.22 ! [V_a,T_a] :
% 1.03/1.22 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.22 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.03/1.22 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zdiv__mono1__neg,axiom,
% 1.03/1.22 ! [V_b,V_a_H,V_a] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.22 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zdiv__mono1,axiom,
% 1.03/1.22 ! [V_b,V_a_H,V_a] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.03/1.22 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_div__neg__neg__trivial,axiom,
% 1.03/1.22 ! [V_b,V_a] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
% 1.03/1.22 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zdiv__mono2__neg,axiom,
% 1.03/1.22 ! [V_b,V_b_H,V_a] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.03/1.22 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_div__nonpos__pos__le0,axiom,
% 1.03/1.22 ! [V_b,V_a] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
% 1.03/1.22 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 1.03/1.22 ! [V_a_2,V_ba_2] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_ba_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_ba_2))
% 1.03/1.22 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_div__pos__pos__trivial,axiom,
% 1.03/1.22 ! [V_b,V_a] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
% 1.03/1.22 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_div__nonneg__neg__le0,axiom,
% 1.03/1.22 ! [V_b,V_a] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.22 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zdiv__mono2,axiom,
% 1.03/1.22 ! [V_b,V_b_H,V_a] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.03/1.22 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)) ) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 1.03/1.22 ! [V_ba_2,V_a_2] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_ba_2))
% 1.03/1.22 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_ba_2,V_a_2)
% 1.03/1.22 & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ba_2) ) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 1.03/1.22 ! [V_i_2,V_k_2] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
% 1.03/1.22 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 1.03/1.22 ! [V_a_2,V_ba_2] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ba_2)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_ba_2))
% 1.03/1.22 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zdiv__eq__0__iff,axiom,
% 1.03/1.22 ! [V_k_2,V_i_2] :
% 1.03/1.22 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.22 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.03/1.22 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2)
% 1.03/1.22 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2) )
% 1.03/1.22 | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.03/1.22 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2) ) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_int__div__less__self,axiom,
% 1.03/1.22 ! [V_k,V_x] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.03/1.22 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
% 1.03/1.22 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_zdiv__zmult2__eq,axiom,
% 1.03/1.22 ! [V_b,V_a,V_c] :
% 1.03/1.22 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
% 1.03/1.22 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b,V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_div__power,axiom,
% 1.03/1.22 ! [V_n,V_x,V_y,T_a] :
% 1.03/1.22 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.22 => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
% 1.03/1.22 => c_Power_Opower__class_Opower(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y),V_n) = c_Divides_Odiv__class_Odiv(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n),c_Power_Opower__class_Opower(T_a,V_y,V_n)) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_div__add,axiom,
% 1.03/1.22 ! [V_y,V_x,V_z,T_a] :
% 1.03/1.22 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.22 => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_x)
% 1.03/1.22 => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_y)
% 1.03/1.22 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)) ) ) ) ).
% 1.03/1.22
% 1.03/1.22 fof(fact_dvd__mult__div__cancel,axiom,
% 1.03/1.22 ! [V_b,V_a,T_a] :
% 1.03/1.22 ( class_Divides_Osemiring__div(T_a)
% 1.03/1.22 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 1.03/1.22 => c_Groups_Otimes__class_Otimes(T_a,V_a,c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ) ).
% 1.03/1.22
% 1.03/1.22 %----Arity declarations (178)
% 1.03/1.22 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.03/1.22 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.03/1.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 1.03/1.22 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 1.03/1.22 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 1.03/1.22 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 1.03/1.22 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 1.03/1.22 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 1.03/1.22 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 1.03/1.22 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 1.03/1.22 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 1.03/1.22 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 1.03/1.22 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 1.03/1.22 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 1.03/1.22 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 1.03/1.22 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 1.03/1.22 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 1.03/1.22 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 1.03/1.22 class_Orderings_Olinorder(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 1.03/1.22 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 1.03/1.22 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 1.03/1.22 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 1.03/1.22 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 1.03/1.22 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 1.03/1.22 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 1.03/1.22 class_Divides_Oring__div(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 1.03/1.22 class_Rings_Omult__zero(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 1.03/1.22 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 1.03/1.22 class_Int_Oring__char__0(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 1.03/1.22 class_Int_Onumber__ring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 1.03/1.22 class_Rings_Osemiring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 1.03/1.22 class_Rings_Oring__1(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Power_Opower,axiom,
% 1.03/1.22 class_Power_Opower(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 1.03/1.22 class_Groups_Ozero(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oring,axiom,
% 1.03/1.22 class_Rings_Oring(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 1.03/1.22 class_Rings_Oidom(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Int_Onumber,axiom,
% 1.03/1.22 class_Int_Onumber(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Groups_Oone,axiom,
% 1.03/1.22 class_Groups_Oone(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 1.03/1.22 class_Rings_Odvd(tc_Int_Oint) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.03/1.22 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.03/1.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 1.03/1.22 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 1.03/1.22 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 1.03/1.22 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 1.03/1.22 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 1.03/1.22 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 1.03/1.22 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 1.03/1.22 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 1.03/1.22 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 1.03/1.22 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 1.03/1.22 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 1.03/1.22 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 1.03/1.22 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 1.03/1.22 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 1.03/1.22 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 1.03/1.22 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 1.03/1.22 class_Rings_Osemiring(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Power_Opower,axiom,
% 1.03/1.22 class_Power_Opower(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 1.03/1.22 class_Groups_Ozero(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 1.03/1.22 class_Int_Onumber(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 1.03/1.22 class_Groups_Oone(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 1.03/1.22 class_Rings_Odvd(tc_Nat_Onat) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.03/1.22 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.03/1.22 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 1.03/1.22 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 1.03/1.22 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 1.03/1.22 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 1.03/1.22 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 1.03/1.22 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 1.03/1.22 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 1.03/1.22 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 1.03/1.22 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 1.03/1.22 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 1.03/1.22 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 1.03/1.22 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 1.03/1.22 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 1.03/1.22 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 1.03/1.22 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 1.03/1.22 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 1.03/1.22 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 1.03/1.22 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 1.03/1.22 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 1.03/1.22 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 1.03/1.22 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 1.03/1.22 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 1.03/1.22 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
% 1.03/1.22 class_Rings_Osemiring__1(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 1.03/1.22 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 1.03/1.22 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 1.03/1.22 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 1.03/1.22 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 1.03/1.22 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
% 1.03/1.22 class_Int_Onumber__ring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 1.03/1.22 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 1.03/1.22 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 1.03/1.22 class_Power_Opower(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 1.03/1.22 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 1.03/1.22 class_Rings_Oring(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 1.03/1.22 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Int_Onumber,axiom,
% 1.03/1.22 class_Int_Onumber(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 1.03/1.22 class_Groups_Oone(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
% 1.03/1.22 class_Rings_Odvd(tc_RealDef_Oreal) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.03/1.22 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 1.03/1.22 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 1.03/1.22 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 1.03/1.22 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 1.03/1.22 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 1.03/1.22 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 1.03/1.22 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 1.03/1.22 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 1.03/1.22 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 1.03/1.22 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 1.03/1.22 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 1.03/1.22 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 1.03/1.22 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 1.03/1.22 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
% 1.03/1.22 class_Rings_Osemiring__1(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 1.03/1.22 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 1.03/1.22 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 1.03/1.22 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 1.03/1.22 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 1.03/1.22 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
% 1.03/1.22 class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 1.03/1.22 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 1.03/1.22 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 1.03/1.22 class_Power_Opower(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 1.03/1.22 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 1.03/1.22 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 1.03/1.22 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
% 1.03/1.22 class_Int_Onumber(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 1.03/1.22 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
% 1.03/1.22 class_Rings_Odvd(tc_Complex_Ocomplex) ).
% 1.03/1.22
% 1.03/1.22 %----Conjectures (2)
% 1.03/1.22 fof(conj_0,hypothesis,
% 1.03/1.22 ( ? [B_m] : v_na____ = 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)
% 1.03/1.22 => v_thesis____ ) ).
% 1.03/1.22
% 1.03/1.22 fof(conj_1,conjecture,
% 1.03/1.22 v_thesis____ ).
% 1.03/1.22
% 1.03/1.22 %------------------------------------------------------------------------------
% 1.03/1.22 %-------------------------------------------
% 1.03/1.22 % Proof found
% 1.03/1.22 % SZS status Theorem for theBenchmark
% 1.03/1.22 % SZS output start Proof
% 1.03/1.22 %ClaNum:1761(EqnAxiom:143)
% 1.03/1.22 %VarNum:8532(SingletonVarNum:2969)
% 1.03/1.22 %MaxLitNum:7
% 1.03/1.22 %MaxfuncDepth:8
% 1.03/1.22 %SharedTerms:262
% 1.03/1.22 %goalClause: 478
% 1.03/1.22 %singleGoalClaCount:1
% 1.03/1.22 [145]P1(a1)
% 1.03/1.22 [146]P1(a12)
% 1.03/1.22 [147]P1(a37)
% 1.03/1.22 [148]P28(a1)
% 1.03/1.22 [149]P28(a12)
% 1.03/1.22 [150]P28(a37)
% 1.03/1.22 [151]P2(a38)
% 1.03/1.22 [152]P2(a1)
% 1.03/1.22 [153]P2(a12)
% 1.03/1.22 [154]P2(a37)
% 1.03/1.22 [155]P29(a38)
% 1.03/1.22 [156]P29(a1)
% 1.03/1.22 [157]P29(a12)
% 1.03/1.22 [158]P29(a37)
% 1.03/1.22 [159]P30(a38)
% 1.03/1.22 [160]P30(a1)
% 1.03/1.22 [161]P30(a12)
% 1.03/1.22 [162]P30(a37)
% 1.03/1.22 [163]P31(a12)
% 1.03/1.22 [164]P31(a37)
% 1.03/1.22 [165]P48(a1)
% 1.03/1.22 [166]P48(a12)
% 1.03/1.22 [167]P48(a37)
% 1.03/1.22 [168]P49(a38)
% 1.03/1.22 [169]P49(a1)
% 1.03/1.22 [170]P49(a12)
% 1.03/1.22 [171]P49(a37)
% 1.03/1.22 [172]P3(a38)
% 1.03/1.22 [173]P3(a1)
% 1.03/1.22 [174]P3(a12)
% 1.03/1.22 [175]P3(a37)
% 1.03/1.22 [176]P37(a38)
% 1.03/1.22 [177]P37(a1)
% 1.03/1.22 [178]P37(a37)
% 1.03/1.22 [179]P38(a1)
% 1.03/1.22 [180]P38(a37)
% 1.03/1.22 [181]P42(a1)
% 1.03/1.22 [182]P42(a37)
% 1.03/1.22 [183]P43(a1)
% 1.03/1.22 [184]P43(a37)
% 1.03/1.22 [185]P39(a38)
% 1.03/1.22 [186]P39(a1)
% 1.03/1.22 [187]P39(a12)
% 1.03/1.22 [188]P39(a37)
% 1.03/1.22 [189]P4(a1)
% 1.03/1.22 [190]P4(a37)
% 1.03/1.22 [191]P57(a38)
% 1.03/1.22 [192]P57(a1)
% 1.03/1.22 [193]P57(a12)
% 1.03/1.22 [194]P57(a37)
% 1.03/1.22 [195]P34(a38)
% 1.03/1.22 [196]P34(a1)
% 1.03/1.22 [197]P34(a12)
% 1.03/1.22 [198]P34(a37)
% 1.03/1.22 [199]P58(a38)
% 1.03/1.22 [200]P58(a1)
% 1.03/1.22 [201]P58(a12)
% 1.03/1.22 [202]P58(a37)
% 1.03/1.22 [203]P40(a1)
% 1.03/1.22 [204]P40(a12)
% 1.03/1.22 [205]P40(a37)
% 1.03/1.22 [206]P59(a38)
% 1.03/1.22 [207]P59(a1)
% 1.03/1.22 [208]P59(a12)
% 1.03/1.22 [209]P59(a37)
% 1.03/1.22 [210]P41(a38)
% 1.03/1.22 [211]P41(a1)
% 1.03/1.22 [212]P41(a37)
% 1.03/1.22 [213]P44(a38)
% 1.03/1.22 [214]P44(a1)
% 1.03/1.22 [215]P44(a37)
% 1.03/1.22 [216]P32(a38)
% 1.03/1.22 [217]P32(a1)
% 1.03/1.22 [218]P32(a12)
% 1.03/1.22 [219]P32(a37)
% 1.03/1.22 [220]P61(a38)
% 1.03/1.22 [221]P61(a1)
% 1.03/1.22 [222]P61(a12)
% 1.03/1.22 [223]P61(a37)
% 1.03/1.22 [224]P50(a1)
% 1.03/1.22 [225]P50(a12)
% 1.03/1.22 [226]P50(a37)
% 1.03/1.22 [227]P60(a38)
% 1.03/1.22 [228]P60(a1)
% 1.03/1.22 [229]P60(a12)
% 1.03/1.22 [230]P60(a37)
% 1.03/1.22 [231]P21(a38)
% 1.03/1.22 [232]P21(a1)
% 1.03/1.22 [233]P21(a12)
% 1.03/1.22 [234]P21(a37)
% 1.03/1.22 [235]P5(a38)
% 1.03/1.22 [236]P5(a1)
% 1.03/1.22 [237]P5(a12)
% 1.03/1.22 [238]P5(a37)
% 1.03/1.22 [239]P6(a38)
% 1.03/1.22 [240]P6(a1)
% 1.03/1.22 [241]P6(a12)
% 1.03/1.22 [242]P6(a37)
% 1.03/1.22 [243]P15(a38)
% 1.03/1.22 [244]P15(a1)
% 1.03/1.22 [245]P15(a12)
% 1.03/1.22 [246]P15(a37)
% 1.03/1.22 [247]P16(a38)
% 1.03/1.22 [248]P16(a1)
% 1.03/1.22 [249]P16(a12)
% 1.03/1.22 [250]P16(a37)
% 1.03/1.22 [251]P20(a38)
% 1.03/1.22 [252]P20(a1)
% 1.03/1.22 [253]P20(a12)
% 1.03/1.22 [254]P20(a37)
% 1.03/1.22 [255]P17(a38)
% 1.03/1.22 [256]P17(a1)
% 1.03/1.22 [257]P17(a12)
% 1.03/1.22 [258]P17(a37)
% 1.03/1.22 [259]P22(a38)
% 1.03/1.22 [260]P22(a1)
% 1.03/1.22 [261]P22(a37)
% 1.03/1.22 [262]P26(a38)
% 1.03/1.22 [263]P26(a1)
% 1.03/1.22 [264]P26(a37)
% 1.03/1.22 [265]P18(a38)
% 1.03/1.22 [266]P18(a1)
% 1.03/1.22 [267]P18(a12)
% 1.03/1.22 [268]P18(a37)
% 1.03/1.22 [269]P27(a38)
% 1.03/1.22 [270]P27(a1)
% 1.03/1.22 [271]P27(a37)
% 1.03/1.22 [272]P23(a38)
% 1.03/1.22 [273]P23(a1)
% 1.03/1.22 [274]P23(a12)
% 1.03/1.22 [275]P23(a37)
% 1.03/1.22 [276]P7(a1)
% 1.03/1.22 [277]P7(a12)
% 1.03/1.22 [278]P7(a37)
% 1.03/1.22 [279]P24(a1)
% 1.03/1.22 [280]P24(a37)
% 1.03/1.22 [281]P51(a1)
% 1.03/1.22 [282]P51(a12)
% 1.03/1.22 [283]P51(a37)
% 1.03/1.22 [284]P52(a1)
% 1.03/1.22 [285]P52(a37)
% 1.03/1.22 [286]P19(a1)
% 1.03/1.22 [287]P19(a12)
% 1.03/1.22 [288]P19(a37)
% 1.03/1.22 [289]P35(a1)
% 1.03/1.22 [290]P35(a12)
% 1.03/1.22 [291]P35(a37)
% 1.03/1.22 [292]P25(a38)
% 1.03/1.22 [293]P25(a1)
% 1.03/1.22 [294]P25(a37)
% 1.03/1.22 [295]P55(a1)
% 1.03/1.22 [296]P55(a12)
% 1.03/1.22 [297]P55(a37)
% 1.03/1.22 [298]P45(a1)
% 1.03/1.22 [299]P45(a37)
% 1.03/1.22 [300]P47(a1)
% 1.03/1.22 [301]P47(a37)
% 1.03/1.22 [302]P53(a38)
% 1.03/1.22 [303]P53(a1)
% 1.03/1.22 [304]P53(a37)
% 1.03/1.22 [305]P56(a38)
% 1.03/1.22 [306]P56(a1)
% 1.03/1.22 [307]P56(a37)
% 1.03/1.22 [308]P54(a38)
% 1.03/1.22 [309]P54(a1)
% 1.03/1.22 [310]P54(a37)
% 1.03/1.22 [311]P33(a38)
% 1.03/1.22 [312]P33(a1)
% 1.03/1.22 [313]P33(a37)
% 1.03/1.22 [314]P36(a1)
% 1.03/1.22 [315]P36(a12)
% 1.03/1.22 [316]P36(a37)
% 1.03/1.22 [317]P46(a38)
% 1.03/1.22 [318]P46(a1)
% 1.03/1.22 [319]P46(a37)
% 1.03/1.22 [320]P8(a38)
% 1.03/1.22 [321]P8(a1)
% 1.03/1.22 [322]P9(a1)
% 1.03/1.22 [323]P10(a38,a39)
% 1.03/1.22 [331]P11(a1,a11,a10)
% 1.03/1.22 [333]P13(a1,a11,a10)
% 1.03/1.22 [477]~E(a11,a10)
% 1.03/1.22 [478]~P62(a500)
% 1.03/1.22 [486]~P11(a1,a10,a10)
% 1.03/1.22 [487]~P11(a1,a10,a11)
% 1.03/1.22 [488]~P11(a1,a11,a11)
% 1.03/1.22 [489]~P13(a1,a10,a11)
% 1.03/1.22 [144]E(f2(a1),a10)
% 1.03/1.22 [326]E(f13(a1,a10),f2(a1))
% 1.03/1.22 [327]E(f13(a38,a10),f2(a38))
% 1.03/1.22 [328]P10(a38,f2(a38))
% 1.03/1.22 [329]P10(a1,f2(a1))
% 1.03/1.22 [343]P11(a1,a11,f2(a1))
% 1.03/1.22 [366]P11(a1,f2(a1),f8(a1))
% 1.03/1.22 [368]P13(a1,f2(a1),f8(a1))
% 1.03/1.22 [371]P13(a1,f2(a1),f13(a1,a10))
% 1.03/1.22 [479]~E(f2(a38),a39)
% 1.03/1.22 [480]~E(f2(a38),a40)
% 1.03/1.22 [481]~E(f8(a1),f2(a1))
% 1.03/1.22 [482]~E(f8(a37),f2(a37))
% 1.03/1.22 [483]~P10(a38,f8(a38))
% 1.03/1.22 [484]~P10(a1,f8(a1))
% 1.03/1.22 [485]~E(f13(a1,a11),f13(a1,a10))
% 1.03/1.22 [494]~P11(a1,a10,f2(a1))
% 1.03/1.22 [385]E(f3(a1,f3(a1,f8(a1),a11),a11),a11)
% 1.03/1.22 [417]E(f13(a1,f3(a1,f3(a1,f8(a1),a10),a10)),f8(a1))
% 1.03/1.22 [418]E(f13(a38,f3(a1,f3(a1,f8(a1),a10),a10)),f8(a38))
% 1.03/1.22 [422]E(f13(a38,f3(a1,f3(a1,f8(a1),a10),a10)),f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [457]E(f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f3(a38,f8(a38),f8(a38)))
% 1.03/1.22 [459]E(f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38)))
% 1.03/1.22 [461]E(f13(a38,f3(a1,f3(a1,f8(a1),f3(a1,f3(a1,f8(a1),a10),a10)),f3(a1,f3(a1,f8(a1),a10),a10))),f3(a38,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38)),f8(a38)))
% 1.03/1.22 [463]P11(a38,f2(a38),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))
% 1.03/1.22 [464]P13(a1,f2(a1),f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))
% 1.03/1.22 [471]P13(a1,f2(a1),f13(a1,f3(a1,f3(a1,f8(a1),f3(a1,f3(a1,f8(a1),a10),a10)),f3(a1,f3(a1,f8(a1),a10),a10))))
% 1.03/1.22 [462]E(f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),a15),a39)
% 1.03/1.22 [339]P14(a38,x3391,x3391)
% 1.03/1.22 [340]P13(a38,x3401,x3401)
% 1.03/1.22 [341]P13(a1,x3411,x3411)
% 1.03/1.22 [342]P13(a37,x3421,x3421)
% 1.03/1.22 [493]~P11(a38,x4931,x4931)
% 1.03/1.22 [324]E(f13(a1,x3241),x3241)
% 1.03/1.22 [335]E(f9(a1,a10,x3351),a10)
% 1.03/1.22 [336]E(f3(a1,x3361,a10),x3361)
% 1.03/1.22 [337]E(f4(a1,x3371,a10),x3371)
% 1.03/1.22 [338]E(f3(a1,a10,x3381),x3381)
% 1.03/1.22 [344]E(f4(a38,x3441,x3441),f2(a38))
% 1.03/1.22 [345]E(f5(a1,x3451,x3451),f2(a1))
% 1.03/1.22 [346]P14(a38,x3461,f2(a38))
% 1.03/1.22 [347]P14(a38,f8(a38),x3471)
% 1.03/1.22 [349]P13(a38,f2(a38),x3491)
% 1.03/1.22 [378]P13(a38,x3781,f9(a38,x3781,x3781))
% 1.03/1.22 [491]~E(f3(a1,x4911,x4911),a11)
% 1.03/1.22 [497]~P11(a38,x4971,f2(a38))
% 1.03/1.22 [350]E(f9(a38,x3501,f8(a38)),x3501)
% 1.03/1.22 [351]E(f9(a1,x3511,f8(a1)),x3511)
% 1.03/1.22 [352]E(f3(a38,x3521,f2(a38)),x3521)
% 1.03/1.22 [353]E(f3(a1,x3531,f2(a1)),x3531)
% 1.03/1.22 [354]E(f4(a38,x3541,f2(a38)),x3541)
% 1.03/1.22 [355]E(f5(a1,x3551,f2(a1)),x3551)
% 1.03/1.22 [356]E(f9(a38,f8(a38),x3561),x3561)
% 1.03/1.22 [357]E(f9(a1,f8(a1),x3571),x3571)
% 1.03/1.22 [358]E(f9(a37,f8(a37),x3581),x3581)
% 1.03/1.22 [359]E(f3(a38,f2(a38),x3591),x3591)
% 1.03/1.22 [360]E(f3(a1,f2(a1),x3601),x3601)
% 1.03/1.22 [361]E(f9(a38,x3611,f2(a38)),f2(a38))
% 1.03/1.22 [362]E(f6(a1,x3621,f2(a1)),f2(a1))
% 1.03/1.22 [363]E(f9(a38,f2(a38),x3631),f2(a38))
% 1.03/1.22 [364]E(f4(a38,f2(a38),x3641),f2(a38))
% 1.03/1.22 [365]E(f5(a1,f2(a1),x3651),f2(a1))
% 1.03/1.22 [370]E(f5(a1,x3701,f13(a1,a11)),f2(a1))
% 1.03/1.22 [388]P11(a38,x3881,f3(a38,x3881,f8(a38)))
% 1.03/1.22 [389]P11(a38,f2(a38),f3(a38,x3891,f8(a38)))
% 1.03/1.22 [391]P14(a38,f3(a38,f2(a38),f8(a38)),x3911)
% 1.03/1.22 [419]P13(a38,x4191,f9(a38,x4191,f9(a38,x4191,x4191)))
% 1.03/1.22 [423]E(f3(a1,f4(a1,a10,x4231),f4(a1,a10,x4231)),f4(a1,a10,f3(a1,x4231,x4231)))
% 1.03/1.22 [446]E(f3(a1,f3(a1,f8(a1),f4(a1,a11,x4461)),f4(a1,a11,x4461)),f4(a1,a11,f3(a1,x4461,x4461)))
% 1.03/1.22 [499]~E(f3(a38,x4991,f8(a38)),x4991)
% 1.03/1.22 [505]~E(f3(a38,x5051,f8(a38)),f2(a38))
% 1.03/1.22 [510]~P13(a38,f3(a38,x5101,f8(a38)),x5101)
% 1.03/1.22 [392]E(f5(a38,x3921,f3(a38,f2(a38),f8(a38))),f2(a38))
% 1.03/1.22 [395]E(f14(a38,f3(a38,f2(a38),f8(a38)),x3951),f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [509]~E(f3(a1,f3(a1,f8(a1),x5091),x5091),a10)
% 1.03/1.22 [511]~E(f3(a1,f3(a1,f8(a1),x5111),x5111),f2(a1))
% 1.03/1.22 [447]E(f4(a1,a11,f3(a1,f3(a1,f8(a1),x4471),x4471)),f3(a1,f4(a1,a11,x4471),f4(a1,a11,x4471)))
% 1.03/1.22 [450]E(f3(a1,f3(a1,f8(a1),f4(a1,a11,x4501)),f4(a1,a11,x4501)),f4(a1,a10,f3(a1,f3(a1,f8(a1),x4501),x4501)))
% 1.03/1.22 [465]E(f14(a12,f7(x4651),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),x4651)
% 1.03/1.22 [466]E(f9(a38,x4661,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f3(a38,x4661,x4661))
% 1.03/1.22 [467]E(f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x4671),f3(a38,x4671,x4671))
% 1.03/1.22 [468]E(f3(a38,x4681,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f3(a38,f3(a38,x4681,f8(a38)),f8(a38)))
% 1.03/1.22 [469]E(f3(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x4691),f3(a38,f3(a38,x4691,f8(a38)),f8(a38)))
% 1.03/1.22 [472]E(f3(a38,f13(a38,f3(a1,f3(a1,f8(a1),f3(a1,f3(a1,f8(a1),a10),a10)),f3(a1,f3(a1,f8(a1),a10),a10))),x4721),f3(a38,f3(a38,f3(a38,x4721,f8(a38)),f8(a38)),f8(a38)))
% 1.03/1.22 [473]P13(a37,f8(a37),f14(a37,f13(a37,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x4731))
% 1.03/1.22 [474]E(f9(a37,f13(a37,f3(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)),f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(a37,x4741,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f14(a37,f9(a37,f13(a37,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x4741),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.22 [372]E(f9(a38,x3721,x3722),f9(a38,x3722,x3721))
% 1.03/1.22 [373]E(f9(a1,x3731,x3732),f9(a1,x3732,x3731))
% 1.03/1.22 [374]E(f9(a37,x3741,x3742),f9(a37,x3742,x3741))
% 1.03/1.22 [375]E(f3(a38,x3751,x3752),f3(a38,x3752,x3751))
% 1.03/1.22 [376]E(f3(a1,x3761,x3762),f3(a1,x3762,x3761))
% 1.03/1.22 [379]P13(a38,x3791,f3(a38,x3792,x3791))
% 1.03/1.22 [380]P13(a38,x3801,f3(a38,x3801,x3802))
% 1.03/1.22 [381]P13(a38,f4(a38,x3811,x3812),x3811)
% 1.03/1.22 [382]P13(a38,f5(a38,x3821,x3822),x3821)
% 1.03/1.22 [506]~P11(a38,f3(a38,x5061,x5062),x5062)
% 1.03/1.22 [507]~P11(a38,f3(a38,x5071,x5072),x5071)
% 1.03/1.22 [383]E(f4(a38,f3(a38,x3831,x3832),x3832),x3831)
% 1.03/1.22 [384]E(f4(a38,f3(a38,x3841,x3842),x3841),x3842)
% 1.03/1.22 [386]E(f4(a38,x3861,f3(a38,x3861,x3862)),f2(a38))
% 1.03/1.22 [387]E(f6(a1,f5(a1,x3871,x3872),x3872),f2(a1))
% 1.03/1.22 [393]E(f9(a1,f13(a1,x3931),f13(a1,x3932)),f13(a1,f9(a1,x3931,x3932)))
% 1.03/1.22 [394]E(f3(a1,f13(a1,x3941),f13(a1,x3942)),f13(a1,f3(a1,x3941,x3942)))
% 1.03/1.22 [396]P11(a38,f4(a38,x3961,x3962),f3(a38,x3961,f8(a38)))
% 1.03/1.22 [420]P11(a38,x4201,f3(a38,f3(a38,x4202,x4201),f8(a38)))
% 1.03/1.22 [421]P11(a38,x4211,f3(a38,f3(a38,x4211,x4212),f8(a38)))
% 1.03/1.22 [443]E(f3(a1,f3(a1,x4431,x4431),f3(a1,x4432,x4432)),f3(a1,f3(a1,x4431,x4432),f3(a1,x4431,x4432)))
% 1.03/1.22 [444]E(f4(a1,f3(a1,x4441,x4441),f3(a1,x4442,x4442)),f3(a1,f4(a1,x4441,x4442),f4(a1,x4441,x4442)))
% 1.03/1.22 [454]E(f3(a1,f3(a1,f3(a1,f8(a1),x4541),x4541),f3(a1,x4542,x4542)),f3(a1,f3(a1,f8(a1),f3(a1,x4541,x4542)),f3(a1,x4541,x4542)))
% 1.03/1.22 [455]E(f4(a1,f3(a1,f3(a1,f8(a1),x4551),x4551),f3(a1,x4552,x4552)),f3(a1,f3(a1,f8(a1),f4(a1,x4551,x4552)),f4(a1,x4551,x4552)))
% 1.03/1.22 [409]E(f9(a38,x4091,f3(a38,x4092,f8(a38))),f3(a38,x4091,f9(a38,x4091,x4092)))
% 1.03/1.22 [410]E(f9(a38,f3(a38,x4101,f8(a38)),x4102),f3(a38,x4102,f9(a38,x4101,x4102)))
% 1.03/1.22 [412]E(f3(a38,f3(a38,x4121,f8(a38)),x4122),f3(a38,f3(a38,x4121,x4122),f8(a38)))
% 1.03/1.22 [413]E(f4(a38,f4(a38,x4131,f8(a38)),x4132),f4(a38,x4131,f3(a38,x4132,f8(a38))))
% 1.03/1.22 [414]E(f3(a38,f3(a38,x4141,f8(a38)),x4142),f3(a38,x4141,f3(a38,x4142,f8(a38))))
% 1.03/1.22 [445]E(f5(a38,f3(a38,f5(a38,x4451,x4452),f8(a38)),x4452),f5(a38,f3(a38,x4451,f8(a38)),x4452))
% 1.03/1.22 [470]E(f5(a1,f13(a1,f3(a1,x4701,x4701)),f13(a1,f3(a1,x4702,x4702))),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f5(a1,f13(a1,x4701),f13(a1,x4702))))
% 1.03/1.22 [513]~E(f3(a1,x5131,x5131),f3(a1,f3(a1,f8(a1),x5132),x5132))
% 1.03/1.22 [452]E(f3(a1,f3(a1,f9(a1,x4521,x4522),f9(a1,x4521,x4522)),x4522),f9(a1,f3(a1,f3(a1,f8(a1),x4521),x4521),x4522))
% 1.03/1.22 [453]E(f3(a1,f3(a1,x4531,x4531),f3(a1,f3(a1,f8(a1),x4532),x4532)),f3(a1,f3(a1,f8(a1),f3(a1,x4531,x4532)),f3(a1,x4531,x4532)))
% 1.03/1.22 [456]E(f4(a1,f3(a1,f3(a1,f8(a1),x4561),x4561),f3(a1,f3(a1,f8(a1),x4562),x4562)),f3(a1,f4(a1,x4561,x4562),f4(a1,x4561,x4562)))
% 1.03/1.22 [475]E(f3(a37,f3(a37,f14(a37,x4751,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(a37,x4752,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f9(a37,f9(a37,f13(a37,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x4751),x4752)),f14(a37,f3(a37,x4751,x4752),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.22 [397]E(f3(a38,x3971,f3(a38,x3972,x3973)),f3(a38,x3972,f3(a38,x3971,x3973)))
% 1.03/1.22 [398]E(f3(a1,x3981,f3(a1,x3982,x3983)),f3(a1,x3982,f3(a1,x3981,x3983)))
% 1.03/1.22 [399]E(f9(a38,f9(a38,x3991,x3992),x3993),f9(a38,x3991,f9(a38,x3992,x3993)))
% 1.03/1.22 [400]E(f9(a1,f9(a1,x4001,x4002),x4003),f9(a1,x4001,f9(a1,x4002,x4003)))
% 1.03/1.22 [401]E(f9(a37,f9(a37,x4011,x4012),x4013),f9(a37,x4011,f9(a37,x4012,x4013)))
% 1.03/1.22 [402]E(f14(a1,f14(a1,x4021,x4022),x4023),f14(a1,x4021,f9(a38,x4022,x4023)))
% 1.03/1.22 [403]E(f3(a38,f3(a38,x4031,x4032),x4033),f3(a38,x4031,f3(a38,x4032,x4033)))
% 1.03/1.22 [404]E(f3(a1,f3(a1,x4041,x4042),x4043),f3(a1,x4041,f3(a1,x4042,x4043)))
% 1.03/1.22 [405]E(f4(a38,f4(a38,x4051,x4052),x4053),f4(a38,x4051,f3(a38,x4052,x4053)))
% 1.03/1.22 [406]E(f4(a38,f4(a38,x4061,x4062),x4063),f4(a38,f4(a38,x4061,x4063),x4062))
% 1.03/1.22 [407]E(f4(a38,f3(a38,x4071,x4072),f3(a38,x4073,x4072)),f4(a38,x4071,x4073))
% 1.03/1.22 [408]E(f4(a38,f3(a38,x4081,x4082),f3(a38,x4081,x4083)),f4(a38,x4082,x4083))
% 1.03/1.22 [425]E(f3(a38,f9(a38,x4251,x4252),f9(a38,x4251,x4253)),f9(a38,x4251,f3(a38,x4252,x4253)))
% 1.03/1.22 [426]E(f4(a38,f9(a38,x4261,x4262),f9(a38,x4261,x4263)),f9(a38,x4261,f4(a38,x4262,x4263)))
% 1.03/1.22 [427]E(f5(a38,f9(a38,x4271,x4272),f9(a38,x4271,x4273)),f9(a38,x4271,f5(a38,x4272,x4273)))
% 1.03/1.22 [428]E(f3(a1,f9(a1,x4281,x4282),f9(a1,x4281,x4283)),f9(a1,x4281,f3(a1,x4282,x4283)))
% 1.03/1.22 [429]E(f4(a1,f9(a1,x4291,x4292),f9(a1,x4291,x4293)),f9(a1,x4291,f4(a1,x4292,x4293)))
% 1.03/1.22 [430]E(f9(a1,f14(a1,x4301,x4302),f14(a1,x4301,x4303)),f14(a1,x4301,f3(a38,x4302,x4303)))
% 1.03/1.22 [431]E(f3(a38,f9(a38,x4311,x4312),f9(a38,x4313,x4312)),f9(a38,f3(a38,x4311,x4313),x4312))
% 1.03/1.22 [432]E(f4(a38,f9(a38,x4321,x4322),f9(a38,x4323,x4322)),f9(a38,f4(a38,x4321,x4323),x4322))
% 1.03/1.22 [433]E(f5(a38,f9(a38,x4331,x4332),f9(a38,x4333,x4332)),f9(a38,f5(a38,x4331,x4333),x4332))
% 1.03/1.22 [434]E(f3(a1,f9(a1,x4341,x4342),f9(a1,x4343,x4342)),f9(a1,f3(a1,x4341,x4343),x4342))
% 1.03/1.22 [436]E(f4(a1,f9(a1,x4361,x4362),f9(a1,x4363,x4362)),f9(a1,f4(a1,x4361,x4363),x4362))
% 1.03/1.22 [437]E(f3(a37,f9(a37,x4371,x4372),f9(a37,x4373,x4372)),f9(a37,f3(a37,x4371,x4373),x4372))
% 1.03/1.22 [424]E(f5(a38,f3(a38,f9(a38,x4241,x4242),x4243),x4242),f5(a38,x4243,x4242))
% 1.03/1.22 [439]E(f5(a1,f9(a1,x4391,f5(a1,x4392,x4393)),x4393),f5(a1,f9(a1,x4391,x4392),x4393))
% 1.03/1.22 [440]E(f5(a1,f4(a1,x4401,f5(a1,x4402,x4403)),x4403),f5(a1,f4(a1,x4401,x4402),x4403))
% 1.03/1.22 [441]E(f5(a1,f14(a1,f5(a1,x4411,x4412),x4413),x4412),f5(a1,f14(a1,x4411,x4413),x4412))
% 1.03/1.22 [442]E(f5(a1,f4(a1,f5(a1,x4421,x4422),x4423),x4422),f5(a1,f4(a1,x4421,x4423),x4422))
% 1.03/1.22 [448]E(f4(a38,f4(a38,f3(a38,x4481,f8(a38)),x4482),f3(a38,x4483,f8(a38))),f4(a38,f4(a38,x4481,x4482),x4483))
% 1.03/1.22 [451]E(f5(a38,f3(a38,f3(a38,f9(a38,x4511,x4512),x4513),f8(a38)),x4512),f5(a38,f3(a38,x4513,f8(a38)),x4512))
% 1.03/1.22 [460]E(f3(a1,f3(a1,f6(a1,x4601,x4602),f6(a1,x4603,x4602)),f6(a1,f3(a1,f5(a1,x4601,x4602),f5(a1,x4603,x4602)),x4602)),f6(a1,f3(a1,x4601,x4603),x4602))
% 1.03/1.22 [449]E(f3(a38,f9(a38,x4491,x4492),f3(a38,f9(a38,x4493,x4492),x4494)),f3(a38,f9(a38,f3(a38,x4491,x4493),x4492),x4494))
% 1.03/1.22 [515]~P61(x5151)+~E(f8(x5151),f2(x5151))
% 1.03/1.22 [517]~P1(x5171)+E(f13(x5171,a10),f2(x5171))
% 1.03/1.22 [518]~P59(x5181)+P12(x5181,f2(x5181))
% 1.03/1.22 [521]~P59(x5211)+~P12(x5211,f8(x5211))
% 1.03/1.22 [522]~P1(x5221)+P12(x5221,f13(x5221,a10))
% 1.03/1.22 [523]~E(a10,x5231)+E(f3(a1,x5231,x5231),a10)
% 1.03/1.22 [524]~E(x5241,a10)+E(f3(a1,x5241,x5241),a10)
% 1.03/1.22 [533]E(x5331,f2(a1))+E(f6(a1,x5331,x5331),f8(a1))
% 1.03/1.22 [536]E(x5361,f2(a38))+P11(a38,f2(a38),x5361)
% 1.03/1.22 [550]~P1(x5501)+~P12(x5501,f13(x5501,a11))
% 1.03/1.22 [574]P10(a38,x5741)+P11(a38,f2(a38),x5741)
% 1.03/1.22 [591]~P37(x5911)+P11(x5911,f2(x5911),f8(x5911))
% 1.03/1.22 [592]~P37(x5921)+P13(x5921,f2(x5921),f8(x5921))
% 1.03/1.22 [598]P13(a1,x5981,a10)+~E(f13(a38,x5981),f2(a38))
% 1.03/1.22 [601]E(x6011,a10)+~E(f3(a1,x6011,x6011),a10)
% 1.03/1.22 [602]E(a10,x6021)+~E(f3(a1,x6021,x6021),a10)
% 1.03/1.22 [620]E(x6201,f2(a38))+~P13(a38,x6201,f2(a38))
% 1.03/1.22 [621]E(x6211,f8(a38))+~P14(a38,x6211,f8(a38))
% 1.03/1.22 [627]~P13(a1,x6271,a10)+E(f13(a38,x6271),f2(a38))
% 1.03/1.22 [657]~P37(x6571)+~P11(x6571,f8(x6571),f2(x6571))
% 1.03/1.22 [658]~P37(x6581)+~P13(x6581,f8(x6581),f2(x6581))
% 1.03/1.22 [705]~P13(a1,f8(a1),x7051)+P11(a1,f2(a1),x7051)
% 1.03/1.22 [706]~P11(a1,f2(a1),x7061)+P13(a1,f8(a1),x7061)
% 1.03/1.22 [721]~P11(a1,a10,x7211)+P11(a38,f2(a38),f13(a38,x7211))
% 1.03/1.22 [723]E(x7231,f2(a37))+P11(a37,f2(a37),f9(a37,x7231,x7231))
% 1.03/1.22 [764]P11(a1,a10,x7641)+~P11(a38,f2(a38),f13(a38,x7641))
% 1.03/1.22 [878]~P11(a1,a10,x8781)+P11(a1,a10,f3(a1,x8781,x8781))
% 1.03/1.22 [879]~P11(a1,a11,x8791)+P11(a1,a11,f3(a1,x8791,x8791))
% 1.03/1.22 [880]~P13(a1,a10,x8801)+P13(a1,a10,f3(a1,x8801,x8801))
% 1.03/1.22 [881]~P11(a1,a11,x8811)+P13(a1,a11,f3(a1,x8811,x8811))
% 1.03/1.22 [882]~P11(a1,x8821,a10)+P11(a1,f3(a1,x8821,x8821),a10)
% 1.03/1.22 [883]~P13(a1,x8831,a11)+P11(a1,f3(a1,x8831,x8831),a11)
% 1.03/1.22 [884]~P13(a1,x8841,a10)+P13(a1,f3(a1,x8841,x8841),a10)
% 1.03/1.22 [885]~P13(a1,x8851,a11)+P13(a1,f3(a1,x8851,x8851),a11)
% 1.03/1.22 [935]~P11(a1,x9351,f2(a1))+P11(a1,f3(a1,x9351,x9351),f2(a1))
% 1.03/1.22 [953]~E(x9531,f2(a37))+~P11(a37,f2(a37),f9(a37,x9531,x9531))
% 1.03/1.22 [1005]P11(a1,x10051,a10)+~P11(a1,f3(a1,x10051,x10051),a10)
% 1.03/1.22 [1006]P13(a1,x10061,a10)+~P13(a1,f3(a1,x10061,x10061),a10)
% 1.03/1.22 [1007]P13(a1,x10071,a11)+~P11(a1,f3(a1,x10071,x10071),a11)
% 1.03/1.22 [1008]P13(a1,x10081,a11)+~P13(a1,f3(a1,x10081,x10081),a11)
% 1.03/1.22 [1009]P11(a1,a10,x10091)+~P11(a1,a10,f3(a1,x10091,x10091))
% 1.03/1.22 [1010]P11(a1,a11,x10101)+~P11(a1,a11,f3(a1,x10101,x10101))
% 1.03/1.22 [1011]P11(a1,a11,x10111)+~P13(a1,a11,f3(a1,x10111,x10111))
% 1.03/1.22 [1012]P13(a1,a10,x10121)+~P13(a1,a10,f3(a1,x10121,x10121))
% 1.03/1.22 [1037]P11(a1,x10371,f2(a1))+~P11(a1,f3(a1,x10371,x10371),f2(a1))
% 1.03/1.22 [669]P10(a38,x6691)+P10(a38,f3(a38,x6691,f8(a38)))
% 1.03/1.22 [709]~P11(a38,f2(a38),x7091)+E(f3(a38,f16(x7091),f8(a38)),x7091)
% 1.03/1.22 [802]~P37(x8021)+P11(x8021,f2(x8021),f3(x8021,f8(x8021),f8(x8021)))
% 1.03/1.22 [828]~P10(a38,x8281)+~P10(a38,f3(a38,x8281,f8(a38)))
% 1.03/1.22 [844]~P11(a1,f2(a1),x8441)+E(f5(a1,f13(a1,a11),x8441),f4(a1,x8441,f8(a1)))
% 1.03/1.22 [942]~P13(a1,f2(a1),x9421)+P11(a1,f2(a1),f3(a1,f8(a1),x9421))
% 1.03/1.22 [946]~P11(a38,f2(a38),x9461)+E(f3(a38,f4(a38,x9461,f8(a38)),f8(a38)),x9461)
% 1.03/1.22 [966]E(x9661,f2(a38))+~P11(a38,x9661,f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [1078]~P14(a38,x10781,f3(a38,f2(a38),f8(a38)))+E(x10781,f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [1263]~P13(a1,f2(a1),f13(a1,x12631))+P13(a1,f2(a1),f13(a1,f3(a1,x12631,x12631)))
% 1.03/1.22 [1270]~P10(a38,x12701)+E(f9(a38,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38)),f30(x12701)),x12701)
% 1.03/1.22 [1404]~P11(a38,f2(a38),x14041)+E(f3(a38,f4(a38,x14041,f3(a38,f2(a38),f8(a38))),f8(a38)),x14041)
% 1.03/1.22 [1624]P10(a38,x16241)+E(f3(a38,f9(a38,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38)),f31(x16241)),f8(a38)),x16241)
% 1.03/1.22 [1700]~P10(a38,x17001)+E(f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f32(x17001)),x17001)
% 1.03/1.22 [1701]~P10(a1,x17011)+E(f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f33(x17011)),x17011)
% 1.03/1.22 [1720]P10(a38,x17201)+E(f3(a38,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f34(x17201)),f8(a38)),x17201)
% 1.03/1.22 [1721]P10(a1,x17211)+E(f3(a1,f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f19(x17211)),f8(a1)),x17211)
% 1.03/1.22 [725]~E(a11,x7251)+E(f3(a1,f3(a1,f8(a1),x7251),x7251),a11)
% 1.03/1.22 [726]~E(x7261,a11)+E(f3(a1,f3(a1,f8(a1),x7261),x7261),a11)
% 1.03/1.22 [954]E(x9541,a11)+~E(f3(a1,f3(a1,f8(a1),x9541),x9541),a11)
% 1.03/1.22 [955]E(a11,x9551)+~E(f3(a1,f3(a1,f8(a1),x9551),x9551),a11)
% 1.03/1.22 [1267]~P10(a38,x12671)+E(f5(a38,x12671,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38))),f2(a38))
% 1.03/1.22 [1349]~P13(a1,a10,x13491)+P11(a1,a10,f3(a1,f3(a1,f8(a1),x13491),x13491))
% 1.03/1.22 [1350]~P11(a1,a11,x13501)+P11(a1,a11,f3(a1,f3(a1,f8(a1),x13501),x13501))
% 1.03/1.22 [1351]~P13(a1,a10,x13511)+P13(a1,a10,f3(a1,f3(a1,f8(a1),x13511),x13511))
% 1.03/1.22 [1352]~P13(a1,a11,x13521)+P13(a1,a11,f3(a1,f3(a1,f8(a1),x13521),x13521))
% 1.03/1.22 [1353]~P11(a1,x13531,a10)+P11(a1,f3(a1,f3(a1,f8(a1),x13531),x13531),a10)
% 1.03/1.22 [1354]~P11(a1,x13541,a11)+P11(a1,f3(a1,f3(a1,f8(a1),x13541),x13541),a11)
% 1.03/1.22 [1355]~P11(a1,x13551,a10)+P13(a1,f3(a1,f3(a1,f8(a1),x13551),x13551),a10)
% 1.03/1.22 [1356]~P13(a1,x13561,a11)+P13(a1,f3(a1,f3(a1,f8(a1),x13561),x13561),a11)
% 1.03/1.22 [1389]P10(a38,x13891)+E(f5(a38,x13891,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38))),f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [1401]~P11(a1,x14011,f2(a1))+P11(a1,f3(a1,f3(a1,f8(a1),x14011),x14011),f2(a1))
% 1.03/1.22 [1538]P10(a38,x15381)+~E(f5(a38,x15381,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38))),f2(a38))
% 1.03/1.22 [1547]P11(a1,x15471,a10)+~P11(a1,f3(a1,f3(a1,f8(a1),x15471),x15471),a10)
% 1.03/1.22 [1548]P11(a1,x15481,a10)+~P13(a1,f3(a1,f3(a1,f8(a1),x15481),x15481),a10)
% 1.03/1.22 [1549]P11(a1,x15491,a11)+~P11(a1,f3(a1,f3(a1,f8(a1),x15491),x15491),a11)
% 1.03/1.22 [1550]P13(a1,x15501,a11)+~P13(a1,f3(a1,f3(a1,f8(a1),x15501),x15501),a11)
% 1.03/1.22 [1551]P11(a1,a11,x15511)+~P11(a1,a11,f3(a1,f3(a1,f8(a1),x15511),x15511))
% 1.03/1.22 [1552]P13(a1,a10,x15521)+~P11(a1,a10,f3(a1,f3(a1,f8(a1),x15521),x15521))
% 1.03/1.22 [1553]P13(a1,a10,x15531)+~P13(a1,a10,f3(a1,f3(a1,f8(a1),x15531),x15531))
% 1.03/1.22 [1554]P13(a1,a11,x15541)+~P13(a1,a11,f3(a1,f3(a1,f8(a1),x15541),x15541))
% 1.03/1.22 [1564]P11(a1,x15641,f2(a1))+~P11(a1,f3(a1,f3(a1,f8(a1),x15641),x15641),f2(a1))
% 1.03/1.22 [1589]~P10(a38,x15891)+~E(f5(a38,x15891,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38))),f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [1125]~P1(x11251)+E(f13(x11251,f3(a1,f3(a1,f8(a1),a10),a10)),f8(x11251))
% 1.03/1.22 [1620]~P13(a1,f2(a1),f13(a1,x16201))+P13(a1,f2(a1),f13(a1,f3(a1,f3(a1,f8(a1),x16201),x16201)))
% 1.03/1.22 [1649]~P1(x16491)+~P12(x16491,f13(x16491,f3(a1,f3(a1,f8(a1),a10),a10)))
% 1.03/1.22 [1667]~P1(x16671)+E(f3(x16671,f8(x16671),f8(x16671)),f13(x16671,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))
% 1.03/1.22 [1696]~P10(a38,x16961)+P14(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x16961)
% 1.03/1.22 [1697]~P10(a1,x16971)+P14(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x16971)
% 1.03/1.22 [1708]P10(a38,x17081)+~P14(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17081)
% 1.03/1.22 [1709]P10(a1,x17091)+~P14(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17091)
% 1.03/1.22 [1694]~P59(x16941)+E(f14(x16941,f2(x16941),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f2(x16941))
% 1.03/1.22 [1695]~P59(x16951)+E(f14(x16951,f8(x16951),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f8(x16951))
% 1.03/1.22 [1699]~P10(a1,x16991)+E(f5(a1,x16991,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f2(a1))
% 1.03/1.22 [1707]P62(a500)+~E(f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17071),a39)
% 1.03/1.22 [1712]P10(a1,x17121)+~E(f5(a1,x17121,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f2(a1))
% 1.03/1.22 [1717]E(f5(a1,x17171,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f8(a1))+E(f5(a1,x17171,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f2(a1))
% 1.03/1.22 [1727]~E(f5(a1,x17271,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f8(a1))+~E(f5(a1,x17271,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f2(a1))
% 1.03/1.22 [528]~E(x5281,x5282)+P14(a38,x5281,x5282)
% 1.03/1.22 [531]~E(x5311,x5312)+P13(a38,x5311,x5312)
% 1.03/1.22 [532]~E(x5321,x5322)+P13(a37,x5321,x5322)
% 1.03/1.22 [543]~P30(x5431)+P14(x5431,x5432,x5432)
% 1.03/1.22 [609]~E(x6091,x6092)+~P11(a38,x6091,x6092)
% 1.03/1.22 [610]~E(x6101,x6102)+~P11(a1,x6101,x6102)
% 1.03/1.22 [611]~E(x6111,x6112)+~P11(a37,x6111,x6112)
% 1.03/1.22 [640]P13(a38,x6402,x6401)+P13(a38,x6401,x6402)
% 1.03/1.22 [641]P13(a1,x6412,x6411)+P13(a1,x6411,x6412)
% 1.03/1.22 [642]P13(a37,x6422,x6421)+P13(a37,x6421,x6422)
% 1.03/1.22 [679]~P11(a38,x6791,x6792)+P13(a38,x6791,x6792)
% 1.03/1.22 [680]~P11(a1,x6801,x6802)+P13(a1,x6801,x6802)
% 1.03/1.22 [682]~P11(a37,x6821,x6822)+P13(a37,x6821,x6822)
% 1.03/1.22 [534]E(f3(a38,x5341,x5342),x5342)+~E(x5341,f2(a38))
% 1.03/1.22 [538]~E(x5382,f2(a38))+E(f9(a38,x5381,x5382),f2(a38))
% 1.03/1.22 [540]~E(x5401,f2(a38))+E(f9(a38,x5401,x5402),f2(a38))
% 1.03/1.22 [541]~E(x5412,f2(a38))+E(f14(a38,x5411,x5412),f8(a38))
% 1.03/1.22 [542]~E(x5422,f2(a1))+E(f6(a1,x5421,x5422),f2(a1))
% 1.03/1.22 [546]~P19(x5461)+E(f4(x5461,x5462,x5462),f2(x5461))
% 1.03/1.22 [547]~P8(x5471)+E(f5(x5471,x5472,x5472),f2(x5471))
% 1.03/1.22 [555]~P30(x5551)+P14(x5551,x5552,f2(x5551))
% 1.03/1.22 [556]~P30(x5561)+P14(x5561,f8(x5561),x5562)
% 1.03/1.22 [612]~E(f3(a38,x6122,x6121),x6122)+E(x6121,f2(a38))
% 1.03/1.22 [613]~P11(a38,x6132,x6131)+~E(x6131,f2(a38))
% 1.03/1.22 [616]E(x6161,f2(a38))+~E(f3(a38,x6162,x6161),f2(a38))
% 1.03/1.22 [617]E(x6171,f2(a38))+~E(f3(a38,x6171,x6172),f2(a38))
% 1.03/1.22 [618]E(x6181,f8(a38))+~E(f9(a38,x6182,x6181),f8(a38))
% 1.03/1.22 [619]E(x6191,f8(a38))+~E(f9(a38,x6191,x6192),f8(a38))
% 1.03/1.22 [670]~P10(a38,x6702)+P10(a38,f9(a38,x6701,x6702))
% 1.03/1.22 [671]~P10(a38,x6711)+P10(a38,f9(a38,x6711,x6712))
% 1.03/1.22 [673]~P10(a1,x6732)+P10(a1,f9(a1,x6731,x6732))
% 1.03/1.22 [675]~P10(a1,x6751)+P10(a1,f9(a1,x6751,x6752))
% 1.03/1.22 [684]~P11(a38,x6841,x6842)+E(f5(a38,x6841,x6842),x6841)
% 1.03/1.22 [687]~P13(a38,x6871,x6872)+E(f4(a38,x6871,x6872),f2(a38))
% 1.03/1.22 [696]P13(a38,x6961,x6962)+~E(f4(a38,x6961,x6962),f2(a38))
% 1.03/1.22 [728]~E(x7282,f2(a38))+P11(a38,f2(a38),f14(a38,x7281,x7282))
% 1.03/1.22 [735]E(x7351,x7352)+~E(f3(a1,x7351,x7351),f3(a1,x7352,x7352))
% 1.03/1.22 [762]~P43(x7621)+P13(x7621,f2(x7621),f9(x7621,x7622,x7622))
% 1.03/1.22 [771]~P13(a1,x7711,a10)+P13(a38,f13(a38,x7711),f13(a38,x7712))
% 1.03/1.22 [785]~P11(a1,x7851,x7852)+P11(a1,f13(a1,x7851),f13(a1,x7852))
% 1.03/1.22 [786]~P13(a1,x7861,x7862)+P13(a38,f13(a38,x7861),f13(a38,x7862))
% 1.03/1.22 [787]~P13(a1,x7871,x7872)+P13(a1,f13(a1,x7871),f13(a1,x7872))
% 1.03/1.22 [793]~E(x7931,f2(a38))+~P10(a1,f14(a1,x7932,x7931))
% 1.03/1.22 [798]P10(a38,x7981)+~P10(a38,f14(a38,x7981,x7982))
% 1.03/1.22 [800]P10(a1,x8001)+~P10(a1,f14(a1,x8001,x8002))
% 1.03/1.22 [803]~P11(a38,x8031,x8032)+P10(a38,f4(a38,x8031,x8032))
% 1.03/1.22 [817]P11(a1,x8171,x8172)+~P11(a38,f13(a38,x8171),f13(a38,x8172))
% 1.03/1.22 [818]P11(a1,x8181,x8182)+~P11(a1,f13(a1,x8181),f13(a1,x8182))
% 1.03/1.22 [819]P13(a1,x8191,x8192)+~P13(a1,f13(a1,x8191),f13(a1,x8192))
% 1.03/1.22 [886]P11(a38,f2(a38),x8861)+~P10(a38,f14(a38,x8862,x8861))
% 1.03/1.22 [894]~P14(a38,x8941,x8942)+P14(a38,x8941,f3(a38,x8942,x8941))
% 1.03/1.22 [901]~P11(a38,x9012,x9011)+P11(a38,f2(a38),f4(a38,x9011,x9012))
% 1.03/1.22 [902]~P11(a1,x9021,x9022)+P11(a1,f4(a1,x9021,x9022),f2(a1))
% 1.03/1.22 [903]~P13(a37,x9031,x9032)+P13(a37,f4(a37,x9031,x9032),f2(a37))
% 1.03/1.22 [907]P11(a1,x9071,f5(a1,x9072,x9071))+~P11(a1,x9071,f2(a1))
% 1.03/1.22 [908]P11(a38,f5(a38,x9081,x9082),x9082)+~P11(a38,f2(a38),x9082)
% 1.03/1.22 [910]P11(a1,f5(a1,x9101,x9102),x9102)+~P11(a1,f2(a1),x9102)
% 1.03/1.22 [911]P13(a38,f5(a38,x9111,x9112),x9112)+~P11(a38,f2(a38),x9112)
% 1.03/1.22 [912]P13(a1,f5(a1,x9121,x9122),x9121)+~P13(a1,f2(a1),x9121)
% 1.03/1.22 [929]~P11(a38,f2(a38),x9291)+P11(a38,f2(a38),f14(a38,x9291,x9292))
% 1.03/1.22 [932]~P13(a1,f2(a1),x9321)+P13(a1,f2(a1),f14(a1,x9321,x9322))
% 1.03/1.22 [934]~P11(a1,f2(a1),x9342)+P13(a1,f2(a1),f5(a1,x9341,x9342))
% 1.03/1.22 [937]~P11(a1,x9372,f2(a1))+P13(a1,f5(a1,x9371,x9372),f2(a1))
% 1.03/1.22 [978]~P43(x9781)+~P11(x9781,f9(x9781,x9782,x9782),f2(x9781))
% 1.03/1.22 [1019]P14(a38,x10191,x10192)+~P14(a38,x10191,f3(a38,x10192,x10191))
% 1.03/1.22 [1031]P11(a38,x10311,x10312)+~P11(a38,f2(a38),f4(a38,x10312,x10311))
% 1.03/1.22 [1032]P11(a1,x10321,x10322)+~P11(a1,f4(a1,x10321,x10322),f2(a1))
% 1.03/1.22 [1033]P13(a37,x10331,x10332)+~P13(a37,f4(a37,x10331,x10332),f2(a37))
% 1.03/1.22 [1038]P11(a38,f2(a38),x10381)+~P11(a38,f2(a38),f9(a38,x10382,x10381))
% 1.03/1.22 [1039]P11(a38,f2(a38),x10391)+~P11(a38,f2(a38),f9(a38,x10391,x10392))
% 1.03/1.22 [1141]~P11(a1,x11411,x11412)+P11(a1,f3(a1,x11411,x11411),f3(a1,x11412,x11412))
% 1.03/1.22 [1153]~P13(a1,x11531,x11532)+P13(a1,f3(a1,x11531,x11531),f3(a1,x11532,x11532))
% 1.03/1.22 [1381]P11(a1,x13811,x13812)+~P11(a1,f3(a1,x13811,x13811),f3(a1,x13812,x13812))
% 1.03/1.22 [1384]P13(a1,x13841,x13842)+~P13(a1,f3(a1,x13841,x13841),f3(a1,x13842,x13842))
% 1.03/1.22 [548]~P30(x5481)+E(f14(x5481,x5482,f8(a38)),x5482)
% 1.03/1.22 [549]~P3(x5491)+E(f14(x5491,x5492,f8(a38)),x5492)
% 1.03/1.22 [557]~P30(x5571)+E(f9(x5571,x5572,f8(x5571)),x5572)
% 1.03/1.22 [558]~P3(x5581)+E(f9(x5581,x5582,f8(x5581)),x5582)
% 1.03/1.22 [559]~P18(x5591)+E(f9(x5591,x5592,f8(x5591)),x5592)
% 1.03/1.22 [560]~P30(x5601)+E(f3(x5601,x5602,f2(x5601)),x5602)
% 1.03/1.22 [561]~P20(x5611)+E(f3(x5611,x5612,f2(x5611)),x5612)
% 1.03/1.22 [562]~P17(x5621)+E(f3(x5621,x5622,f2(x5621)),x5622)
% 1.03/1.22 [563]~P19(x5631)+E(f4(x5631,x5632,f2(x5631)),x5632)
% 1.03/1.22 [564]~P8(x5641)+E(f5(x5641,x5642,f2(x5641)),x5642)
% 1.03/1.22 [565]~P8(x5651)+E(f6(x5651,x5652,f8(x5651)),x5652)
% 1.03/1.22 [566]~P30(x5661)+E(f9(x5661,f8(x5661),x5662),x5662)
% 1.03/1.22 [567]~P3(x5671)+E(f9(x5671,f8(x5671),x5672),x5672)
% 1.03/1.22 [568]~P18(x5681)+E(f9(x5681,f8(x5681),x5682),x5682)
% 1.03/1.22 [569]~P30(x5691)+E(f3(x5691,f2(x5691),x5692),x5692)
% 1.03/1.22 [570]~P20(x5701)+E(f3(x5701,f2(x5701),x5702),x5702)
% 1.03/1.22 [571]~P17(x5711)+E(f3(x5711,f2(x5711),x5712),x5712)
% 1.03/1.22 [572]~P30(x5721)+E(f14(x5721,x5722,f2(a38)),f8(x5721))
% 1.03/1.22 [573]~P32(x5731)+E(f14(x5731,x5732,f2(a38)),f8(x5731))
% 1.03/1.22 [580]~P29(x5801)+E(f9(x5801,x5802,f2(x5801)),f2(x5801))
% 1.03/1.22 [581]~P30(x5811)+E(f9(x5811,x5812,f2(x5811)),f2(x5811))
% 1.03/1.22 [583]~P31(x5831)+E(f9(x5831,x5832,f2(x5831)),f2(x5831))
% 1.03/1.22 [584]~P8(x5841)+E(f5(x5841,x5842,f8(x5841)),f2(x5841))
% 1.03/1.22 [585]~P29(x5851)+E(f9(x5851,f2(x5851),x5852),f2(x5851))
% 1.03/1.22 [586]~P30(x5861)+E(f9(x5861,f2(x5861),x5862),f2(x5861))
% 1.03/1.22 [588]~P31(x5881)+E(f9(x5881,f2(x5881),x5882),f2(x5881))
% 1.03/1.22 [589]~P3(x5891)+E(f14(x5891,f8(x5891),x5892),f8(x5891))
% 1.03/1.22 [590]~P8(x5901)+E(f5(x5901,f2(x5901),x5902),f2(x5901))
% 1.03/1.22 [603]~P1(x6031)+E(f3(x6031,x6032,f13(x6031,a10)),x6032)
% 1.03/1.22 [604]~P1(x6041)+E(f3(x6041,f13(x6041,a10),x6042),x6042)
% 1.03/1.22 [662]~E(x6622,f2(a38))+E(f14(a38,x6621,x6622),f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [707]P11(a38,f2(a38),x7071)+~E(x7071,f3(a38,x7072,f8(a38)))
% 1.03/1.22 [724]~P13(a38,x7241,x7242)+E(f3(a38,x7241,f17(x7242,x7241)),x7242)
% 1.03/1.22 [729]~E(x7291,x7292)+P11(a38,x7291,f3(a38,x7292,f8(a38)))
% 1.03/1.22 [730]~E(x7301,x7302)+P11(a1,x7301,f3(a1,x7302,f8(a1)))
% 1.03/1.22 [731]~E(f5(a38,x7312,x7311),f2(a38))+E(f9(a38,x7311,f20(x7311,x7312)),x7312)
% 1.03/1.22 [732]~E(f5(a1,x7322,x7321),f2(a1))+E(f9(a1,x7321,f21(x7321,x7322)),x7322)
% 1.03/1.22 [738]~E(x7381,f2(a38))+P11(a38,x7381,f3(a38,x7382,f8(a38)))
% 1.03/1.22 [779]~P37(x7791)+P11(x7791,x7792,f3(x7791,x7792,f8(x7791)))
% 1.03/1.22 [784]~P11(a1,x7841,a10)+E(f9(a38,f13(a38,x7841),f13(a38,x7842)),f2(a38))
% 1.03/1.22 [795]~P11(a1,x7951,a10)+E(f3(a38,f13(a38,x7951),f13(a38,x7952)),f13(a38,x7952))
% 1.03/1.22 [815]~E(x8151,f3(a38,f2(a38),f8(a38)))+E(f14(a38,x8151,x8152),f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [823]P11(a38,x8232,x8231)+E(f3(a38,x8231,f4(a38,x8232,x8231)),x8232)
% 1.03/1.22 [830]P11(a38,x8301,x8302)+P11(a38,x8302,f3(a38,x8301,f8(a38)))
% 1.03/1.22 [831]P13(a38,x8311,x8312)+P13(a38,f3(a38,x8312,f8(a38)),x8311)
% 1.03/1.22 [876]E(x8761,f3(a38,f2(a38),f8(a38)))+~E(f9(a38,x8762,x8761),f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [877]E(x8771,f3(a38,f2(a38),f8(a38)))+~E(f9(a38,x8771,x8772),f3(a38,f2(a38),f8(a38)))
% 1.03/1.22 [898]~P13(a38,x8981,x8982)+E(f3(a38,x8981,f4(a38,x8982,x8981)),x8982)
% 1.03/1.22 [899]~P13(a38,x8992,x8991)+E(f4(a38,x8991,f4(a38,x8991,x8992)),x8992)
% 1.03/1.22 [900]~P13(a38,x9002,x9001)+E(f3(a38,f4(a38,x9001,x9002),x9002),x9001)
% 1.03/1.22 [916]~P13(a38,x9161,x9162)+P11(a38,x9161,f3(a38,x9162,f8(a38)))
% 1.03/1.22 [917]~P11(a1,x9171,x9172)+P11(a1,x9171,f3(a1,x9172,f8(a1)))
% 1.03/1.22 [918]~P13(a1,x9181,x9182)+P11(a1,x9181,f3(a1,x9182,f8(a1)))
% 1.03/1.22 [921]~P11(a1,x9211,x9212)+P13(a1,x9211,f4(a1,x9212,f8(a1)))
% 1.03/1.22 [924]~P11(a38,x9241,x9242)+P13(a38,f3(a38,x9241,f8(a38)),x9242)
% 1.03/1.22 [926]~P11(a1,x9261,x9262)+P13(a1,f3(a1,x9261,f8(a1)),x9262)
% 1.03/1.22 [950]~P14(a1,f13(a1,x9502),f13(a1,x9501))+E(f5(a1,f13(a1,x9501),f13(a1,x9502)),f2(a1))
% 1.03/1.22 [956]P14(a1,f13(a1,x9561),f13(a1,x9562))+~E(f5(a1,f13(a1,x9562),f13(a1,x9561)),f2(a1))
% 1.03/1.22 [961]P11(a38,x9611,x9612)+E(f5(a38,f4(a38,x9611,x9612),x9612),f5(a38,x9611,x9612))
% 1.03/1.22 [965]P11(a1,x9651,a10)+E(f9(a38,f13(a38,x9651),f13(a38,x9652)),f13(a38,f9(a1,x9651,x9652)))
% 1.03/1.22 [1001]~P13(a38,x10012,x10011)+E(f5(a38,f4(a38,x10011,x10012),x10012),f5(a38,x10011,x10012))
% 1.03/1.22 [1016]~P11(a38,x10161,x10162)+E(f3(a38,f3(a38,x10161,f18(x10162,x10161)),f8(a38)),x10162)
% 1.03/1.22 [1042]P11(a1,x10421,x10422)+~P13(a1,x10421,f4(a1,x10422,f8(a1)))
% 1.03/1.22 [1043]P13(a38,x10431,x10432)+~P11(a38,x10431,f3(a38,x10432,f8(a38)))
% 1.03/1.22 [1044]P13(a1,x10441,x10442)+~P11(a1,x10441,f3(a1,x10442,f8(a1)))
% 1.03/1.22 [1048]P11(a38,x10481,x10482)+~P13(a38,f3(a38,x10481,f8(a38)),x10482)
% 1.03/1.22 [1049]P11(a1,x10491,x10492)+~P13(a1,f3(a1,x10491,f8(a1)),x10492)
% 1.03/1.22 [1108]~P1(x11081)+E(f9(x11081,f3(x11081,f8(x11081),f8(x11081)),f13(x11081,x11082)),f13(x11081,f3(a1,x11082,x11082)))
% 1.03/1.22 [1126]~P11(a38,x11261,x11262)+~P11(a38,x11262,f3(a38,x11261,f8(a38)))
% 1.03/1.22 [1127]~P13(a38,x11271,x11272)+~P13(a38,f3(a38,x11272,f8(a38)),x11271)
% 1.03/1.22 [1225]~P1(x12251)+E(f3(x12251,f3(x12251,f2(x12251),f13(x12251,x12252)),f13(x12251,x12252)),f13(x12251,f3(a1,x12252,x12252)))
% 1.03/1.22 [1264]E(x12641,f2(a37))+~E(f3(a37,f9(a37,x12642,x12642),f9(a37,x12641,x12641)),f2(a37))
% 1.03/1.22 [1265]E(x12651,f2(a37))+~E(f3(a37,f9(a37,x12651,x12651),f9(a37,x12652,x12652)),f2(a37))
% 1.03/1.22 [1304]E(x13041,f2(a38))+E(f3(a38,f3(a38,f4(a38,x13041,f8(a38)),x13042),f8(a38)),f3(a38,x13041,x13042))
% 1.03/1.22 [1407]P11(a38,x14071,x14072)+~P11(a38,f3(a38,x14071,f8(a38)),f3(a38,x14072,f8(a38)))
% 1.03/1.22 [1408]P13(a38,x14081,x14082)+~P13(a38,f3(a38,x14081,f8(a38)),f3(a38,x14082,f8(a38)))
% 1.03/1.22 [1450]~P13(a38,f3(a38,f2(a38),f8(a38)),x14501)+P13(a38,f3(a38,f2(a38),f8(a38)),f14(a38,x14501,x14502))
% 1.03/1.22 [1521]P13(a38,f3(a38,f2(a38),f8(a38)),x15211)+~P13(a38,f3(a38,f2(a38),f8(a38)),f9(a38,x15212,x15211))
% 1.03/1.23 [1522]P13(a38,f3(a38,f2(a38),f8(a38)),x15221)+~P13(a38,f3(a38,f2(a38),f8(a38)),f9(a38,x15221,x15222))
% 1.03/1.23 [1664]~P10(a38,x16641)+~E(x16641,f3(a38,f9(a38,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38)),x16642),f8(a38)))
% 1.03/1.23 [1729]~P10(a38,x17291)+~E(x17291,f3(a38,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17292),f8(a38)))
% 1.03/1.23 [1730]~P10(a1,x17301)+~E(x17301,f3(a1,f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17302),f8(a1)))
% 1.03/1.23 [927]~P30(x9271)+E(f3(x9271,x9272,x9272),f9(x9271,f3(x9271,f8(x9271),f8(x9271)),x9272))
% 1.03/1.23 [1268]~E(f3(a38,f5(a38,x12681,x12682),f8(a38)),x12682)+E(f5(a38,f3(a38,x12681,f8(a38)),x12682),f2(a38))
% 1.03/1.23 [1385]~P11(a38,f2(a38),x13851)+P11(a38,f4(a38,x13851,f3(a38,x13852,f8(a38))),x13851)
% 1.03/1.23 [1390]~P51(x13901)+E(f9(x13901,f3(x13901,x13902,f8(x13901)),f4(x13901,x13902,f8(x13901))),f4(x13901,f9(x13901,x13902,x13902),f8(x13901)))
% 1.03/1.23 [1409]E(f3(a38,f5(a38,x14091,x14092),f8(a38)),x14092)+E(f5(a38,f3(a38,x14091,f8(a38)),x14092),f3(a38,f5(a38,x14091,x14092),f8(a38)))
% 1.03/1.23 [1434]E(x14341,x14342)+~E(f3(a1,f3(a1,f8(a1),x14341),x14341),f3(a1,f3(a1,f8(a1),x14342),x14342))
% 1.03/1.23 [1488]~P13(a1,x14881,x14882)+P11(a1,f3(a1,x14881,x14881),f3(a1,f3(a1,f8(a1),x14882),x14882))
% 1.03/1.23 [1490]~P13(a1,x14901,x14902)+P13(a1,f3(a1,x14901,x14901),f3(a1,f3(a1,f8(a1),x14902),x14902))
% 1.03/1.23 [1492]~P11(a1,x14921,x14922)+P11(a1,f3(a1,f3(a1,f8(a1),x14921),x14921),f3(a1,x14922,x14922))
% 1.03/1.23 [1494]~P11(a1,x14941,x14942)+P13(a1,f3(a1,f3(a1,f8(a1),x14941),x14941),f3(a1,x14942,x14942))
% 1.03/1.23 [1537]P10(a38,x15371)+~E(x15371,f9(a38,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38)),x15372))
% 1.03/1.23 [1600]~P11(a1,x16001,x16002)+P11(a1,f3(a1,f3(a1,f8(a1),x16001),x16001),f3(a1,f3(a1,f8(a1),x16002),x16002))
% 1.03/1.23 [1602]~P13(a1,x16021,x16022)+P13(a1,f3(a1,f3(a1,f8(a1),x16021),x16021),f3(a1,f3(a1,f8(a1),x16022),x16022))
% 1.03/1.23 [1608]P13(a1,x16081,x16082)+~P11(a1,f3(a1,x16081,x16081),f3(a1,f3(a1,f8(a1),x16082),x16082))
% 1.03/1.23 [1610]P13(a1,x16101,x16102)+~P13(a1,f3(a1,x16101,x16101),f3(a1,f3(a1,f8(a1),x16102),x16102))
% 1.03/1.23 [1612]P11(a1,x16121,x16122)+~P11(a1,f3(a1,f3(a1,f8(a1),x16121),x16121),f3(a1,x16122,x16122))
% 1.03/1.23 [1614]P11(a1,x16141,x16142)+~P13(a1,f3(a1,f3(a1,f8(a1),x16141),x16141),f3(a1,x16142,x16142))
% 1.03/1.23 [1658]P11(a1,x16581,x16582)+~P11(a1,f3(a1,f3(a1,f8(a1),x16581),x16581),f3(a1,f3(a1,f8(a1),x16582),x16582))
% 1.03/1.23 [1660]P13(a1,x16601,x16602)+~P13(a1,f3(a1,f3(a1,f8(a1),x16601),x16601),f3(a1,f3(a1,f8(a1),x16602),x16602))
% 1.03/1.23 [1724]~P13(a1,f2(a1),f13(a1,x17242))+E(f5(a1,f13(a1,f3(a1,f3(a1,f8(a1),x17241),x17241)),f13(a1,f3(a1,x17242,x17242))),f3(a1,f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f5(a1,f13(a1,x17241),f13(a1,x17242))),f8(a1)))
% 1.03/1.23 [1725]P13(a1,f2(a1),f13(a1,x17252))+E(f5(a1,f13(a1,f3(a1,f3(a1,f8(a1),x17251),x17251)),f13(a1,f3(a1,x17252,x17252))),f4(a1,f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f5(a1,f3(a1,f13(a1,x17251),f8(a1)),f13(a1,x17252))),f8(a1)))
% 1.03/1.23 [1736]~P1(x17361)+E(f14(x17361,f13(x17361,a11),f3(a38,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17362),f8(a38))),f13(x17361,a11))
% 1.03/1.23 [1286]E(x12861,f2(a38))+E(f9(a38,x12862,f14(a38,x12862,f4(a38,x12861,f8(a38)))),f14(a38,x12862,x12861))
% 1.03/1.23 [1287]E(x12871,f2(a38))+E(f3(a38,x12872,f9(a38,f4(a38,x12871,f8(a38)),x12872)),f9(a38,x12871,x12872))
% 1.03/1.23 [1520]~P1(x15201)+E(f3(x15201,f3(x15201,f8(x15201),f13(x15201,x15202)),f13(x15201,x15202)),f13(x15201,f3(a1,f3(a1,f8(a1),x15202),x15202)))
% 1.03/1.23 [1584]~P1(x15841)+E(f9(x15841,x15842,f13(x15841,f3(a1,f3(a1,f8(a1),a10),a10))),x15842)
% 1.03/1.23 [1585]~P1(x15851)+E(f9(x15851,f13(x15851,f3(a1,f3(a1,f8(a1),a10),a10)),x15852),x15852)
% 1.03/1.23 [1618]~P1(x16181)+E(f3(x16181,f8(x16181),f13(x16181,x16182)),f13(x16181,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),x16182)))
% 1.03/1.23 [1619]~P1(x16191)+E(f3(x16191,f13(x16191,x16192),f8(x16191)),f13(x16191,f3(a1,x16192,f3(a1,f3(a1,f8(a1),a10),a10))))
% 1.03/1.23 [1675]~P11(a38,f13(a38,a10),x16752)+E(f4(a38,x16751,f4(a38,x16752,f13(a38,f3(a1,f3(a1,f8(a1),a10),a10)))),f4(a38,f3(a38,x16751,f8(a38)),x16752))
% 1.03/1.23 [1702]~P30(x17021)+E(f9(x17021,x17022,x17022),f14(x17021,x17022,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.23 [1703]~P3(x17031)+E(f14(x17031,x17032,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f9(x17031,x17032,x17032))
% 1.03/1.23 [1704]~P1(x17041)+E(f9(x17041,x17042,f13(x17041,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f3(x17041,x17042,x17042))
% 1.03/1.23 [1705]~P1(x17051)+E(f9(x17051,f13(x17051,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17052),f3(x17051,x17052,x17052))
% 1.03/1.23 [1710]P10(a38,x17101)+~E(x17101,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17102))
% 1.03/1.23 [1711]P10(a1,x17111)+~E(x17111,f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17112))
% 1.03/1.23 [1716]~P3(x17161)+E(f14(x17161,x17162,f13(a38,f3(a1,f3(a1,f8(a1),f3(a1,f3(a1,f8(a1),a10),a10)),f3(a1,f3(a1,f8(a1),a10),a10)))),f9(x17161,f9(x17161,x17162,x17162),x17162))
% 1.03/1.23 [1718]~P38(x17181)+P13(x17181,f2(x17181),f14(x17181,x17182,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.23 [1728]~P38(x17281)+~P11(x17281,f14(x17281,x17282,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f2(x17281))
% 1.03/1.23 [1722]~P1(x17221)+E(f14(x17221,f13(x17221,a11),f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17222)),f8(x17221))
% 1.03/1.23 [1738]~P13(a1,f2(a1),x17382)+E(f6(a1,f3(a1,f8(a1),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17381)),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17382)),f6(a1,x17381,x17382))
% 1.03/1.23 [1739]~P13(a1,x17392,f2(a1))+E(f6(a1,f3(a1,f8(a1),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17391)),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17392)),f6(a1,f3(a1,x17391,f8(a1)),x17392))
% 1.03/1.23 [1741]E(x17411,f2(a37))+~E(f3(a37,f14(a37,x17412,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(a37,x17411,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(a37))
% 1.03/1.23 [1742]E(x17421,f2(a37))+~E(f3(a37,f14(a37,x17421,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(a37,x17422,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(a37))
% 1.03/1.23 [1753]~P13(a1,f2(a1),x17532)+E(f5(a1,f3(a1,f8(a1),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17531)),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17532)),f3(a1,f8(a1),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f5(a1,x17531,x17532))))
% 1.03/1.23 [1754]~P13(a1,x17542,f2(a1))+E(f5(a1,f3(a1,f8(a1),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17541)),f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17542)),f4(a1,f9(a1,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),f5(a1,f3(a1,x17541,f8(a1)),x17542)),f8(a1)))
% 1.03/1.23 [654]E(f9(a38,x6541,x6542),f9(a38,x6543,x6542))+~E(x6542,f2(a38))
% 1.03/1.23 [656]E(f9(a38,x6561,x6562),f9(a38,x6561,x6563))+~E(x6561,f2(a38))
% 1.03/1.23 [659]~P30(x6591)+E(f9(x6591,x6592,x6593),f9(x6591,x6593,x6592))
% 1.03/1.23 [660]~P30(x6601)+E(f3(x6601,x6602,x6603),f3(x6601,x6603,x6602))
% 1.03/1.23 [685]P13(a38,x6851,x6852)+~E(x6852,f3(a38,x6851,x6853))
% 1.03/1.23 [694]~E(x6941,f9(a38,x6942,x6943))+E(f5(a38,x6941,x6942),f2(a38))
% 1.03/1.23 [695]~E(x6951,f9(a1,x6952,x6953))+E(f5(a1,x6951,x6952),f2(a1))
% 1.03/1.23 [733]E(x7331,x7332)+~E(f3(a38,x7333,x7331),f3(a38,x7333,x7332))
% 1.03/1.23 [734]E(x7341,x7342)+~E(f3(a38,x7341,x7343),f3(a38,x7342,x7343))
% 1.03/1.23 [736]~P30(x7361)+P14(x7361,x7362,f9(x7361,x7363,x7362))
% 1.03/1.23 [737]~P30(x7371)+P14(x7371,x7372,f9(x7371,x7372,x7373))
% 1.03/1.23 [892]~P11(a38,x8921,x8923)+P11(a38,x8921,f3(a38,x8922,x8923))
% 1.03/1.23 [893]~P11(a38,x8931,x8932)+P11(a38,x8931,f3(a38,x8932,x8933))
% 1.03/1.23 [895]~P13(a38,x8951,x8953)+P13(a38,x8951,f3(a38,x8952,x8953))
% 1.03/1.23 [896]~P13(a38,x8961,x8962)+P13(a38,x8961,f3(a38,x8962,x8963))
% 1.03/1.23 [897]~P11(a38,x8971,x8973)+P11(a38,f4(a38,x8971,x8972),x8973)
% 1.03/1.23 [964]~E(x9641,f2(a38))+P14(a38,f9(a38,x9641,x9642),f9(a38,x9641,x9643))
% 1.03/1.23 [1020]P11(a38,x10201,x10202)+~P11(a38,f3(a38,x10201,x10203),x10202)
% 1.03/1.23 [1023]P13(a38,x10231,x10232)+~P13(a38,f3(a38,x10233,x10231),x10232)
% 1.03/1.23 [1024]P13(a38,x10241,x10242)+~P13(a38,f3(a38,x10241,x10243),x10242)
% 1.03/1.23 [1060]P13(a38,f9(a38,x10602,x10601),f9(a38,x10603,x10601))+P11(a38,f2(a38),x10601)
% 1.03/1.23 [1061]P13(a38,f9(a38,x10611,x10612),f9(a38,x10611,x10613))+P11(a38,f2(a38),x10611)
% 1.03/1.23 [1071]~E(f5(a1,x10712,x10711),f5(a1,x10713,x10711))+P14(a1,x10711,f4(a1,x10712,x10713))
% 1.03/1.23 [1137]~P11(a38,x11372,x11373)+P11(a38,f3(a38,x11371,x11372),f3(a38,x11371,x11373))
% 1.03/1.23 [1138]~P11(a38,x11381,x11383)+P11(a38,f3(a38,x11381,x11382),f3(a38,x11383,x11382))
% 1.03/1.23 [1139]~P11(a1,x11391,x11393)+P11(a1,f3(a1,x11391,x11392),f3(a1,x11393,x11392))
% 1.03/1.23 [1142]~P14(a38,x11422,x11423)+P14(a38,f9(a38,x11421,x11422),f9(a38,x11421,x11423))
% 1.03/1.23 [1144]~P13(a38,x11442,x11443)+P13(a38,f9(a38,x11441,x11442),f9(a38,x11441,x11443))
% 1.03/1.23 [1146]~P13(a38,x11461,x11463)+P13(a38,f9(a38,x11461,x11462),f9(a38,x11463,x11462))
% 1.03/1.23 [1147]~P13(a38,x11472,x11473)+P13(a38,f3(a38,x11471,x11472),f3(a38,x11471,x11473))
% 1.03/1.23 [1148]~P13(a38,x11481,x11483)+P13(a38,f3(a38,x11481,x11482),f3(a38,x11483,x11482))
% 1.03/1.23 [1149]~P13(a38,x11493,x11492)+P13(a38,f4(a38,x11491,x11492),f4(a38,x11491,x11493))
% 1.03/1.23 [1150]~P13(a38,x11501,x11503)+P13(a38,f4(a38,x11501,x11502),f4(a38,x11503,x11502))
% 1.03/1.23 [1151]~P13(a1,x11512,x11513)+P13(a1,f3(a1,x11511,x11512),f3(a1,x11511,x11513))
% 1.03/1.23 [1154]~P13(a37,x11542,x11543)+P13(a37,f3(a37,x11541,x11542),f3(a37,x11541,x11543))
% 1.03/1.23 [1174]E(f5(a1,x11741,x11742),f5(a1,x11743,x11742))+~P14(a1,x11742,f4(a1,x11741,x11743))
% 1.03/1.23 [1256]~P11(a38,f3(a38,x12561,x12563),x12562)+P11(a38,x12561,f4(a38,x12562,x12563))
% 1.03/1.23 [1257]~P13(a38,f4(a38,x12571,x12573),x12572)+P13(a38,x12571,f3(a38,x12572,x12573))
% 1.03/1.23 [1258]~P11(a38,x12581,f4(a38,x12583,x12582))+P11(a38,f3(a38,x12581,x12582),x12583)
% 1.03/1.23 [1259]~P13(a38,x12591,f3(a38,x12593,x12592))+P13(a38,f4(a38,x12591,x12592),x12593)
% 1.03/1.23 [1377]P11(a38,x13771,x13772)+~P11(a38,f3(a38,x13773,x13771),f3(a38,x13773,x13772))
% 1.03/1.23 [1378]P11(a38,x13781,x13782)+~P11(a38,f9(a38,x13783,x13781),f9(a38,x13783,x13782))
% 1.03/1.23 [1379]P11(a38,x13791,x13792)+~P11(a38,f9(a38,x13791,x13793),f9(a38,x13792,x13793))
% 1.03/1.23 [1382]P13(a38,x13821,x13822)+~P13(a38,f3(a38,x13823,x13821),f3(a38,x13823,x13822))
% 1.03/1.23 [1386]~P11(a38,f9(a38,x13862,x13861),f9(a38,x13863,x13861))+P11(a38,f2(a38),x13861)
% 1.03/1.23 [1387]~P11(a38,f9(a38,x13871,x13872),f9(a38,x13871,x13873))+P11(a38,f2(a38),x13871)
% 1.03/1.23 [739]~P19(x7391)+E(f3(x7391,f4(x7391,x7392,x7393),x7393),x7392)
% 1.03/1.23 [740]~P19(x7401)+E(f4(x7401,f3(x7401,x7402,x7403),x7403),x7402)
% 1.03/1.23 [754]~P8(x7541)+E(f5(x7541,f9(x7541,x7542,x7543),x7543),f2(x7541))
% 1.03/1.23 [755]~P8(x7551)+E(f5(x7551,f9(x7551,x7552,x7553),x7552),f2(x7551))
% 1.03/1.23 [756]~P8(x7561)+E(f6(x7561,f5(x7561,x7562,x7563),x7563),f2(x7561))
% 1.03/1.23 [850]~P8(x8501)+E(f5(x8501,f3(x8501,x8502,x8503),x8503),f5(x8501,x8502,x8503))
% 1.03/1.23 [851]~P8(x8511)+E(f5(x8511,f3(x8511,x8512,x8513),x8512),f5(x8511,x8513,x8512))
% 1.03/1.23 [852]~P8(x8521)+E(f5(x8521,f5(x8521,x8522,x8523),x8523),f5(x8521,x8522,x8523))
% 1.03/1.23 [870]~P1(x8701)+E(f4(x8701,f13(x8701,x8702),f13(x8701,x8703)),f13(x8701,f4(a1,x8702,x8703)))
% 1.03/1.23 [871]~P1(x8711)+E(f9(x8711,f13(x8711,x8712),f13(x8711,x8713)),f13(x8711,f9(a1,x8712,x8713)))
% 1.03/1.23 [872]~P1(x8721)+E(f3(x8721,f13(x8721,x8722),f13(x8721,x8723)),f13(x8721,f3(a1,x8722,x8723)))
% 1.03/1.23 [1036]P11(a38,x10361,x10362)+~E(x10362,f3(a38,f3(a38,x10361,x10363),f8(a38)))
% 1.03/1.23 [1072]~P64(x10721,x10722,x10723)+P63(f26(x10721,f5(a1,x10722,x10723)))
% 1.03/1.23 [1088]~P3(x10881)+E(f9(x10881,f14(x10881,x10882,x10883),x10882),f9(x10881,x10882,f14(x10881,x10882,x10883)))
% 1.03/1.23 [1247]~P13(a38,x12472,x12473)+E(f4(a38,f3(a38,x12471,x12472),x12473),f4(a38,x12471,f4(a38,x12473,x12472)))
% 1.03/1.23 [1248]~P13(a38,x12483,x12482)+E(f4(a38,f3(a38,x12481,x12482),x12483),f3(a38,x12481,f4(a38,x12482,x12483)))
% 1.03/1.23 [1250]~P13(a38,x12503,x12501)+E(f4(a38,f3(a38,x12501,x12502),x12503),f3(a38,f4(a38,x12501,x12503),x12502))
% 1.03/1.23 [1252]~P11(a1,f2(a1),x12523)+E(f6(a1,f6(a1,x12521,x12522),x12523),f6(a1,x12521,f9(a1,x12522,x12523)))
% 1.03/1.23 [1284]P64(x12841,x12842,x12843)+~P63(f26(x12841,f5(a1,x12842,x12843)))
% 1.03/1.23 [1336]~P14(a1,x13361,x13362)+P14(a1,x13361,f3(a1,x13362,f9(a1,x13361,x13363)))
% 1.03/1.23 [1337]~P13(a38,x13373,x13372)+P13(a38,x13371,f4(a38,f3(a38,x13372,x13371),x13373))
% 1.03/1.23 [1523]~P43(x15231)+P13(x15231,f2(x15231),f3(x15231,f9(x15231,x15232,x15232),f9(x15231,x15233,x15233)))
% 1.03/1.23 [1534]P14(a1,x15341,x15342)+~P14(a1,x15341,f3(a1,x15342,f9(a1,x15341,x15343)))
% 1.03/1.23 [1634]~P43(x16341)+~P11(x16341,f3(x16341,f9(x16341,x16342,x16342),f9(x16341,x16343,x16343)),f2(x16341))
% 1.03/1.23 [1041]~P11(a1,x10411,a10)+E(f9(a38,f13(a38,x10411),f9(a38,f13(a38,x10412),x10413)),f2(a38))
% 1.03/1.23 [1101]~P30(x11011)+E(f9(x11011,x11012,f14(x11011,x11012,x11013)),f14(x11011,x11012,f3(a38,x11013,f8(a38))))
% 1.03/1.23 [1102]~P30(x11021)+E(f9(x11021,f14(x11021,x11022,x11023),x11022),f14(x11021,x11022,f3(a38,x11023,f8(a38))))
% 1.03/1.23 [1103]~P30(x11031)+E(f14(x11031,x11032,f3(a38,x11033,f8(a38))),f9(x11031,x11032,f14(x11031,x11032,x11033)))
% 1.03/1.23 [1104]~P32(x11041)+E(f14(x11041,x11042,f3(a38,x11043,f8(a38))),f9(x11041,x11042,f14(x11041,x11042,x11043)))
% 1.03/1.23 [1105]~P3(x11051)+E(f14(x11051,x11052,f3(a38,x11053,f8(a38))),f9(x11051,f14(x11051,x11052,x11053),x11052))
% 1.03/1.23 [1132]~P30(x11321)+E(f3(x11321,x11322,f9(x11321,x11323,x11322)),f9(x11321,f3(x11321,x11323,f8(x11321)),x11322))
% 1.03/1.23 [1133]~P30(x11331)+E(f3(x11331,f9(x11331,x11332,x11333),x11333),f9(x11331,f3(x11331,x11332,f8(x11331)),x11333))
% 1.03/1.23 [1433]E(x14331,x14332)+~E(f9(a38,f3(a38,x14333,f8(a38)),x14331),f9(a38,f3(a38,x14333,f8(a38)),x14332))
% 1.03/1.23 [1486]P11(a1,x14861,a10)+E(f9(a38,f13(a38,x14861),f9(a38,f13(a38,x14862),x14863)),f9(a38,f13(a38,f9(a1,x14861,x14862)),x14863))
% 1.03/1.23 [1587]~P13(a38,x15872,x15873)+E(f4(a38,f3(a38,x15871,x15872),f3(a38,x15873,f8(a38))),f4(a38,x15871,f3(a38,f4(a38,x15873,x15872),f8(a38))))
% 1.03/1.23 [1588]~P13(a38,x15882,x15881)+E(f4(a38,f3(a38,f4(a38,x15881,x15882),f8(a38)),x15883),f4(a38,f3(a38,x15881,f8(a38)),f3(a38,x15882,x15883)))
% 1.03/1.23 [1597]~P11(a38,x15972,x15973)+P11(a38,f9(a38,f3(a38,x15971,f8(a38)),x15972),f9(a38,f3(a38,x15971,f8(a38)),x15973))
% 1.03/1.23 [1656]P13(a38,x16561,x16562)+~P13(a38,f9(a38,f3(a38,x16563,f8(a38)),x16561),f9(a38,f3(a38,x16563,f8(a38)),x16562))
% 1.03/1.23 [1737]~P30(x17371)+E(f14(x17371,x17372,f3(a38,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17373),f8(a38))),f9(x17371,x17372,f9(x17371,f14(x17371,x17372,x17373),f14(x17371,x17372,x17373))))
% 1.03/1.23 [1680]~P35(x16801)+E(f4(x16801,f14(x16801,x16802,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38))),f14(x16801,x16803,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38)))),f9(x16801,f4(x16801,x16802,x16803),f3(x16801,x16802,x16803)))
% 1.03/1.23 [1723]~P30(x17231)+E(f14(x17231,x17232,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17233)),f9(x17231,f14(x17231,x17232,x17233),f14(x17231,x17232,x17233)))
% 1.03/1.23 [1726]~P3(x17261)+E(f14(x17261,f14(x17261,x17262,x17263),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17261,x17262,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17263)))
% 1.03/1.23 [1735]~P38(x17351)+P13(x17351,f2(x17351),f14(x17351,x17352,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17353)))
% 1.03/1.23 [1740]~P3(x17401)+E(f14(x17401,x17402,f3(a38,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17403),f8(a38))),f9(x17401,x17402,f14(x17401,f14(x17401,x17402,x17403),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))))
% 1.03/1.23 [1748]~P38(x17481)+P13(x17481,f2(x17481),f3(x17481,f14(x17481,x17482,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17481,x17483,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))))
% 1.03/1.23 [1755]~P38(x17551)+~P11(x17551,f3(x17551,f14(x17551,x17552,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17551,x17553,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(x17551))
% 1.03/1.23 [1760]~P1(x17601)+E(f3(x17601,f3(x17601,f14(x17601,x17602,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17601,x17603,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f9(x17601,f9(x17601,f13(x17601,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17602),x17603)),f14(x17601,f3(x17601,x17602,x17603),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.23 [1761]~P1(x17611)+E(f4(x17611,f3(x17611,f14(x17611,x17612,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17611,x17613,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f9(x17611,f9(x17611,f13(x17611,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17612),x17613)),f14(x17611,f4(x17611,x17612,x17613),f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.23 [1079]~P30(x10791)+E(f14(x10791,f14(x10791,x10792,x10793),x10794),f14(x10791,x10792,f9(a38,x10793,x10794)))
% 1.03/1.23 [1080]~P3(x10801)+E(f14(x10801,f14(x10801,x10802,x10803),x10804),f14(x10801,x10802,f9(a38,x10803,x10804)))
% 1.03/1.23 [1082]~P30(x10821)+E(f9(x10821,x10822,f9(x10821,x10823,x10824)),f9(x10821,x10823,f9(x10821,x10822,x10824)))
% 1.03/1.23 [1083]~P30(x10831)+E(f3(x10831,x10832,f3(x10831,x10833,x10834)),f3(x10831,x10833,f3(x10831,x10832,x10834)))
% 1.03/1.23 [1086]~P30(x10861)+E(f9(x10861,f9(x10861,x10862,x10863),x10864),f9(x10861,x10862,f9(x10861,x10863,x10864)))
% 1.03/1.23 [1087]~P5(x10871)+E(f9(x10871,f9(x10871,x10872,x10873),x10874),f9(x10871,x10872,f9(x10871,x10873,x10874)))
% 1.03/1.23 [1089]~P30(x10891)+E(f3(x10891,f3(x10891,x10892,x10893),x10894),f3(x10891,x10892,f3(x10891,x10893,x10894)))
% 1.03/1.23 [1090]~P6(x10901)+E(f3(x10901,f3(x10901,x10902,x10903),x10904),f3(x10901,x10902,f3(x10901,x10903,x10904)))
% 1.03/1.23 [1091]~P30(x10911)+E(f9(x10911,f9(x10911,x10912,x10913),x10914),f9(x10911,f9(x10911,x10912,x10914),x10913))
% 1.03/1.23 [1092]~P30(x10921)+E(f3(x10921,f3(x10921,x10922,x10923),x10924),f3(x10921,f3(x10921,x10922,x10924),x10923))
% 1.03/1.23 [1302]~P3(x13021)+E(f9(x13021,f14(x13021,x13022,x13023),f14(x13021,x13022,x13024)),f14(x13021,x13022,f3(a38,x13023,x13024)))
% 1.03/1.23 [1303]~P30(x13031)+E(f9(x13031,f14(x13031,x13032,x13033),f14(x13031,x13032,x13034)),f14(x13031,x13032,f3(a38,x13033,x13034)))
% 1.03/1.23 [1307]~P30(x13071)+E(f3(x13071,f9(x13071,x13072,x13073),f9(x13071,x13072,x13074)),f9(x13071,x13072,f3(x13071,x13073,x13074)))
% 1.03/1.23 [1309]~P31(x13091)+E(f3(x13091,f9(x13091,x13092,x13093),f9(x13091,x13092,x13094)),f9(x13091,x13092,f3(x13091,x13093,x13094)))
% 1.03/1.23 [1311]~P31(x13111)+E(f4(x13111,f9(x13111,x13112,x13113),f9(x13111,x13112,x13114)),f9(x13111,x13112,f4(x13111,x13113,x13114)))
% 1.03/1.23 [1314]~P31(x13141)+E(f3(x13141,f9(x13141,x13142,x13143),f9(x13141,x13144,x13143)),f9(x13141,f3(x13141,x13142,x13144),x13143))
% 1.03/1.23 [1315]~P34(x13151)+E(f3(x13151,f9(x13151,x13152,x13153),f9(x13151,x13154,x13153)),f9(x13151,f3(x13151,x13152,x13154),x13153))
% 1.03/1.23 [1317]~P31(x13171)+E(f4(x13171,f9(x13171,x13172,x13173),f9(x13171,x13174,x13173)),f9(x13171,f4(x13171,x13172,x13174),x13173))
% 1.03/1.23 [1318]~P30(x13181)+E(f9(x13181,f14(x13181,x13182,x13183),f14(x13181,x13184,x13183)),f14(x13181,f9(x13181,x13182,x13184),x13183))
% 1.03/1.23 [1319]~P18(x13191)+E(f9(x13191,f14(x13191,x13192,x13193),f14(x13191,x13194,x13193)),f14(x13191,f9(x13191,x13192,x13194),x13193))
% 1.03/1.23 [1320]~P8(x13201)+E(f5(x13201,f9(x13201,x13202,x13203),f9(x13201,x13202,x13204)),f9(x13201,x13202,f5(x13201,x13203,x13204)))
% 1.03/1.23 [1321]~P30(x13211)+E(f3(x13211,f9(x13211,x13212,x13213),f9(x13211,x13214,x13213)),f9(x13211,f3(x13211,x13212,x13214),x13213))
% 1.03/1.23 [1322]~P8(x13221)+E(f5(x13221,f9(x13221,x13222,x13223),f9(x13221,x13224,x13223)),f9(x13221,f5(x13221,x13222,x13224),x13223))
% 1.03/1.23 [1305]~P8(x13051)+E(f5(x13051,f3(x13051,x13052,f9(x13051,x13053,x13054)),x13054),f5(x13051,x13052,x13054))
% 1.03/1.23 [1306]~P8(x13061)+E(f5(x13061,f3(x13061,x13062,f9(x13061,x13063,x13064)),x13063),f5(x13061,x13062,x13063))
% 1.03/1.23 [1444]~P1(x14441)+E(f9(x14441,f13(x14441,x14442),f9(x14441,f13(x14441,x14443),x14444)),f9(x14441,f13(x14441,f9(a1,x14442,x14443)),x14444))
% 1.03/1.23 [1445]~P1(x14451)+E(f3(x14451,f13(x14451,x14452),f3(x14451,f13(x14451,x14453),x14454)),f3(x14451,f13(x14451,f3(a1,x14452,x14453)),x14454))
% 1.03/1.23 [1446]~P1(x14461)+E(f3(x14461,f13(x14461,x14462),f4(x14461,f13(x14461,x14463),x14464)),f4(x14461,f13(x14461,f3(a1,x14462,x14463)),x14464))
% 1.03/1.23 [1453]~P8(x14531)+E(f5(x14531,f9(x14531,x14532,f5(x14531,x14533,x14534)),x14534),f5(x14531,f9(x14531,x14532,x14533),x14534))
% 1.03/1.23 [1455]~P9(x14551)+E(f5(x14551,f4(x14551,x14552,f5(x14551,x14553,x14554)),x14554),f5(x14551,f4(x14551,x14552,x14553),x14554))
% 1.03/1.23 [1458]~P9(x14581)+E(f5(x14581,f4(x14581,f5(x14581,x14582,x14583),x14584),x14583),f5(x14581,f4(x14581,x14582,x14584),x14583))
% 1.03/1.23 [1459]~P8(x14591)+E(f5(x14591,f3(x14591,x14592,f5(x14591,x14593,x14594)),x14594),f5(x14591,f3(x14591,x14592,x14593),x14594))
% 1.03/1.23 [1460]~P8(x14601)+E(f5(x14601,f9(x14601,f5(x14601,x14602,x14603),x14604),x14603),f5(x14601,f9(x14601,x14602,x14604),x14603))
% 1.03/1.23 [1461]~P8(x14611)+E(f5(x14611,f3(x14611,f5(x14611,x14612,x14613),x14614),x14613),f5(x14611,f3(x14611,x14612,x14614),x14613))
% 1.03/1.23 [1594]~P8(x15941)+E(f5(x15941,f9(x15941,f5(x15941,x15942,x15943),f5(x15941,x15944,x15943)),x15943),f5(x15941,f9(x15941,x15942,x15944),x15943))
% 1.03/1.23 [1595]~P8(x15951)+E(f5(x15951,f3(x15951,f5(x15951,x15952,x15953),f5(x15951,x15954,x15953)),x15953),f5(x15951,f3(x15951,x15952,x15954),x15953))
% 1.03/1.23 [1596]~P9(x15961)+E(f5(x15961,f4(x15961,f5(x15961,x15962,x15963),f5(x15961,x15964,x15963)),x15963),f5(x15961,f4(x15961,x15962,x15964),x15963))
% 1.03/1.23 [1462]~P30(x14621)+E(f9(x14621,f9(x14621,x14622,x14623),f9(x14621,x14624,x14625)),f9(x14621,f9(x14621,x14622,x14624),f9(x14621,x14623,x14625)))
% 1.03/1.23 [1463]~P30(x14631)+E(f3(x14631,f3(x14631,x14632,x14633),f3(x14631,x14634,x14635)),f3(x14631,f3(x14631,x14632,x14634),f3(x14631,x14633,x14635)))
% 1.03/1.23 [1623]~P58(x16231)+E(f3(x16231,f9(x16231,x16232,x16233),f3(x16231,f9(x16231,x16234,x16233),x16235)),f3(x16231,f9(x16231,f3(x16231,x16232,x16234),x16233),x16235))
% 1.03/1.23 [1640]~P55(x16401)+E(f3(x16401,f9(x16401,x16402,f4(x16401,x16403,x16404)),f9(x16401,f4(x16401,x16402,x16405),x16404)),f4(x16401,f9(x16401,x16402,x16403),f9(x16401,x16405,x16404)))
% 1.03/1.23 [1693]~P31(x16931)+E(f3(x16931,f3(x16931,f9(x16931,f4(x16931,x16932,x16933),f4(x16931,x16934,x16935)),f9(x16931,f4(x16931,x16932,x16933),x16935)),f9(x16931,x16933,f4(x16931,x16934,x16935))),f4(x16931,f9(x16931,x16932,x16934),f9(x16931,x16933,x16935)))
% 1.03/1.23 [1673]~P13(a38,x16731,x16734)+E(f4(a38,f3(a38,f9(a38,x16731,x16732),x16733),f3(a38,f9(a38,x16734,x16732),x16735)),f4(a38,x16733,f3(a38,f9(a38,f4(a38,x16734,x16731),x16732),x16735)))
% 1.03/1.23 [1674]~P13(a38,x16744,x16741)+E(f4(a38,f3(a38,f9(a38,x16741,x16742),x16743),f3(a38,f9(a38,x16744,x16742),x16745)),f4(a38,f3(a38,f9(a38,f4(a38,x16741,x16744),x16742),x16743),x16745))
% 1.03/1.23 [855]P10(a38,x8551)+~P11(a38,f2(a38),x8551)+P10(a38,f4(a38,x8551,f8(a38)))
% 1.03/1.23 [1027]~P10(a38,x10271)+~P11(a38,f2(a38),x10271)+~P10(a38,f4(a38,x10271,f8(a38)))
% 1.03/1.23 [1577]E(x15771,f2(a38))+E(x15771,f3(a38,f2(a38),f8(a38)))+~P11(a38,x15771,f3(a38,f3(a38,f2(a38),f8(a38)),f8(a38)))
% 1.03/1.23 [1714]E(x17141,f2(a38))+E(x17141,f3(a38,f2(a38),f8(a38)))+~P11(a38,x17141,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))
% 1.03/1.23 [645]E(x6451,x6452)+P11(a38,x6452,x6451)+P11(a38,x6451,x6452)
% 1.03/1.23 [646]E(x6461,x6462)+P11(a1,x6462,x6461)+P11(a1,x6461,x6462)
% 1.03/1.23 [690]E(x6901,x6902)+P11(a38,x6901,x6902)+~P13(a38,x6901,x6902)
% 1.03/1.23 [691]E(x6911,x6912)+P11(a1,x6911,x6912)+~P13(a1,x6911,x6912)
% 1.03/1.23 [693]E(x6931,x6932)+P11(a37,x6931,x6932)+~P13(a37,x6931,x6932)
% 1.03/1.23 [749]E(x7491,x7492)+~P14(a38,x7492,x7491)+~P14(a38,x7491,x7492)
% 1.03/1.23 [750]E(x7501,x7502)+~P13(a38,x7502,x7501)+~P13(a38,x7501,x7502)
% 1.03/1.23 [751]E(x7511,x7512)+~P13(a1,x7512,x7511)+~P13(a1,x7511,x7512)
% 1.03/1.23 [752]E(x7521,x7522)+~P13(a37,x7522,x7521)+~P13(a37,x7521,x7522)
% 1.03/1.23 [519]~P59(x5191)+P12(x5191,x5192)+~E(x5192,f2(x5191))
% 1.03/1.23 [520]~P59(x5202)+~P12(x5202,x5201)+E(x5201,f2(x5202))
% 1.03/1.23 [552]~E(x5522,f8(a38))+~E(x5521,f8(a38))+E(f9(a38,x5521,x5522),f8(a38))
% 1.03/1.23 [553]~E(x5532,f8(a1))+~E(x5531,f8(a1))+E(f9(a1,x5531,x5532),f8(a1))
% 1.03/1.23 [554]~E(x5542,f2(a38))+~E(x5541,f2(a38))+E(f3(a38,x5541,x5542),f2(a38))
% 1.03/1.23 [577]~P8(x5772)+E(f6(x5772,x5771,x5771),f8(x5772))+E(x5771,f2(x5772))
% 1.03/1.23 [596]~P4(x5961)+~E(x5962,f2(x5961))+E(f3(x5961,x5962,x5962),f2(x5961))
% 1.03/1.23 [622]~E(f9(a38,x6222,x6221),x6222)+E(x6221,f8(a38))+E(x6222,f2(a38))
% 1.03/1.23 [623]~E(x6231,f13(a1,a11))+~E(x6232,f13(a1,a11))+E(f9(a1,x6231,x6232),f8(a1))
% 1.03/1.23 [625]E(x6251,f2(a38))+E(x6252,f2(a38))+~E(f9(a38,x6252,x6251),f2(a38))
% 1.03/1.23 [632]E(x6322,f13(a1,a11))+E(x6321,f8(a1))+~E(f9(a1,x6321,x6322),f8(a1))
% 1.03/1.23 [633]E(x6332,f13(a1,a11))+E(x6331,f8(a1))+~E(f9(a1,x6332,x6331),f8(a1))
% 1.03/1.23 [634]E(x6341,f13(a1,a11))+E(x6341,f8(a1))+~E(f9(a1,x6342,x6341),f8(a1))
% 1.03/1.23 [636]E(x6361,f13(a1,a11))+E(x6361,f8(a1))+~E(f9(a1,x6361,x6362),f8(a1))
% 1.03/1.23 [639]~P4(x6392)+~E(f3(x6392,x6391,x6391),f2(x6392))+E(x6391,f2(x6392))
% 1.03/1.23 [643]~P30(x6432)+~P14(x6432,f2(x6432),x6431)+E(x6431,f2(x6432))
% 1.03/1.23 [697]~P10(a1,x6972)+E(x6971,f2(a38))+P10(a1,f14(a1,x6972,x6971))
% 1.03/1.23 [700]P10(a38,x7001)+P10(a38,x7002)+P10(a38,f3(a38,x7002,x7001))
% 1.03/1.23 [701]P10(a38,x7011)+P10(a38,x7012)+P10(a38,f4(a38,x7012,x7011))
% 1.03/1.23 [703]P10(a1,x7031)+P10(a1,x7032)+P10(a1,f3(a1,x7032,x7031))
% 1.03/1.23 [704]P10(a1,x7041)+P10(a1,x7042)+P10(a1,f4(a1,x7042,x7041))
% 1.03/1.23 [716]~P10(a38,x7162)+~P10(a38,x7161)+P10(a38,f3(a38,x7161,x7162))
% 1.03/1.23 [717]~P10(a38,x7172)+~P10(a38,x7171)+P10(a38,f4(a38,x7171,x7172))
% 1.03/1.23 [719]~P10(a1,x7192)+~P10(a1,x7191)+P10(a1,f3(a1,x7191,x7192))
% 1.03/1.23 [720]~P10(a1,x7202)+~P10(a1,x7201)+P10(a1,f4(a1,x7201,x7202))
% 1.03/1.23 [766]E(x7661,x7662)+~E(f4(a38,x7662,x7661),f2(a38))+~E(f4(a38,x7661,x7662),f2(a38))
% 1.03/1.23 [769]E(x7691,f8(a1))+~P11(a1,f2(a1),x7692)+~E(f9(a1,x7692,x7691),f8(a1))
% 1.03/1.23 [770]E(x7701,f8(a1))+~P11(a1,f2(a1),x7701)+~E(f9(a1,x7701,x7702),f8(a1))
% 1.03/1.23 [820]P10(a38,x8201)+P10(a38,x8202)+~P10(a38,f9(a38,x8202,x8201))
% 1.03/1.23 [822]P10(a1,x8221)+P10(a1,x8222)+~P10(a1,f9(a1,x8222,x8221))
% 1.03/1.23 [836]P10(a38,x8361)+~P10(a38,x8362)+~P10(a38,f3(a38,x8362,x8361))
% 1.03/1.23 [837]P10(a38,x8371)+~P10(a38,x8372)+~P10(a38,f3(a38,x8371,x8372))
% 1.03/1.23 [840]P10(a1,x8401)+~P10(a1,x8402)+~P10(a1,f3(a1,x8402,x8401))
% 1.03/1.23 [841]P10(a1,x8411)+~P10(a1,x8412)+~P10(a1,f4(a1,x8411,x8412))
% 1.03/1.23 [842]P10(a1,x8421)+~P10(a1,x8422)+~P10(a1,f4(a1,x8422,x8421))
% 1.03/1.23 [843]P10(a1,x8431)+~P10(a1,x8432)+~P10(a1,f3(a1,x8431,x8432))
% 1.03/1.23 [856]~P10(a38,x8561)+~P11(a38,f2(a38),x8562)+P10(a38,f14(a38,x8561,x8562))
% 1.03/1.23 [857]~P14(a38,x8571,x8572)+P13(a38,x8571,x8572)+~P11(a38,f2(a38),x8572)
% 1.03/1.23 [858]~P14(a1,x8581,x8582)+P13(a1,x8581,x8582)+~P11(a1,f2(a1),x8582)
% 1.03/1.23 [859]~P11(a1,x8592,x8591)+E(f5(a1,x8591,x8592),x8591)+~P13(a1,x8591,f2(a1))
% 1.03/1.23 [860]~P11(a1,x8601,x8602)+E(f5(a1,x8601,x8602),x8601)+~P13(a1,f2(a1),x8601)
% 1.03/1.23 [863]~P11(a1,x8632,x8631)+~P13(a1,x8631,f2(a1))+E(f6(a1,x8631,x8632),f2(a1))
% 1.03/1.23 [865]~P11(a1,x8651,x8652)+~P13(a1,f2(a1),x8651)+E(f6(a1,x8651,x8652),f2(a1))
% 1.03/1.23 [866]~P14(a38,x8661,x8662)+~P11(a38,f2(a38),x8662)+P11(a38,f2(a38),x8661)
% 1.03/1.23 [939]P14(a38,f9(a38,x9391,x9392),x9391)+~E(x9392,f8(a38))+~P11(a38,f2(a38),x9391)
% 1.03/1.23 [940]P14(a38,f9(a38,x9401,x9402),x9402)+~E(x9401,f8(a38))+~P11(a38,f2(a38),x9402)
% 1.03/1.23 [948]~P14(a38,x9482,x9481)+~P11(a38,x9481,x9482)+~P11(a38,f2(a38),x9481)
% 1.03/1.23 [949]~P14(a1,x9492,x9491)+~P11(a1,x9491,x9492)+~P11(a1,f2(a1),x9491)
% 1.03/1.23 [957]P13(a1,x9571,x9572)+P13(a1,x9571,a10)+~P13(a38,f13(a38,x9571),f13(a38,x9572))
% 1.03/1.23 [963]~P11(a1,x9631,x9632)+~P11(a1,a10,x9632)+P11(a38,f13(a38,x9631),f13(a38,x9632))
% 1.03/1.23 [970]~P4(x9701)+~P11(x9701,f2(x9701),x9702)+P11(x9701,f2(x9701),f3(x9701,x9702,x9702))
% 1.03/1.23 [973]~P4(x9731)+~P13(x9731,f2(x9731),x9732)+P13(x9731,f2(x9731),f3(x9731,x9732,x9732))
% 1.03/1.23 [975]~P38(x9751)+~P11(x9751,x9752,f2(x9751))+P11(x9751,f3(x9751,x9752,x9752),f2(x9751))
% 1.03/1.23 [976]~P4(x9761)+~P11(x9761,x9762,f2(x9761))+P11(x9761,f3(x9761,x9762,x9762),f2(x9761))
% 1.03/1.23 [977]~P4(x9771)+~P13(x9771,x9772,f2(x9771))+P13(x9771,f3(x9771,x9772,x9772),f2(x9771))
% 1.03/1.23 [999]~P11(a1,x9992,x9991)+P11(a1,a10,x9991)+~P11(a38,f13(a38,x9992),f13(a38,x9991))
% 1.03/1.23 [1052]E(x10521,f2(a38))+P11(a38,f2(a38),x10522)+~P11(a38,f2(a38),f14(a38,x10522,x10521))
% 1.03/1.23 [1095]~P38(x10951)+~P11(x10951,f3(x10951,x10952,x10952),f2(x10951))+P11(x10951,x10952,f2(x10951))
% 1.03/1.23 [1096]~P4(x10961)+~P11(x10961,f3(x10961,x10962,x10962),f2(x10961))+P11(x10961,x10962,f2(x10961))
% 1.03/1.23 [1097]~P4(x10971)+~P13(x10971,f3(x10971,x10972,x10972),f2(x10971))+P13(x10971,x10972,f2(x10971))
% 1.03/1.23 [1098]~P4(x10981)+~P11(x10981,f2(x10981),f3(x10981,x10982,x10982))+P11(x10981,f2(x10981),x10982)
% 1.03/1.23 [1099]~P4(x10991)+~P13(x10991,f2(x10991),f3(x10991,x10992,x10992))+P13(x10991,f2(x10991),x10992)
% 1.03/1.23 [1100]~P13(a1,x11002,x11001)+~P11(a1,f2(a1),x11002)+P11(a1,f2(a1),f6(a1,x11001,x11002))
% 1.03/1.23 [1106]P11(a38,f4(a38,x11061,x11062),x11061)+~P11(a38,f2(a38),x11061)+~P11(a38,f2(a38),x11062)
% 1.03/1.23 [1107]P11(a1,f6(a1,x11071,x11072),x11071)+~P11(a1,f2(a1),x11071)+~P11(a1,f8(a1),x11072)
% 1.03/1.23 [1112]~P11(a1,x11122,f2(a1))+~P13(a1,x11121,f2(a1))+P13(a1,f2(a1),f6(a1,x11121,x11122))
% 1.03/1.23 [1113]~P11(a38,f2(a38),x11132)+~P11(a38,f2(a38),x11131)+P11(a38,f2(a38),f9(a38,x11131,x11132))
% 1.03/1.23 [1114]~P11(a37,f2(a37),x11142)+~P11(a37,f2(a37),x11141)+P11(a37,f2(a37),f9(a37,x11141,x11142))
% 1.03/1.23 [1115]~P13(a1,f2(a1),x11152)+~P13(a1,f2(a1),x11151)+P13(a1,f2(a1),f9(a1,x11151,x11152))
% 1.03/1.23 [1116]~P13(a1,f2(a1),x11162)+~P13(a1,f2(a1),x11161)+P13(a1,f2(a1),f3(a1,x11161,x11162))
% 1.03/1.23 [1117]~P13(a1,f2(a1),x11172)+~P13(a1,f2(a1),x11171)+P13(a1,f2(a1),f5(a1,x11171,x11172))
% 1.03/1.23 [1118]~P11(a1,f2(a1),x11182)+~P13(a1,f2(a1),x11181)+P13(a1,f2(a1),f6(a1,x11181,x11182))
% 1.03/1.23 [1119]~P11(a1,x11192,f2(a1))+~P13(a1,f2(a1),x11191)+P13(a1,f6(a1,x11191,x11192),f2(a1))
% 1.03/1.23 [1120]~P13(a1,x11201,f2(a1))+~P11(a1,f2(a1),x11202)+P13(a1,f6(a1,x11201,x11202),f2(a1))
% 1.03/1.23 [1121]~P14(a38,f9(a38,x11212,x11211),x11212)+E(x11211,f8(a38))+~P11(a38,f2(a38),x11212)
% 1.03/1.23 [1122]~P14(a38,f9(a38,x11221,x11222),x11222)+E(x11221,f8(a38))+~P11(a38,f2(a38),x11222)
% 1.03/1.23 [1192]P11(a38,f2(a38),x11921)+P11(a38,f2(a38),x11922)+~P11(a38,f2(a38),f3(a38,x11922,x11921))
% 1.03/1.23 [1240]P13(a1,x12401,x12402)+~P11(a1,f2(a1),x12401)+~P11(a1,f2(a1),f6(a1,x12402,x12401))
% 1.03/1.23 [1241]P13(a1,x12411,x12412)+~P13(a1,f2(a1),x12412)+~P11(a1,f2(a1),f6(a1,x12412,x12411))
% 1.03/1.23 [1243]P13(a1,x12431,f2(a1))+~P11(a1,x12432,f2(a1))+~P13(a1,f2(a1),f6(a1,x12431,x12432))
% 1.03/1.23 [1244]P11(a1,f2(a1),x12441)+~P13(a1,f2(a1),x12442)+~P11(a1,f2(a1),f6(a1,x12442,x12441))
% 1.03/1.23 [1245]P13(a1,f2(a1),x12451)+~P11(a1,f2(a1),x12452)+~P13(a1,f2(a1),f6(a1,x12451,x12452))
% 1.03/1.23 [1329]E(f5(a1,x13291,x13292),f3(a1,x13291,x13292))+~P11(a1,f2(a1),x13291)+~P13(a1,f3(a1,x13291,x13292),f2(a1))
% 1.03/1.23 [648]~P1(x6481)+~P10(a38,x6482)+E(f14(x6481,f13(x6481,a11),x6482),f8(x6481))
% 1.03/1.23 [650]~P1(x6501)+P10(a38,x6502)+E(f14(x6501,f13(x6501,a11),x6502),f13(x6501,a11))
% 1.03/1.23 [788]E(x7881,f2(a38))+E(x7882,f2(a38))+~E(f3(a38,x7882,x7881),f3(a38,f2(a38),f8(a38)))
% 1.03/1.23 [789]E(x7891,f2(a38))+E(x7892,f2(a38))+~E(f3(a38,f2(a38),f8(a38)),f3(a38,x7892,x7891))
% 1.03/1.23 [824]~E(x8242,f2(a38))+~E(x8241,f3(a38,f2(a38),f8(a38)))+E(f3(a38,x8241,x8242),f3(a38,f2(a38),f8(a38)))
% 1.03/1.23 [825]~E(x8251,f2(a38))+~E(x8252,f3(a38,f2(a38),f8(a38)))+E(f3(a38,x8251,x8252),f3(a38,f2(a38),f8(a38)))
% 1.03/1.23 [826]~E(x8262,f2(a38))+~E(x8261,f3(a38,f2(a38),f8(a38)))+E(f3(a38,f2(a38),f8(a38)),f3(a38,x8261,x8262))
% 1.03/1.23 [827]~E(x8271,f2(a38))+~E(x8272,f3(a38,f2(a38),f8(a38)))+E(f3(a38,f2(a38),f8(a38)),f3(a38,x8271,x8272))
% 1.03/1.23 [887]E(x8871,f2(a38))+E(x8872,f3(a38,f2(a38),f8(a38)))+~E(f14(a38,x8872,x8871),f3(a38,f2(a38),f8(a38)))
% 1.03/1.23 [888]E(x8881,f2(a38))+E(x8881,f3(a38,f2(a38),f8(a38)))+~E(f3(a38,x8882,x8881),f3(a38,f2(a38),f8(a38)))
% 1.03/1.23 [889]E(x8891,f2(a38))+E(x8891,f3(a38,f2(a38),f8(a38)))+~E(f3(a38,x8891,x8892),f3(a38,f2(a38),f8(a38)))
% 1.03/1.23 [890]E(x8901,f2(a38))+E(x8901,f3(a38,f2(a38),f8(a38)))+~E(f3(a38,f2(a38),f8(a38)),f3(a38,x8902,x8901))
% 1.03/1.23 [891]E(x8911,f2(a38))+E(x8911,f3(a38,f2(a38),f8(a38)))+~E(f3(a38,f2(a38),f8(a38)),f3(a38,x8911,x8912))
% 1.03/1.23 [904]P11(a1,x9041,a10)+~P11(a1,x9042,a10)+E(f3(a38,f13(a38,x9041),f13(a38,x9042)),f13(a38,x9041))
% 1.03/1.23 [982]~E(x9822,f2(a37))+~E(x9821,f2(a37))+E(f3(a37,f9(a37,x9821,x9821),f9(a37,x9822,x9822)),f2(a37))
% 1.03/1.23 [1017]E(x10171,f3(a38,f2(a38),f8(a38)))+E(x10172,f3(a38,f2(a38),f8(a38)))+~E(f3(a38,x10171,x10172),f3(a38,f2(a38),f8(a38)))
% 1.03/1.23 [1018]E(x10181,f3(a38,f2(a38),f8(a38)))+E(x10182,f3(a38,f2(a38),f8(a38)))+~E(f3(a38,f2(a38),f8(a38)),f3(a38,x10181,x10182))
% 1.03/1.23 [1026]~E(x10262,f3(a38,f2(a38),f8(a38)))+~E(x10261,f3(a38,f2(a38),f8(a38)))+E(f9(a38,x10261,x10262),f3(a38,f2(a38),f8(a38)))
% 1.03/1.23 [1030]~P11(a38,x10301,x10302)+P11(a38,f3(a38,x10301,f8(a38)),x10302)+E(f3(a38,x10301,f8(a38)),x10302)
% 1.03/1.23 [1056]E(x10561,x10562)+P11(a38,x10561,x10562)+~P11(a38,x10561,f3(a38,x10562,f8(a38)))
% 1.03/1.23 [1057]E(x10571,x10572)+P11(a1,x10571,x10572)+~P11(a1,x10571,f3(a1,x10572,f8(a1)))
% 1.03/1.23 [1062]P11(a1,x10621,a10)+P11(a1,x10622,a10)+E(f3(a38,f13(a38,x10621),f13(a38,x10622)),f13(a38,f3(a1,x10621,x10622)))
% 1.03/1.23 [1123]P11(a38,f29(x11232,x11231),x11232)+E(x11231,f2(a38))+~P11(a38,x11231,f3(a38,x11232,f8(a38)))
% 1.03/1.23 [1134]E(x11341,x11342)+~P13(a38,x11342,x11341)+~P11(a38,x11341,f3(a38,x11342,f8(a38)))
% 1.03/1.23 [1135]E(x11351,f2(a38))+~P11(a38,x11351,f3(a38,x11352,f8(a38)))+E(f3(a38,f29(x11352,x11351),f8(a38)),x11351)
% 1.03/1.23 [1222]P13(a38,x12221,x12222)+~P13(a38,x12221,f3(a38,x12222,f8(a38)))+E(x12221,f3(a38,x12222,f8(a38)))
% 1.03/1.23 [1578]P11(a38,x15781,f9(a38,x15782,x15781))+~P11(a38,f3(a38,f2(a38),f8(a38)),x15782)+~P11(a38,f3(a38,f2(a38),f8(a38)),x15781)
% 1.03/1.23 [1579]P11(a38,x15791,f9(a38,x15791,x15792))+~P11(a38,f3(a38,f2(a38),f8(a38)),x15792)+~P11(a38,f3(a38,f2(a38),f8(a38)),x15791)
% 1.03/1.23 [1604]~P11(a38,f3(a38,f2(a38),f8(a38)),x16041)+~P11(a38,f3(a38,f2(a38),f8(a38)),x16042)+P11(a38,f3(a38,f2(a38),f8(a38)),f9(a38,x16041,x16042))
% 1.03/1.23 [1605]~P13(a38,f3(a38,f2(a38),f8(a38)),x16052)+~P13(a38,f3(a38,f2(a38),f8(a38)),x16051)+P13(a38,f3(a38,f2(a38),f8(a38)),f9(a38,x16051,x16052))
% 1.03/1.23 [792]~P32(x7921)+~P60(x7921)+E(f14(x7921,f2(x7921),f3(a38,x7922,f8(a38))),f2(x7921))
% 1.03/1.23 [1651]~P28(x16511)+~P1(x16511)+~P12(x16511,f13(x16511,f3(a1,f3(a1,f8(a1),x16512),x16512)))
% 1.03/1.23 [1698]~P50(x16981)+~E(x16982,f2(x16981))+E(f14(x16981,x16982,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f2(x16981))
% 1.03/1.23 [1719]~P38(x17192)+E(x17191,f2(x17192))+P11(x17192,f2(x17192),f14(x17192,x17191,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.23 [1731]~P38(x17312)+~E(x17311,f2(x17312))+~P11(x17312,f2(x17312),f14(x17312,x17311,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.23 [1733]~E(x17332,f2(a37))+~E(x17331,f2(a37))+E(f3(a37,f14(a37,x17331,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(a37,x17332,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(a37))
% 1.03/1.23 [846]~P14(a38,x8461,x8463)+P14(a38,x8461,x8462)+~P14(a38,x8463,x8462)
% 1.03/1.23 [847]~P13(a38,x8471,x8473)+P13(a38,x8471,x8472)+~P13(a38,x8473,x8472)
% 1.03/1.23 [848]~P13(a1,x8481,x8483)+P13(a1,x8481,x8482)+~P13(a1,x8483,x8482)
% 1.03/1.23 [849]~P13(a37,x8491,x8493)+P13(a37,x8491,x8492)+~P13(a37,x8493,x8492)
% 1.03/1.23 [575]~E(x5752,x5753)+~P7(x5751)+E(f4(x5751,x5752,x5753),f2(x5751))
% 1.03/1.23 [576]~E(x5762,x5763)+~P19(x5761)+E(f4(x5761,x5762,x5763),f2(x5761))
% 1.03/1.23 [578]~P57(x5781)+~E(x5783,f2(x5781))+E(f3(x5781,x5782,x5783),x5782)
% 1.03/1.23 [579]~P32(x5791)+E(f14(x5791,x5792,x5793),f8(x5791))+~E(x5793,f2(a38))
% 1.03/1.23 [594]~P48(x5941)+~E(x5943,f2(x5941))+E(f9(x5941,x5942,x5943),f2(x5941))
% 1.03/1.23 [595]~P48(x5951)+~E(x5952,f2(x5951))+E(f9(x5951,x5952,x5953),f2(x5951))
% 1.03/1.23 [629]~P57(x6292)+~E(f3(x6292,x6293,x6291),x6293)+E(x6291,f2(x6292))
% 1.03/1.23 [630]~P7(x6303)+E(x6301,x6302)+~E(f4(x6303,x6301,x6302),f2(x6303))
% 1.03/1.23 [631]~P19(x6313)+E(x6311,x6312)+~E(f4(x6313,x6311,x6312),f2(x6313))
% 1.03/1.23 [638]~P50(x6382)+~E(f14(x6382,x6381,x6383),f2(x6382))+E(x6381,f2(x6382))
% 1.03/1.23 [664]~P64(x6641,x6642,x6643)+~E(x6643,f2(a1))+P63(f26(x6641,x6642))
% 1.03/1.23 [711]~P8(x7111)+~P14(x7111,x7113,x7112)+E(f5(x7111,x7112,x7113),f2(x7111))
% 1.03/1.23 [712]~P8(x7121)+P14(x7121,x7122,x7123)+~E(f5(x7121,x7123,x7122),f2(x7121))
% 1.03/1.23 [758]E(x7581,x7582)+~E(f9(a38,x7583,x7581),f9(a38,x7583,x7582))+E(x7583,f2(a38))
% 1.03/1.23 [759]E(x7591,x7592)+~E(f9(a37,x7593,x7591),f9(a37,x7593,x7592))+E(x7593,f2(a37))
% 1.03/1.23 [760]E(x7601,x7602)+~E(f9(a38,x7601,x7603),f9(a38,x7602,x7603))+E(x7603,f2(a38))
% 1.03/1.23 [761]E(x7611,x7612)+~E(f9(a37,x7611,x7613),f9(a37,x7612,x7613))+E(x7613,f2(a37))
% 1.03/1.23 [765]~P30(x7651)+P14(x7651,x7652,f14(x7651,x7652,x7653))+~E(x7652,f8(x7651))
% 1.03/1.23 [777]~P38(x7771)+P11(x7771,f2(x7771),f14(x7771,x7772,x7773))+~E(x7773,f2(a38))
% 1.03/1.23 [797]~P38(x7971)+P13(x7971,f2(x7971),f14(x7971,x7972,x7973))+~P10(a38,x7973)
% 1.03/1.23 [853]~P13(a38,x8533,x8531)+~E(f4(a38,x8531,x8533),x8532)+E(x8531,f3(a38,x8532,x8533))
% 1.03/1.23 [854]~P13(a38,x8542,x8541)+~E(x8541,f3(a38,x8543,x8542))+E(f4(a38,x8541,x8542),x8543)
% 1.03/1.23 [951]E(x9511,x9512)+~E(f9(a38,x9513,x9511),f9(a38,x9513,x9512))+~P11(a38,f2(a38),x9513)
% 1.03/1.23 [952]~P30(x9521)+P14(x9521,x9522,f14(x9521,x9522,x9523))+~P11(a38,f2(a38),x9523)
% 1.03/1.23 [958]~P24(x9581)+~P11(x9581,x9582,x9583)+P11(x9581,f4(x9581,x9582,x9583),f2(x9581))
% 1.03/1.23 [959]~P24(x9591)+~P13(x9591,x9592,x9593)+P13(x9591,f4(x9591,x9592,x9593),f2(x9591))
% 1.03/1.23 [969]~P37(x9691)+~P11(x9691,f2(x9691),x9692)+P11(x9691,f2(x9691),f14(x9691,x9692,x9693))
% 1.03/1.23 [971]~P37(x9711)+~P13(x9711,f2(x9711),x9712)+P13(x9711,f2(x9711),f14(x9711,x9712,x9713))
% 1.03/1.23 [972]~P38(x9721)+~P13(x9721,f2(x9721),x9722)+P13(x9721,f2(x9721),f14(x9721,x9722,x9723))
% 1.03/1.23 [974]~P37(x9741)+~P13(x9741,f8(x9741),x9742)+P13(x9741,f8(x9741),f14(x9741,x9742,x9743))
% 1.03/1.23 [986]~P38(x9862)+~P13(x9862,f14(x9862,x9863,x9861),f2(x9862))+~E(x9861,f2(a38))
% 1.03/1.23 [998]~P38(x9981)+~P11(x9981,f14(x9981,x9983,x9982),f2(x9981))+~P10(a38,x9982)
% 1.03/1.23 [1073]~P14(a38,x10731,x10733)+~P14(a38,x10731,x10732)+P14(a38,x10731,f4(a38,x10732,x10733))
% 1.03/1.23 [1074]~P14(a1,x10741,x10743)+~P14(a1,x10741,x10742)+P14(a1,x10741,f5(a1,x10742,x10743))
% 1.03/1.23 [1075]~P24(x10751)+P11(x10751,x10752,x10753)+~P11(x10751,f4(x10751,x10752,x10753),f2(x10751))
% 1.03/1.23 [1076]~P24(x10761)+P13(x10761,x10762,x10763)+~P13(x10761,f4(x10761,x10762,x10763),f2(x10761))
% 1.03/1.23 [1094]~P38(x10941)+~P11(x10941,f14(x10941,x10942,x10943),f2(x10941))+P11(x10941,x10942,f2(x10941))
% 1.03/1.23 [1160]~P14(a38,x11602,x11603)+E(x11601,f2(a38))+P14(a38,f14(a38,x11602,x11601),f14(a38,x11603,x11601))
% 1.03/1.23 [1161]~P14(a1,x11612,x11613)+E(x11611,f2(a38))+P14(a1,f14(a1,x11612,x11611),f14(a1,x11613,x11611))
% 1.03/1.23 [1162]~P14(a1,x11622,x11623)+E(x11621,f2(a1))+P14(a1,f9(a1,x11621,x11622),f9(a1,x11621,x11623))
% 1.03/1.23 [1229]P14(a1,x12291,x12292)+~P14(a1,x12291,x12293)+~P14(a1,x12291,f4(a1,x12292,x12293))
% 1.03/1.23 [1230]P14(a1,x12301,x12302)+~P14(a1,x12301,x12303)+~P14(a1,x12301,f5(a1,x12302,x12303))
% 1.03/1.23 [1279]~P11(a38,x12793,x12791)+~P11(a38,x12793,x12792)+P11(a38,f4(a38,x12791,x12792),f4(a38,x12791,x12793))
% 1.03/1.23 [1280]~P11(a38,x12801,x12803)+~P13(a38,x12802,x12801)+P11(a38,f4(a38,x12801,x12802),f4(a38,x12803,x12802))
% 1.03/1.23 [1288]~P13(a1,x12883,x12881)+P13(a1,f6(a1,x12881,x12882),f6(a1,x12883,x12882))+~P11(a1,x12882,f2(a1))
% 1.03/1.23 [1292]~P11(a38,x12921,x12923)+P11(a38,f9(a38,x12921,x12922),f9(a38,x12923,x12922))+~P11(a38,f2(a38),x12922)
% 1.03/1.23 [1293]~P11(a38,x12932,x12933)+P11(a38,f9(a38,x12931,x12932),f9(a38,x12931,x12933))+~P11(a38,f2(a38),x12931)
% 1.03/1.23 [1294]~P11(a1,x12942,x12943)+P11(a1,f9(a1,x12941,x12942),f9(a1,x12941,x12943))+~P11(a1,f2(a1),x12941)
% 1.03/1.23 [1295]~P11(a37,x12951,x12953)+P11(a37,f9(a37,x12951,x12952),f9(a37,x12953,x12952))+~P11(a37,f2(a37),x12952)
% 1.03/1.23 [1296]~P11(a37,x12962,x12963)+P11(a37,f9(a37,x12961,x12962),f9(a37,x12961,x12963))+~P11(a37,f2(a37),x12961)
% 1.03/1.23 [1299]~P13(a1,x12991,x12993)+P13(a1,f6(a1,x12991,x12992),f6(a1,x12993,x12992))+~P11(a1,f2(a1),x12992)
% 1.03/1.23 [1300]~P13(a37,x13002,x13003)+P13(a37,f9(a37,x13001,x13002),f9(a37,x13001,x13003))+~P11(a37,f2(a37),x13001)
% 1.03/1.23 [1301]~P13(a37,x13011,x13013)+P13(a37,f9(a37,x13011,x13012),f9(a37,x13013,x13012))+~P11(a37,f2(a37),x13012)
% 1.03/1.23 [1392]P14(a38,x13922,x13923)+E(x13921,f2(a38))+~P14(a38,f14(a38,x13922,x13921),f14(a38,x13923,x13921))
% 1.03/1.23 [1394]P14(a1,x13942,x13943)+E(x13941,f2(a38))+~P14(a1,f14(a1,x13942,x13941),f14(a1,x13943,x13941))
% 1.03/1.23 [1395]P14(a38,x13952,x13953)+E(x13951,f2(a38))+~P14(a38,f9(a38,x13951,x13952),f9(a38,x13951,x13953))
% 1.03/1.23 [1397]P14(a1,x13972,x13973)+E(x13971,f2(a1))+~P14(a1,f9(a1,x13971,x13972),f9(a1,x13971,x13973))
% 1.03/1.23 [1419]~P13(a38,x14193,x14192)+~P13(a38,f3(a38,x14191,x14193),x14192)+P13(a38,x14191,f4(a38,x14192,x14193))
% 1.03/1.23 [1420]~P13(a38,x14202,x14203)+~P13(a38,x14201,f4(a38,x14203,x14202))+P13(a38,f3(a38,x14201,x14202),x14203)
% 1.03/1.23 [1476]P11(a38,x14761,x14762)+~P11(a38,f14(a38,x14763,x14761),f14(a38,x14763,x14762))+~P11(a38,f2(a38),x14763)
% 1.03/1.23 [1477]P11(a37,x14771,x14772)+~P11(a37,f9(a37,x14771,x14773),f9(a37,x14772,x14773))+~P11(a37,f2(a37),x14773)
% 1.03/1.23 [1479]P14(a38,x14791,x14792)+~P14(a38,f9(a38,x14793,x14791),f9(a38,x14793,x14792))+~P11(a38,f2(a38),x14793)
% 1.03/1.23 [1481]P13(a38,x14811,x14812)+~P13(a38,f9(a38,x14813,x14811),f9(a38,x14813,x14812))+~P11(a38,f2(a38),x14813)
% 1.03/1.23 [1482]P13(a38,x14821,x14822)+~P14(a38,f14(a38,x14823,x14821),f14(a38,x14823,x14822))+~P11(a38,f8(a38),x14823)
% 1.03/1.23 [1483]P13(a38,x14831,x14832)+~P13(a38,f9(a38,x14831,x14833),f9(a38,x14832,x14833))+~P11(a38,f2(a38),x14833)
% 1.03/1.23 [1484]P13(a37,x14841,x14842)+~P13(a37,f9(a37,x14843,x14841),f9(a37,x14843,x14842))+~P11(a37,f2(a37),x14843)
% 1.03/1.23 [1485]P13(a37,x14851,x14852)+~P13(a37,f9(a37,x14851,x14853),f9(a37,x14852,x14853))+~P11(a37,f2(a37),x14853)
% 1.03/1.23 [947]~P8(x9471)+~P14(x9471,x9472,x9473)+E(f9(x9471,x9472,f6(x9471,x9473,x9472)),x9473)
% 1.03/1.23 [1093]~P11(a38,x10931,x10933)+~P11(a38,x10933,x10932)+P11(a38,f3(a38,x10931,f8(a38)),x10932)
% 1.03/1.23 [1110]~P11(a38,x11103,x11102)+P11(a38,x11101,f3(a38,x11102,f8(a38)))+~E(x11101,f3(a38,x11103,f8(a38)))
% 1.03/1.23 [1325]~P42(x13252)+E(x13251,f2(x13252))+~E(f3(x13252,f9(x13252,x13253,x13253),f9(x13252,x13251,x13251)),f2(x13252))
% 1.03/1.23 [1326]~P42(x13262)+E(x13261,f2(x13262))+~E(f3(x13262,f9(x13262,x13261,x13261),f9(x13262,x13263,x13263)),f2(x13262))
% 1.03/1.23 [1338]P11(a38,x13382,x13381)+E(f3(a38,x13381,f22(x13381,x13382,x13383)),x13382)+P63(f26(x13383,f4(a38,x13382,x13381)))
% 1.03/1.23 [1339]P11(a38,x13392,x13391)+E(f3(a38,x13391,f23(x13391,x13392,x13393)),x13392)+P63(f26(x13393,f4(a38,x13392,x13391)))
% 1.03/1.23 [1345]E(f3(a38,x13451,f22(x13451,x13452,x13453)),x13452)+P63(f26(x13453,f4(a38,x13452,x13451)))+~P63(f26(x13453,f2(a38)))
% 1.03/1.23 [1346]E(f3(a38,x13461,f23(x13461,x13462,x13463)),x13462)+P63(f26(x13463,f4(a38,x13462,x13461)))+~P63(f26(x13463,f2(a38)))
% 1.03/1.23 [1403]~P13(a38,x14032,x14033)+~P13(a38,x14032,x14031)+E(f4(a38,f4(a38,x14031,x14032),f4(a38,x14033,x14032)),f4(a38,x14031,x14033))
% 1.03/1.23 [1418]~P37(x14181)+~P11(x14181,f8(x14181),x14182)+P11(x14181,f8(x14181),f9(x14181,x14182,f14(x14181,x14182,x14183)))
% 1.03/1.23 [1427]~P11(a38,x14272,x14273)+~P63(f26(x14271,f4(a38,x14272,x14273)))+P63(f26(x14271,f2(a38)))
% 1.03/1.23 [1516]~P37(x15161)+~P11(x15161,f8(x15161),x15162)+P11(x15161,f14(x15161,x15162,x15163),f9(x15161,x15162,f14(x15161,x15162,x15163)))
% 1.03/1.23 [1528]~P42(x15282)+E(x15281,f2(x15282))+P11(x15282,f2(x15282),f3(x15282,f9(x15282,x15283,x15283),f9(x15282,x15281,x15281)))
% 1.03/1.23 [1529]~P42(x15292)+E(x15291,f2(x15292))+P11(x15292,f2(x15292),f3(x15292,f9(x15292,x15291,x15291),f9(x15292,x15293,x15293)))
% 1.03/1.23 [1568]P11(a38,x15681,x15682)+~P63(f26(x15683,f22(x15682,x15681,x15683)))+P63(f26(x15683,f4(a38,x15681,x15682)))
% 1.03/1.23 [1569]P11(a38,x15691,x15692)+~P63(f26(x15693,f23(x15692,x15691,x15693)))+P63(f26(x15693,f4(a38,x15691,x15692)))
% 1.03/1.23 [1570]~P63(f26(x15701,f22(x15703,x15702,x15701)))+P63(f26(x15701,f4(a38,x15702,x15703)))+~P63(f26(x15701,f2(a38)))
% 1.03/1.23 [1571]~P63(f26(x15711,f23(x15713,x15712,x15711)))+P63(f26(x15711,f4(a38,x15712,x15713)))+~P63(f26(x15711,f2(a38)))
% 1.03/1.23 [1635]~P42(x16352)+E(x16351,f2(x16352))+~P13(x16352,f3(x16352,f9(x16352,x16353,x16353),f9(x16352,x16351,x16351)),f2(x16352))
% 1.03/1.23 [1636]~P42(x16362)+E(x16361,f2(x16362))+~P13(x16362,f3(x16362,f9(x16362,x16361,x16361),f9(x16362,x16363,x16363)),f2(x16362))
% 1.03/1.23 [1425]~P37(x14251)+~P11(x14251,f8(x14251),x14252)+P11(x14251,f8(x14251),f14(x14251,x14252,f3(a38,x14253,f8(a38))))
% 1.03/1.23 [1752]~P38(x17521)+~P11(x17521,x17522,f2(x17521))+P11(x17521,f14(x17521,x17522,f3(a38,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17523),f8(a38))),f2(x17521))
% 1.03/1.23 [1759]~P38(x17591)+P13(x17591,f2(x17591),x17592)+~P13(x17591,f2(x17591),f14(x17591,x17592,f3(a38,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17593),f8(a38))))
% 1.03/1.23 [1330]~P32(x13302)+E(x13301,f2(a38))+E(f9(x13302,x13303,f14(x13302,x13303,f4(a38,x13301,f8(a38)))),f14(x13302,x13303,x13301))
% 1.03/1.23 [1443]~P3(x14431)+~P11(a38,f2(a38),x14433)+E(f9(x14431,f14(x14431,x14432,f4(a38,x14433,f8(a38))),x14432),f14(x14431,x14432,x14433))
% 1.03/1.23 [1743]~P38(x17432)+E(x17431,f2(x17432))+~E(f3(x17432,f14(x17432,x17433,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17432,x17431,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(x17432))
% 1.03/1.23 [1744]~P38(x17442)+E(x17441,f2(x17442))+~E(f3(x17442,f14(x17442,x17441,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17442,x17443,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(x17442))
% 1.03/1.23 [1747]~P38(x17472)+E(x17471,f2(x17472))+~P13(x17472,f14(x17472,x17471,f9(a38,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))),x17473)),f2(x17472))
% 1.03/1.23 [1749]~P38(x17492)+E(x17491,f2(x17492))+P11(x17492,f2(x17492),f3(x17492,f14(x17492,x17493,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17492,x17491,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))))
% 1.03/1.23 [1750]~P38(x17502)+E(x17501,f2(x17502))+P11(x17502,f2(x17502),f3(x17502,f14(x17502,x17501,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17502,x17503,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))))
% 1.03/1.23 [1756]~P38(x17562)+E(x17561,f2(x17562))+~P13(x17562,f3(x17562,f14(x17562,x17563,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17562,x17561,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(x17562))
% 1.03/1.23 [1757]~P38(x17572)+E(x17571,f2(x17572))+~P13(x17572,f3(x17572,f14(x17572,x17571,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17572,x17573,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(x17572))
% 1.03/1.23 [708]~P39(x7081)+P14(x7081,x7082,x7083)+~E(x7083,f9(x7081,x7082,x7084))
% 1.03/1.23 [773]~P15(x7733)+E(x7731,x7732)+~E(f3(x7733,x7734,x7731),f3(x7733,x7734,x7732))
% 1.03/1.23 [774]~P16(x7743)+E(x7741,x7742)+~E(f3(x7743,x7744,x7741),f3(x7743,x7744,x7742))
% 1.03/1.23 [776]~P15(x7763)+E(x7761,x7762)+~E(f3(x7763,x7761,x7764),f3(x7763,x7762,x7764))
% 1.03/1.23 [943]~P30(x9431)+~P14(x9431,x9432,x9434)+P14(x9431,x9432,f9(x9431,x9433,x9434))
% 1.03/1.23 [944]~P30(x9441)+~P14(x9441,x9442,x9443)+P14(x9441,x9442,f9(x9441,x9443,x9444))
% 1.03/1.23 [995]~P40(x9951)+P14(x9951,f9(x9951,x9952,x9953),f9(x9951,x9954,x9953))+~E(x9953,f2(x9951))
% 1.03/1.23 [996]~P40(x9961)+P14(x9961,f9(x9961,x9962,x9963),f9(x9961,x9962,x9964))+~E(x9962,f2(x9961))
% 1.03/1.23 [1029]~P11(a38,x10293,x10294)+P11(a38,x10291,x10292)+~E(f3(a38,x10293,x10292),f3(a38,x10291,x10294))
% 1.03/1.23 [1058]~P30(x10581)+P14(x10581,x10582,x10583)+~P14(x10581,f9(x10581,x10584,x10582),x10583)
% 1.03/1.23 [1059]~P30(x10591)+P14(x10591,x10592,x10593)+~P14(x10591,f9(x10591,x10592,x10594),x10593)
% 1.03/1.23 [1179]~P30(x11791)+~P13(a38,x11793,x11794)+P14(x11791,f14(x11791,x11792,x11793),f14(x11791,x11792,x11794))
% 1.03/1.23 [1181]~P22(x11811)+~P11(x11811,x11813,x11814)+P11(x11811,f3(x11811,x11812,x11813),f3(x11811,x11812,x11814))
% 1.03/1.23 [1182]~P26(x11821)+~P11(x11821,x11823,x11824)+P11(x11821,f3(x11821,x11822,x11823),f3(x11821,x11822,x11824))
% 1.03/1.23 [1183]~P22(x11831)+~P11(x11831,x11832,x11834)+P11(x11831,f3(x11831,x11832,x11833),f3(x11831,x11834,x11833))
% 1.03/1.23 [1184]~P26(x11841)+~P11(x11841,x11842,x11844)+P11(x11841,f3(x11841,x11842,x11843),f3(x11841,x11844,x11843))
% 1.03/1.23 [1185]~P40(x11851)+~P14(x11851,x11853,x11854)+P14(x11851,f9(x11851,x11852,x11853),f9(x11851,x11852,x11854))
% 1.03/1.23 [1186]~P40(x11861)+~P14(x11861,x11862,x11864)+P14(x11861,f9(x11861,x11862,x11863),f9(x11861,x11864,x11863))
% 1.03/1.23 [1187]~P30(x11871)+~P14(x11871,x11872,x11874)+P14(x11871,f14(x11871,x11872,x11873),f14(x11871,x11874,x11873))
% 1.03/1.23 [1188]~P22(x11881)+~P13(x11881,x11883,x11884)+P13(x11881,f3(x11881,x11882,x11883),f3(x11881,x11882,x11884))
% 1.03/1.23 [1189]~P25(x11891)+~P13(x11891,x11893,x11894)+P13(x11891,f3(x11891,x11892,x11893),f3(x11891,x11892,x11894))
% 1.03/1.23 [1190]~P22(x11901)+~P13(x11901,x11902,x11904)+P13(x11901,f3(x11901,x11902,x11903),f3(x11901,x11904,x11903))
% 1.03/1.23 [1191]~P25(x11911)+~P13(x11911,x11912,x11914)+P13(x11911,f3(x11911,x11912,x11913),f3(x11911,x11914,x11913))
% 1.03/1.23 [1278]~P11(a38,x12782,x12784)+~P11(a38,x12781,x12783)+P11(a38,f3(a38,x12781,x12782),f3(a38,x12783,x12784))
% 1.03/1.23 [1281]~P11(a1,x12811,x12813)+~P13(a1,x12812,x12814)+P11(a1,f3(a1,x12811,x12812),f3(a1,x12813,x12814))
% 1.03/1.23 [1282]~P13(a38,x12822,x12824)+~P13(a38,x12821,x12823)+P13(a38,f9(a38,x12821,x12822),f9(a38,x12823,x12824))
% 1.03/1.23 [1283]~P13(a38,x12832,x12834)+~P13(a38,x12831,x12833)+P13(a38,f3(a38,x12831,x12832),f3(a38,x12833,x12834))
% 1.03/1.23 [1411]~P22(x14111)+P11(x14111,x14112,x14113)+~P11(x14111,f3(x14111,x14114,x14112),f3(x14111,x14114,x14113))
% 1.03/1.23 [1413]~P22(x14131)+P11(x14131,x14132,x14133)+~P11(x14131,f3(x14131,x14132,x14134),f3(x14131,x14133,x14134))
% 1.03/1.23 [1415]~P22(x14151)+P13(x14151,x14152,x14153)+~P13(x14151,f3(x14151,x14154,x14152),f3(x14151,x14154,x14153))
% 1.03/1.23 [1417]~P22(x14171)+P13(x14171,x14172,x14173)+~P13(x14171,f3(x14171,x14172,x14174),f3(x14171,x14173,x14174))
% 1.03/1.23 [1040]~P8(x10401)+~P14(x10401,x10404,x10403)+E(f5(x10401,f5(x10401,x10402,x10403),x10404),f5(x10401,x10402,x10404))
% 1.03/1.23 [1424]~E(x14243,f3(a38,x14244,x14242))+P63(f26(x14241,x14242))+~P63(f26(x14241,f4(a38,x14243,x14244)))
% 1.03/1.23 [1441]~P8(x14411)+~P14(x14411,x14414,x14412)+E(f6(x14411,f14(x14411,x14412,x14413),f14(x14411,x14414,x14413)),f14(x14411,f6(x14411,x14412,x14414),x14413))
% 1.03/1.23 [1496]~P2(x14961)+~P58(x14961)+E(f3(x14961,f9(x14961,f13(x14961,x14962),x14963),f9(x14961,f13(x14961,x14962),x14964)),f9(x14961,f13(x14961,x14962),f3(x14961,x14963,x14964)))
% 1.03/1.23 [1497]~P2(x14971)+~P55(x14971)+E(f4(x14971,f9(x14971,f13(x14971,x14972),x14973),f9(x14971,f13(x14971,x14972),x14974)),f9(x14971,f13(x14971,x14972),f4(x14971,x14973,x14974)))
% 1.03/1.23 [1498]~P2(x14981)+~P58(x14981)+E(f3(x14981,f9(x14981,x14982,f13(x14981,x14983)),f9(x14981,x14984,f13(x14981,x14983))),f9(x14981,f3(x14981,x14982,x14984),f13(x14981,x14983)))
% 1.03/1.23 [1499]~P2(x14991)+~P55(x14991)+E(f4(x14991,f9(x14991,x14992,f13(x14991,x14993)),f9(x14991,x14994,f13(x14991,x14993))),f9(x14991,f4(x14991,x14992,x14994),f13(x14991,x14993)))
% 1.03/1.23 [1617]~P3(x16171)+~P13(a38,x16174,x16173)+E(f14(x16171,x16172,f4(a38,f3(a38,x16173,f8(a38)),x16174)),f9(x16171,f14(x16171,x16172,f4(a38,x16173,x16174)),x16172))
% 1.03/1.23 [1470]~E(x14702,x14704)+~P57(x14701)+E(f3(x14701,f9(x14701,x14702,x14703),f9(x14701,x14704,x14705)),f3(x14701,f9(x14701,x14702,x14705),f9(x14701,x14704,x14703)))
% 1.03/1.23 [1632]~P13(a38,x16323,x16322)+~E(f3(a38,f9(a38,x16323,x16324),x16321),f3(a38,f9(a38,x16322,x16324),x16325))+E(x16321,f3(a38,f9(a38,f4(a38,x16322,x16323),x16324),x16325))
% 1.03/1.23 [1633]~P13(a38,x16332,x16331)+~E(f3(a38,f9(a38,x16331,x16333),x16334),f3(a38,f9(a38,x16332,x16333),x16335))+E(f3(a38,f9(a38,f4(a38,x16331,x16332),x16333),x16334),x16335)
% 1.03/1.23 [1641]~P13(a38,x16414,x16411)+E(f3(a38,f9(a38,x16411,x16412),x16413),f3(a38,f9(a38,x16414,x16412),x16415))+~E(x16415,f3(a38,f9(a38,f4(a38,x16411,x16414),x16412),x16413))
% 1.03/1.23 [1642]~P13(a38,x16424,x16421)+E(f3(a38,f9(a38,x16421,x16422),x16423),f3(a38,f9(a38,x16424,x16422),x16425))+~E(f3(a38,f9(a38,f4(a38,x16421,x16424),x16422),x16423),x16425)
% 1.03/1.23 [1652]~P14(a1,x16521,x16524)+~P14(a1,x16521,f3(a1,x16522,x16525))+P14(a1,x16521,f3(a1,f3(a1,x16522,f9(a1,x16523,x16524)),x16525))
% 1.03/1.23 [1668]~P14(a1,x16681,x16684)+P14(a1,x16681,f3(a1,x16682,x16683))+~P14(a1,x16681,f3(a1,f3(a1,x16682,f9(a1,x16685,x16684)),x16683))
% 1.03/1.23 [1681]~P13(a38,x16813,x16812)+~P11(a38,f3(a38,f9(a38,x16813,x16814),x16811),f3(a38,f9(a38,x16812,x16814),x16815))+P11(a38,x16811,f3(a38,f9(a38,f4(a38,x16812,x16813),x16814),x16815))
% 1.03/1.23 [1682]~P13(a38,x16823,x16822)+~P13(a38,f3(a38,f9(a38,x16823,x16824),x16821),f3(a38,f9(a38,x16822,x16824),x16825))+P13(a38,x16821,f3(a38,f9(a38,f4(a38,x16822,x16823),x16824),x16825))
% 1.03/1.23 [1683]~P13(a38,x16832,x16831)+~P11(a38,f3(a38,f9(a38,x16831,x16833),x16834),f3(a38,f9(a38,x16832,x16833),x16835))+P11(a38,f3(a38,f9(a38,f4(a38,x16831,x16832),x16833),x16834),x16835)
% 1.03/1.23 [1684]~P13(a38,x16842,x16841)+~P13(a38,f3(a38,f9(a38,x16841,x16843),x16844),f3(a38,f9(a38,x16842,x16843),x16845))+P13(a38,f3(a38,f9(a38,f4(a38,x16841,x16842),x16843),x16844),x16845)
% 1.03/1.23 [1689]~P13(a38,x16891,x16894)+P11(a38,f3(a38,f9(a38,x16891,x16892),x16893),f3(a38,f9(a38,x16894,x16892),x16895))+~P11(a38,x16893,f3(a38,f9(a38,f4(a38,x16894,x16891),x16892),x16895))
% 1.03/1.23 [1690]~P13(a38,x16901,x16904)+P13(a38,f3(a38,f9(a38,x16901,x16902),x16903),f3(a38,f9(a38,x16904,x16902),x16905))+~P13(a38,x16903,f3(a38,f9(a38,f4(a38,x16904,x16901),x16902),x16905))
% 1.03/1.23 [1691]~P13(a38,x16914,x16911)+P11(a38,f3(a38,f9(a38,x16911,x16912),x16913),f3(a38,f9(a38,x16914,x16912),x16915))+~P11(a38,f3(a38,f9(a38,f4(a38,x16911,x16914),x16912),x16913),x16915)
% 1.03/1.23 [1692]~P13(a38,x16924,x16921)+P13(a38,f3(a38,f9(a38,x16921,x16922),x16923),f3(a38,f9(a38,x16924,x16922),x16925))+~P13(a38,f3(a38,f9(a38,f4(a38,x16921,x16924),x16922),x16923),x16925)
% 1.03/1.23 [1626]~P55(x16262)+~E(f3(x16262,f9(x16262,x16264,x16265),x16261),f3(x16262,f9(x16262,x16263,x16265),x16266))+E(x16261,f3(x16262,f9(x16262,f4(x16262,x16263,x16264),x16265),x16266))
% 1.03/1.23 [1627]~P55(x16271)+~E(f3(x16271,f9(x16271,x16272,x16274),x16275),f3(x16271,f9(x16271,x16273,x16274),x16276))+E(f3(x16271,f9(x16271,f4(x16271,x16272,x16273),x16274),x16275),x16276)
% 1.03/1.23 [1630]~P55(x16301)+E(f3(x16301,f9(x16301,x16302,x16303),x16304),f3(x16301,f9(x16301,x16305,x16303),x16306))+~E(x16306,f3(x16301,f9(x16301,f4(x16301,x16302,x16305),x16303),x16304))
% 1.03/1.23 [1631]~P55(x16311)+E(f3(x16311,f9(x16311,x16312,x16313),x16314),f3(x16311,f9(x16311,x16315,x16313),x16316))+~E(f3(x16311,f9(x16311,f4(x16311,x16312,x16315),x16313),x16314),x16316)
% 1.03/1.23 [1676]~P52(x16761)+~P11(x16761,f3(x16761,f9(x16761,x16764,x16765),x16762),f3(x16761,f9(x16761,x16763,x16765),x16766))+P11(x16761,x16762,f3(x16761,f9(x16761,f4(x16761,x16763,x16764),x16765),x16766))
% 1.03/1.23 [1677]~P52(x16771)+~P13(x16771,f3(x16771,f9(x16771,x16774,x16775),x16772),f3(x16771,f9(x16771,x16773,x16775),x16776))+P13(x16771,x16772,f3(x16771,f9(x16771,f4(x16771,x16773,x16774),x16775),x16776))
% 1.03/1.23 [1678]~P52(x16781)+~P11(x16781,f3(x16781,f9(x16781,x16782,x16784),x16785),f3(x16781,f9(x16781,x16783,x16784),x16786))+P11(x16781,f3(x16781,f9(x16781,f4(x16781,x16782,x16783),x16784),x16785),x16786)
% 1.03/1.23 [1679]~P52(x16791)+~P13(x16791,f3(x16791,f9(x16791,x16792,x16794),x16795),f3(x16791,f9(x16791,x16793,x16794),x16796))+P13(x16791,f3(x16791,f9(x16791,f4(x16791,x16792,x16793),x16794),x16795),x16796)
% 1.03/1.23 [1685]~P52(x16851)+P11(x16851,f3(x16851,f9(x16851,x16852,x16853),x16854),f3(x16851,f9(x16851,x16855,x16853),x16856))+~P11(x16851,x16854,f3(x16851,f9(x16851,f4(x16851,x16855,x16852),x16853),x16856))
% 1.03/1.23 [1686]~P52(x16861)+P13(x16861,f3(x16861,f9(x16861,x16862,x16863),x16864),f3(x16861,f9(x16861,x16865,x16863),x16866))+~P13(x16861,x16864,f3(x16861,f9(x16861,f4(x16861,x16865,x16862),x16863),x16866))
% 1.03/1.23 [1687]~P52(x16871)+P11(x16871,f3(x16871,f9(x16871,x16872,x16873),x16874),f3(x16871,f9(x16871,x16875,x16873),x16876))+~P11(x16871,f3(x16871,f9(x16871,f4(x16871,x16872,x16875),x16873),x16874),x16876)
% 1.03/1.23 [1688]~P52(x16881)+P13(x16881,f3(x16881,f9(x16881,x16882,x16883),x16884),f3(x16881,f9(x16881,x16885,x16883),x16886))+~P13(x16881,f3(x16881,f9(x16881,f4(x16881,x16882,x16885),x16883),x16884),x16886)
% 1.03/1.23 [1715]E(x17151,f8(a1))+E(x17151,f2(a1))+~P13(a1,f2(a1),x17151)+~P11(a1,x17151,f13(a1,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))
% 1.03/1.23 [780]~P1(x7801)+~P38(x7801)+P11(x7801,f2(x7801),f13(x7801,x7802))+~P11(a1,a10,x7802)
% 1.03/1.23 [781]~P1(x7811)+~P38(x7811)+P13(x7811,f2(x7811),f13(x7811,x7812))+~P13(a1,a10,x7812)
% 1.03/1.23 [782]~P1(x7821)+~P38(x7821)+P11(x7821,f13(x7821,x7822),f2(x7821))+~P11(a1,x7822,a10)
% 1.03/1.23 [783]~P1(x7831)+~P38(x7831)+P13(x7831,f13(x7831,x7832),f2(x7831))+~P13(a1,x7832,a10)
% 1.03/1.23 [801]P11(a1,x8011,x8012)+P11(a1,x8012,x8011)+E(x8011,f2(a1))+~E(f6(a1,x8012,x8011),f2(a1))
% 1.03/1.23 [805]P11(a1,x8052,x8051)+E(x8051,f2(a1))+P13(a1,x8052,f2(a1))+~E(f6(a1,x8052,x8051),f2(a1))
% 1.03/1.23 [806]P11(a1,x8061,x8062)+E(x8061,f2(a1))+P13(a1,f2(a1),x8062)+~E(f6(a1,x8062,x8061),f2(a1))
% 1.03/1.23 [808]~P38(x8082)+~P1(x8082)+~P11(x8082,f13(x8082,x8081),f2(x8082))+P11(a1,x8081,a10)
% 1.03/1.23 [809]~P38(x8092)+~P1(x8092)+~P13(x8092,f13(x8092,x8091),f2(x8092))+P13(a1,x8091,a10)
% 1.03/1.23 [810]~P38(x8102)+~P1(x8102)+~P11(x8102,f2(x8102),f13(x8102,x8101))+P11(a1,a10,x8101)
% 1.03/1.23 [811]~P38(x8112)+~P1(x8112)+~P13(x8112,f2(x8112),f13(x8112,x8111))+P13(a1,a10,x8111)
% 1.03/1.23 [967]P11(a38,x9671,x9672)+~P10(a38,x9672)+P10(a38,x9671)+~P10(a38,f4(a38,x9671,x9672))
% 1.03/1.23 [968]P11(a38,x9682,x9681)+~P10(a38,x9682)+P10(a38,x9681)+~P10(a38,f4(a38,x9682,x9681))
% 1.03/1.23 [599]~P32(x5992)+~P60(x5992)+E(x5991,f2(a38))+E(f14(x5992,f2(x5992),x5991),f2(x5992))
% 1.03/1.23 [1077]~P1(x10771)+~P28(x10771)+~P12(x10771,f13(x10771,x10772))+P12(x10771,f13(x10771,f3(a1,x10772,x10772)))
% 1.03/1.23 [1327]~P1(x13271)+~P28(x13271)+P12(x13271,f13(x13271,x13272))+~P12(x13271,f13(x13271,f3(a1,x13272,x13272)))
% 1.03/1.23 [1435]~P38(x14352)+~P1(x14352)+~P11(x14352,f13(x14352,x14351),f8(x14352))+P11(a1,x14351,f3(a1,f3(a1,f8(a1),a10),a10))
% 1.03/1.23 [1436]~P38(x14362)+~P1(x14362)+~P13(x14362,f13(x14362,x14361),f8(x14362))+P13(a1,x14361,f3(a1,f3(a1,f8(a1),a10),a10))
% 1.03/1.23 [1437]~P38(x14372)+~P1(x14372)+~P11(x14372,f8(x14372),f13(x14372,x14371))+P11(a1,f3(a1,f3(a1,f8(a1),a10),a10),x14371)
% 1.03/1.23 [1438]~P38(x14382)+~P1(x14382)+~P13(x14382,f8(x14382),f13(x14382,x14381))+P13(a1,f3(a1,f3(a1,f8(a1),a10),a10),x14381)
% 1.03/1.23 [1572]~P1(x15721)+~P38(x15721)+P11(x15721,f8(x15721),f13(x15721,x15722))+~P11(a1,f3(a1,f3(a1,f8(a1),a10),a10),x15722)
% 1.03/1.23 [1573]~P1(x15731)+~P38(x15731)+P13(x15731,f8(x15731),f13(x15731,x15732))+~P13(a1,f3(a1,f3(a1,f8(a1),a10),a10),x15732)
% 1.03/1.23 [1574]~P1(x15741)+~P38(x15741)+P11(x15741,f13(x15741,x15742),f8(x15741))+~P11(a1,x15742,f3(a1,f3(a1,f8(a1),a10),a10))
% 1.03/1.23 [1575]~P1(x15751)+~P38(x15751)+P13(x15751,f13(x15751,x15752),f8(x15751))+~P13(a1,x15752,f3(a1,f3(a1,f8(a1),a10),a10))
% 1.03/1.23 [663]P11(x6633,x6631,x6632)+~P38(x6633)+E(x6631,x6632)+P11(x6633,x6632,x6631)
% 1.03/1.23 [537]~P1(x5373)+~P28(x5373)+E(x5371,x5372)+~E(f13(x5373,x5371),f13(x5373,x5372))
% 1.03/1.23 [651]~P48(x6512)+~E(f9(x6512,x6513,x6511),f2(x6512))+E(x6511,f2(x6512))+E(x6513,f2(x6512))
% 1.03/1.23 [653]~P49(x6532)+~E(f9(x6532,x6533,x6531),f2(x6532))+E(x6531,f2(x6532))+E(x6533,f2(x6532))
% 1.03/1.23 [804]~P38(x8042)+P11(x8042,f2(x8042),f14(x8042,x8041,x8043))+~P10(a38,x8043)+E(x8041,f2(x8042))
% 1.03/1.23 [807]~P3(x8071)+~P43(x8071)+P13(x8071,f2(x8071),f14(x8071,x8072,x8073))+~P10(a38,x8073)
% 1.03/1.23 [813]~P1(x8131)+~P38(x8131)+~P11(a1,x8132,x8133)+P11(x8131,f13(x8131,x8132),f13(x8131,x8133))
% 1.03/1.23 [814]~P1(x8141)+~P38(x8141)+~P13(a1,x8142,x8143)+P13(x8141,f13(x8141,x8142),f13(x8141,x8143))
% 1.03/1.23 [829]P64(x8291,x8292,x8293)+P11(a1,x8293,f2(a1))+P11(a1,f2(a1),x8293)+~P63(f26(x8291,x8292))
% 1.03/1.23 [861]~P2(x8611)+~P33(x8611)+P11(x8611,f13(x8611,x8612),f13(x8611,x8613))+P13(x8611,f13(x8611,x8613),f13(x8611,x8612))
% 1.03/1.23 [874]~P38(x8743)+~P1(x8743)+~P11(x8743,f13(x8743,x8741),f13(x8743,x8742))+P11(a1,x8741,x8742)
% 1.03/1.23 [875]~P38(x8753)+~P1(x8753)+~P13(x8753,f13(x8753,x8751),f13(x8753,x8752))+P13(a1,x8751,x8752)
% 1.03/1.23 [983]P64(x9832,x9833,x9831)+P11(a1,f24(x9831,x9833,x9832),x9831)+E(x9831,f2(a1))+P11(a1,x9831,f2(a1))
% 1.03/1.23 [984]P64(x9842,x9843,x9841)+P11(a1,x9841,f27(x9841,x9843,x9842))+E(x9841,f2(a1))+P11(a1,f2(a1),x9841)
% 1.03/1.23 [988]P64(x9882,x9883,x9881)+E(x9881,f2(a1))+P11(a1,x9881,f2(a1))+P13(a1,f2(a1),f24(x9881,x9883,x9882))
% 1.03/1.23 [989]P64(x9892,x9893,x9891)+E(x9891,f2(a1))+P11(a1,f2(a1),x9891)+P13(a1,f27(x9891,x9893,x9892),f2(a1))
% 1.03/1.23 [992]~P38(x9922)+~P11(x9922,f2(x9922),x9923)+P11(x9922,f2(x9922),f14(x9922,x9923,x9921))+P10(a38,x9921)
% 1.03/1.23 [994]~P38(x9942)+~P11(x9942,x9943,f2(x9942))+P11(x9942,f14(x9942,x9943,x9941),f2(x9942))+P10(a38,x9941)
% 1.03/1.23 [1013]~P38(x10132)+~P13(x10132,f14(x10132,x10131,x10133),f2(x10132))+E(x10131,f2(x10132))+~P10(a38,x10133)
% 1.03/1.23 [1063]P64(x10631,x10632,x10633)+P11(a1,f24(x10633,x10632,x10631),x10633)+P11(a1,x10633,f2(a1))+~P63(f26(x10631,x10632))
% 1.03/1.23 [1064]P64(x10641,x10642,x10643)+P11(a1,x10643,f27(x10643,x10642,x10641))+P11(a1,f2(a1),x10643)+~P63(f26(x10641,x10642))
% 1.03/1.23 [1069]P64(x10691,x10692,x10693)+P11(a1,x10693,f2(a1))+P13(a1,f2(a1),f24(x10693,x10692,x10691))+~P63(f26(x10691,x10692))
% 1.03/1.23 [1070]P64(x10701,x10702,x10703)+P11(a1,f2(a1),x10703)+P13(a1,f27(x10703,x10702,x10701),f2(a1))+~P63(f26(x10701,x10702))
% 1.03/1.23 [1109]E(x11091,x11092)+~P13(a38,x11093,x11092)+~P13(a38,x11093,x11091)+~E(f4(a38,x11091,x11093),f4(a38,x11092,x11093))
% 1.03/1.23 [1111]~P38(x11112)+~P13(x11112,f14(x11112,x11111,x11113),f2(x11112))+P13(x11112,x11111,f2(x11112))+E(x11111,f2(x11112))
% 1.03/1.23 [1155]~P38(x11552)+~P13(x11552,f14(x11552,x11553,x11551),f2(x11552))+P13(x11552,x11553,f2(x11552))+P10(a38,x11551)
% 1.03/1.23 [1158]~P38(x11582)+~P13(x11582,f2(x11582),f14(x11582,x11583,x11581))+P13(x11582,f2(x11582),x11583)+P10(a38,x11581)
% 1.03/1.23 [1165]~P33(x11651)+~P2(x11651)+~P11(x11651,f13(x11651,x11652),f13(x11651,x11653))+~P13(x11651,f13(x11651,x11653),f13(x11651,x11652))
% 1.03/1.23 [1180]~P37(x11801)+~P11(x11801,f8(x11801),x11802)+P11(x11801,f8(x11801),f14(x11801,x11802,x11803))+~P11(a38,f2(a38),x11803)
% 1.03/1.23 [1193]~P42(x11931)+~P11(x11931,x11933,f2(x11931))+~P11(x11931,x11932,f2(x11931))+P11(x11931,f2(x11931),f9(x11931,x11932,x11933))
% 1.03/1.23 [1194]~P42(x11941)+~P13(x11941,x11943,f2(x11941))+~P13(x11941,x11942,f2(x11941))+P13(x11941,f2(x11941),f9(x11941,x11942,x11943))
% 1.03/1.23 [1196]~P52(x11961)+~P13(x11961,x11963,f2(x11961))+~P13(x11961,x11962,f2(x11961))+P13(x11961,f2(x11961),f9(x11961,x11962,x11963))
% 1.03/1.23 [1197]~P44(x11971)+~P11(x11971,f2(x11971),x11973)+~P11(x11971,f2(x11971),x11972)+P11(x11971,f2(x11971),f9(x11971,x11972,x11973))
% 1.03/1.23 [1198]~P27(x11981)+~P11(x11981,f2(x11981),x11983)+~P11(x11981,f2(x11981),x11982)+P11(x11981,f2(x11981),f3(x11981,x11982,x11983))
% 1.03/1.23 [1201]~P37(x12011)+~P11(x12011,f8(x12011),x12013)+~P11(x12011,f8(x12011),x12012)+P11(x12011,f8(x12011),f9(x12011,x12012,x12013))
% 1.03/1.23 [1202]~P42(x12021)+~P13(x12021,f2(x12021),x12023)+~P13(x12021,f2(x12021),x12022)+P13(x12021,f2(x12021),f9(x12021,x12022,x12023))
% 1.03/1.23 [1203]~P52(x12031)+~P13(x12031,f2(x12031),x12033)+~P13(x12031,f2(x12031),x12032)+P13(x12031,f2(x12031),f9(x12031,x12032,x12033))
% 1.03/1.23 [1204]~P53(x12041)+~P13(x12041,f2(x12041),x12043)+~P13(x12041,f2(x12041),x12042)+P13(x12041,f2(x12041),f9(x12041,x12042,x12043))
% 1.03/1.23 [1206]~P27(x12061)+~P11(x12061,x12063,f2(x12061))+~P11(x12061,x12062,f2(x12061))+P11(x12061,f3(x12061,x12062,x12063),f2(x12061))
% 1.03/1.23 [1207]~P27(x12071)+~P11(x12071,x12073,f2(x12071))+~P13(x12071,x12072,f2(x12071))+P11(x12071,f3(x12071,x12072,x12073),f2(x12071))
% 1.03/1.23 [1208]~P27(x12081)+~P11(x12081,x12082,f2(x12081))+~P13(x12081,x12083,f2(x12081))+P11(x12081,f3(x12081,x12082,x12083),f2(x12081))
% 1.03/1.23 [1209]~P27(x12091)+~P13(x12091,x12093,f2(x12091))+~P13(x12091,x12092,f2(x12091))+P13(x12091,f3(x12091,x12092,x12093),f2(x12091))
% 1.03/1.23 [1211]~P44(x12111)+~P11(x12111,x12113,f2(x12111))+~P11(x12111,f2(x12111),x12112)+P11(x12111,f9(x12111,x12112,x12113),f2(x12111))
% 1.03/1.23 [1212]~P44(x12121)+~P11(x12121,x12122,f2(x12121))+~P11(x12121,f2(x12121),x12123)+P11(x12121,f9(x12121,x12122,x12123),f2(x12121))
% 1.03/1.23 [1214]~P42(x12141)+~P13(x12141,x12143,f2(x12141))+~P13(x12141,f2(x12141),x12142)+P13(x12141,f9(x12141,x12142,x12143),f2(x12141))
% 1.03/1.23 [1215]~P42(x12151)+~P13(x12151,x12152,f2(x12151))+~P13(x12151,f2(x12151),x12153)+P13(x12151,f9(x12151,x12152,x12153),f2(x12151))
% 1.03/1.23 [1217]~P53(x12171)+~P13(x12171,x12173,f2(x12171))+~P13(x12171,f2(x12171),x12172)+P13(x12171,f9(x12171,x12172,x12173),f2(x12171))
% 1.03/1.23 [1219]~P53(x12191)+~P13(x12191,x12192,f2(x12191))+~P13(x12191,f2(x12191),x12193)+P13(x12191,f9(x12191,x12192,x12193),f2(x12191))
% 1.03/1.23 [1226]P64(x12262,x12263,x12261)+P11(a1,x12261,f27(x12261,x12263,x12262))+P11(a1,f24(x12261,x12263,x12262),x12261)+E(x12261,f2(a1))
% 1.03/1.23 [1227]P64(x12272,x12273,x12271)+P11(a1,x12271,f27(x12271,x12273,x12272))+E(x12271,f2(a1))+P13(a1,f2(a1),f24(x12271,x12273,x12272))
% 1.03/1.23 [1228]P64(x12282,x12283,x12281)+P11(a1,f24(x12281,x12283,x12282),x12281)+E(x12281,f2(a1))+P13(a1,f27(x12281,x12283,x12282),f2(a1))
% 1.03/1.23 [1231]P64(x12312,x12313,x12311)+E(x12311,f2(a1))+P13(a1,f2(a1),f24(x12311,x12313,x12312))+P13(a1,f27(x12311,x12313,x12312),f2(a1))
% 1.03/1.23 [1232]~P42(x12321)+~P13(x12321,f9(x12321,x12323,x12322),f2(x12321))+P13(x12321,x12322,f2(x12321))+P13(x12321,x12323,f2(x12321))
% 1.03/1.23 [1233]~P42(x12331)+~P13(x12331,f2(x12331),f9(x12331,x12333,x12332))+P13(x12331,x12332,f2(x12331))+P13(x12331,f2(x12331),x12333)
% 1.03/1.23 [1234]~P42(x12341)+~P13(x12341,f2(x12341),f9(x12341,x12342,x12343))+P13(x12341,x12342,f2(x12341))+P13(x12341,f2(x12341),x12343)
% 1.03/1.23 [1235]~P42(x12351)+P13(x12351,f2(x12351),x12352)+~P13(x12351,f2(x12351),f9(x12351,x12353,x12352))+P13(x12351,x12352,f2(x12351))
% 1.03/1.23 [1236]~P42(x12361)+P13(x12361,f2(x12361),x12362)+~P13(x12361,f2(x12361),f9(x12361,x12362,x12363))+P13(x12361,x12362,f2(x12361))
% 1.03/1.23 [1237]~P42(x12371)+P13(x12371,f2(x12371),x12372)+~P13(x12371,f9(x12371,x12373,x12372),f2(x12371))+P13(x12371,x12372,f2(x12371))
% 1.03/1.23 [1238]~P42(x12381)+P13(x12381,f2(x12381),x12382)+~P13(x12381,f9(x12381,x12382,x12383),f2(x12381))+P13(x12381,x12382,f2(x12381))
% 1.03/1.23 [1239]~P42(x12391)+~P13(x12391,f9(x12391,x12392,x12393),f2(x12391))+P13(x12391,f2(x12391),x12392)+P13(x12391,f2(x12391),x12393)
% 1.03/1.23 [1272]P64(x12721,x12722,x12723)+P11(a1,x12723,f27(x12723,x12722,x12721))+P11(a1,f24(x12723,x12722,x12721),x12723)+~P63(f26(x12721,x12722))
% 1.03/1.23 [1273]P64(x12731,x12732,x12733)+P11(a1,x12733,f27(x12733,x12732,x12731))+P13(a1,f2(a1),f24(x12733,x12732,x12731))+~P63(f26(x12731,x12732))
% 1.03/1.23 [1274]P64(x12741,x12742,x12743)+P11(a1,f24(x12743,x12742,x12741),x12743)+P13(a1,f27(x12743,x12742,x12741),f2(a1))+~P63(f26(x12741,x12742))
% 1.03/1.23 [1276]~P44(x12761)+~P11(x12761,f2(x12761),f9(x12761,x12763,x12762))+P11(x12761,f2(x12761),x12762)+~P11(x12761,f2(x12761),x12763)
% 1.03/1.23 [1277]~P44(x12771)+~P11(x12771,f2(x12771),f9(x12771,x12772,x12773))+P11(x12771,f2(x12771),x12772)+~P11(x12771,f2(x12771),x12773)
% 1.03/1.23 [1285]P64(x12851,x12852,x12853)+P13(a1,f2(a1),f24(x12853,x12852,x12851))+P13(a1,f27(x12853,x12852,x12851),f2(a1))+~P63(f26(x12851,x12852))
% 1.03/1.23 [1398]~P13(a38,x13982,x13983)+P14(a38,x13981,x13982)+~P14(a38,x13981,x13983)+~P14(a38,x13981,f4(a38,x13983,x13982))
% 1.03/1.23 [1399]~P13(a38,x13993,x13992)+P14(a38,x13991,x13992)+~P14(a38,x13991,x13993)+~P14(a38,x13991,f4(a38,x13992,x13993))
% 1.03/1.23 [1439]~P13(a1,x14392,x14393)+P13(a1,f6(a1,x14391,x14392),f6(a1,x14391,x14393))+~P11(a1,x14391,f2(a1))+~P11(a1,f2(a1),x14392)
% 1.03/1.23 [1440]~P13(a1,x14403,x14402)+P13(a1,f6(a1,x14401,x14402),f6(a1,x14401,x14403))+~P11(a1,f2(a1),x14403)+~P13(a1,f2(a1),x14401)
% 1.03/1.23 [1535]~P13(a38,x15353,x15351)+P11(a38,x15351,x15352)+~P13(a38,x15353,x15352)+~P11(a38,f4(a38,x15351,x15353),f4(a38,x15352,x15353))
% 1.03/1.23 [1536]~P13(a38,x15363,x15361)+P13(a38,x15361,x15362)+~P13(a38,x15363,x15362)+~P13(a38,f4(a38,x15361,x15363),f4(a38,x15362,x15363))
% 1.03/1.23 [1004]~P42(x10041)+~E(x10043,f2(x10041))+~E(x10042,f2(x10041))+E(f3(x10041,f9(x10041,x10042,x10042),f9(x10041,x10043,x10043)),f2(x10041))
% 1.03/1.23 [1402]~P11(a1,x14022,x14023)+~P11(a1,f2(a1),x14023)+P13(a1,f8(a1),x14021)+~E(f3(a1,x14022,f9(a1,x14023,x14021)),x14023)
% 1.03/1.23 [1405]~P11(a1,f2(a1),x14053)+~P13(a1,f2(a1),x14052)+P13(a1,x14051,f8(a1))+~E(f3(a1,x14052,f9(a1,x14053,x14051)),x14053)
% 1.03/1.23 [1428]P64(x14282,x14283,x14281)+E(x14281,f2(a1))+P11(a1,x14281,f2(a1))+~P63(f26(x14282,f24(x14281,x14283,x14282)))
% 1.03/1.23 [1429]P64(x14292,x14293,x14291)+E(x14291,f2(a1))+P11(a1,f2(a1),x14291)+~P63(f26(x14292,f27(x14291,x14293,x14292)))
% 1.03/1.23 [1451]P64(x14511,x14512,x14513)+P11(a1,x14513,f2(a1))+~P63(f26(x14511,x14512))+~P63(f26(x14511,f24(x14513,x14512,x14511)))
% 1.03/1.23 [1452]P64(x14521,x14522,x14523)+P11(a1,f2(a1),x14523)+~P63(f26(x14521,x14522))+~P63(f26(x14521,f27(x14523,x14522,x14521)))
% 1.03/1.23 [1518]P64(x15183,x15182,x15181)+E(x15181,f2(a1))+P11(a1,x15181,f2(a1))+E(f3(a1,f9(a1,x15181,f25(x15181,x15182,x15183)),f24(x15181,x15182,x15183)),x15182)
% 1.03/1.23 [1519]P64(x15193,x15192,x15191)+E(x15191,f2(a1))+P11(a1,f2(a1),x15191)+E(f3(a1,f9(a1,x15191,f28(x15191,x15192,x15193)),f27(x15191,x15192,x15193)),x15192)
% 1.03/1.23 [1524]P64(x15242,x15243,x15241)+P11(a1,x15241,f27(x15241,x15243,x15242))+E(x15241,f2(a1))+~P63(f26(x15242,f24(x15241,x15243,x15242)))
% 1.03/1.23 [1525]P64(x15252,x15253,x15251)+P11(a1,f24(x15251,x15253,x15252),x15251)+E(x15251,f2(a1))+~P63(f26(x15252,f27(x15251,x15253,x15252)))
% 1.03/1.23 [1526]P64(x15262,x15263,x15261)+E(x15261,f2(a1))+P13(a1,f2(a1),f24(x15261,x15263,x15262))+~P63(f26(x15262,f27(x15261,x15263,x15262)))
% 1.03/1.23 [1527]P64(x15272,x15273,x15271)+E(x15271,f2(a1))+P13(a1,f27(x15271,x15273,x15272),f2(a1))+~P63(f26(x15272,f24(x15271,x15273,x15272)))
% 1.03/1.23 [1531]~P42(x15311)+~E(x15313,f2(x15311))+~E(x15312,f2(x15311))+P13(x15311,f3(x15311,f9(x15311,x15312,x15312),f9(x15311,x15313,x15313)),f2(x15311))
% 1.03/1.23 [1539]P64(x15393,x15392,x15391)+P11(a1,x15391,f2(a1))+~P63(f26(x15393,x15392))+E(f3(a1,f9(a1,x15391,f25(x15391,x15392,x15393)),f24(x15391,x15392,x15393)),x15392)
% 1.03/1.23 [1540]P64(x15403,x15402,x15401)+P11(a1,f2(a1),x15401)+~P63(f26(x15403,x15402))+E(f3(a1,f9(a1,x15401,f28(x15401,x15402,x15403)),f27(x15401,x15402,x15403)),x15402)
% 1.03/1.23 [1556]P64(x15561,x15562,x15563)+P11(a1,x15563,f27(x15563,x15562,x15561))+~P63(f26(x15561,x15562))+~P63(f26(x15561,f24(x15563,x15562,x15561)))
% 1.03/1.23 [1557]P64(x15571,x15572,x15573)+P11(a1,f24(x15573,x15572,x15571),x15573)+~P63(f26(x15571,x15572))+~P63(f26(x15571,f27(x15573,x15572,x15571)))
% 1.03/1.23 [1558]P64(x15581,x15582,x15583)+P13(a1,f2(a1),f24(x15583,x15582,x15581))+~P63(f26(x15581,x15582))+~P63(f26(x15581,f27(x15583,x15582,x15581)))
% 1.03/1.23 [1559]P64(x15591,x15592,x15593)+P13(a1,f27(x15593,x15592,x15591),f2(a1))+~P63(f26(x15591,x15592))+~P63(f26(x15591,f24(x15593,x15592,x15591)))
% 1.03/1.23 [1576]~P37(x15761)+~P11(x15761,x15762,f8(x15761))+~P11(x15761,f2(x15761),x15762)+P11(x15761,f9(x15761,x15762,f14(x15761,x15762,x15763)),f14(x15761,x15762,x15763))
% 1.03/1.23 [1580]P64(x15803,x15802,x15801)+P11(a1,x15801,f27(x15801,x15802,x15803))+E(x15801,f2(a1))+E(f3(a1,f9(a1,x15801,f25(x15801,x15802,x15803)),f24(x15801,x15802,x15803)),x15802)
% 1.03/1.23 [1581]P64(x15813,x15812,x15811)+P11(a1,f24(x15811,x15812,x15813),x15811)+E(x15811,f2(a1))+E(f3(a1,f9(a1,x15811,f28(x15811,x15812,x15813)),f27(x15811,x15812,x15813)),x15812)
% 1.03/1.23 [1582]P64(x15823,x15822,x15821)+E(x15821,f2(a1))+P13(a1,f2(a1),f24(x15821,x15822,x15823))+E(f3(a1,f9(a1,x15821,f28(x15821,x15822,x15823)),f27(x15821,x15822,x15823)),x15822)
% 1.03/1.23 [1583]P64(x15833,x15832,x15831)+E(x15831,f2(a1))+P13(a1,f27(x15831,x15832,x15833),f2(a1))+E(f3(a1,f9(a1,x15831,f25(x15831,x15832,x15833)),f24(x15831,x15832,x15833)),x15832)
% 1.03/1.23 [1590]P64(x15903,x15902,x15901)+P11(a1,x15901,f27(x15901,x15902,x15903))+~P63(f26(x15903,x15902))+E(f3(a1,f9(a1,x15901,f25(x15901,x15902,x15903)),f24(x15901,x15902,x15903)),x15902)
% 1.03/1.23 [1591]P64(x15913,x15912,x15911)+P11(a1,f24(x15911,x15912,x15913),x15911)+~P63(f26(x15913,x15912))+E(f3(a1,f9(a1,x15911,f28(x15911,x15912,x15913)),f27(x15911,x15912,x15913)),x15912)
% 1.03/1.23 [1592]P64(x15923,x15922,x15921)+P13(a1,f2(a1),f24(x15921,x15922,x15923))+~P63(f26(x15923,x15922))+E(f3(a1,f9(a1,x15921,f28(x15921,x15922,x15923)),f27(x15921,x15922,x15923)),x15922)
% 1.03/1.23 [1593]P64(x15933,x15932,x15931)+P13(a1,f27(x15931,x15932,x15933),f2(a1))+~P63(f26(x15933,x15932))+E(f3(a1,f9(a1,x15931,f25(x15931,x15932,x15933)),f24(x15931,x15932,x15933)),x15932)
% 1.03/1.23 [1606]~P11(a1,x16062,x16063)+~P11(a1,f2(a1),x16063)+P13(a1,f2(a1),x16061)+~P13(a1,f2(a1),f3(a1,f9(a1,x16063,x16061),x16062))
% 1.03/1.23 [1615]P13(a1,x16151,f2(a1))+~P11(a1,f2(a1),x16152)+~P13(a1,f2(a1),x16153)+~P11(a1,f3(a1,f9(a1,x16152,x16151),x16153),f2(a1))
% 1.03/1.23 [1616]P64(x16162,x16163,x16161)+E(x16161,f2(a1))+~P63(f26(x16162,f24(x16161,x16163,x16162)))+~P63(f26(x16162,f27(x16161,x16163,x16162)))
% 1.03/1.23 [1625]P64(x16251,x16252,x16253)+~P63(f26(x16251,x16252))+~P63(f26(x16251,f24(x16253,x16252,x16251)))+~P63(f26(x16251,f27(x16253,x16252,x16251)))
% 1.03/1.23 [1628]P64(x16283,x16282,x16281)+E(x16281,f2(a1))+E(f3(a1,f9(a1,x16281,f25(x16281,x16282,x16283)),f24(x16281,x16282,x16283)),x16282)+~P63(f26(x16283,f27(x16281,x16282,x16283)))
% 1.03/1.23 [1629]P64(x16293,x16292,x16291)+E(x16291,f2(a1))+E(f3(a1,f9(a1,x16291,f28(x16291,x16292,x16293)),f27(x16291,x16292,x16293)),x16292)+~P63(f26(x16293,f24(x16291,x16292,x16293)))
% 1.03/1.23 [1637]~P42(x16372)+~E(x16371,f2(x16372))+~E(x16373,f2(x16372))+~P11(x16372,f2(x16372),f3(x16372,f9(x16372,x16373,x16373),f9(x16372,x16371,x16371)))
% 1.03/1.23 [1638]P64(x16383,x16382,x16381)+~P63(f26(x16383,x16382))+E(f3(a1,f9(a1,x16381,f25(x16381,x16382,x16383)),f24(x16381,x16382,x16383)),x16382)+~P63(f26(x16383,f27(x16381,x16382,x16383)))
% 1.03/1.23 [1639]P64(x16393,x16392,x16391)+~P63(f26(x16393,x16392))+E(f3(a1,f9(a1,x16391,f28(x16391,x16392,x16393)),f27(x16391,x16392,x16393)),x16392)+~P63(f26(x16393,f24(x16391,x16392,x16393)))
% 1.03/1.23 [1644]P64(x16443,x16442,x16441)+E(x16441,f2(a1))+E(f3(a1,f9(a1,x16441,f28(x16441,x16442,x16443)),f27(x16441,x16442,x16443)),x16442)+E(f3(a1,f9(a1,x16441,f25(x16441,x16442,x16443)),f24(x16441,x16442,x16443)),x16442)
% 1.03/1.23 [1650]P64(x16503,x16502,x16501)+~P63(f26(x16503,x16502))+E(f3(a1,f9(a1,x16501,f28(x16501,x16502,x16503)),f27(x16501,x16502,x16503)),x16502)+E(f3(a1,f9(a1,x16501,f25(x16501,x16502,x16503)),f24(x16501,x16502,x16503)),x16502)
% 1.03/1.23 [1515]~P37(x15151)+~P13(x15151,x15152,f8(x15151))+~P13(x15151,f2(x15151),x15152)+P13(x15151,f14(x15151,x15152,f3(a38,x15153,f8(a38))),x15152)
% 1.03/1.23 [1517]~P37(x15171)+~P11(x15171,x15172,f8(x15171))+~P11(x15171,f2(x15171),x15172)+P11(x15171,f14(x15171,x15172,f3(a38,x15173,f8(a38))),f8(x15171))
% 1.03/1.23 [1746]~P37(x17461)+P13(x17461,x17462,x17463)+~P13(x17461,f2(x17461),x17463)+~P13(x17461,f14(x17461,x17462,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17461,x17463,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.23 [1734]~P38(x17341)+~E(x17343,f2(x17341))+~E(x17342,f2(x17341))+E(f3(x17341,f14(x17341,x17342,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17341,x17343,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(x17341))
% 1.03/1.23 [1751]~P38(x17511)+~E(x17513,f2(x17511))+~E(x17512,f2(x17511))+P13(x17511,f3(x17511,f14(x17511,x17512,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17511,x17513,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))),f2(x17511))
% 1.03/1.23 [1758]~P38(x17582)+~E(x17581,f2(x17582))+~E(x17583,f2(x17582))+~P11(x17582,f2(x17582),f3(x17582,f14(x17582,x17583,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17582,x17581,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10))))))
% 1.03/1.23 [873]~P30(x8731)+~P14(x8731,x8732,x8734)+P14(x8731,x8732,x8733)+~P14(x8731,x8734,x8733)
% 1.03/1.23 [985]~P37(x9853)+E(x9851,x9852)+~P11(x9853,f8(x9853),x9854)+~E(f14(x9853,x9854,x9851),f14(x9853,x9854,x9852))
% 1.03/1.23 [1128]~P30(x11281)+~P14(x11281,x11282,x11284)+~P14(x11281,x11282,x11283)+P14(x11281,x11282,f3(x11281,x11283,x11284))
% 1.03/1.23 [1129]~P35(x11291)+~P14(x11291,x11292,x11294)+~P14(x11291,x11292,x11293)+P14(x11291,x11292,f4(x11291,x11293,x11294))
% 1.03/1.23 [1131]~P8(x11311)+~P14(x11311,x11312,x11314)+~P14(x11311,x11312,x11313)+P14(x11311,x11312,f5(x11311,x11313,x11314))
% 1.03/1.23 [1166]~P37(x11661)+~P11(x11661,x11662,x11664)+~P11(x11661,f2(x11661),x11663)+P11(x11661,x11662,f3(x11661,x11663,x11664))
% 1.03/1.23 [1167]~P27(x11671)+~P11(x11671,x11672,x11674)+~P13(x11671,f2(x11671),x11673)+P11(x11671,x11672,f3(x11671,x11673,x11674))
% 1.03/1.23 [1168]~P27(x11681)+~P13(x11681,x11682,x11684)+~P11(x11681,f2(x11681),x11683)+P11(x11681,x11682,f3(x11681,x11683,x11684))
% 1.03/1.23 [1169]~P27(x11691)+~P13(x11691,x11692,x11693)+~P13(x11691,f2(x11691),x11694)+P13(x11691,x11692,f3(x11691,x11693,x11694))
% 1.03/1.23 [1170]~P27(x11701)+~P13(x11701,x11702,x11704)+~P13(x11701,f2(x11701),x11703)+P13(x11701,x11702,f3(x11701,x11703,x11704))
% 1.03/1.23 [1224]~P38(x12242)+~P13(x12242,x12243,x12244)+P13(x12242,f14(x12242,x12243,x12241),f14(x12242,x12244,x12241))+P10(a38,x12241)
% 1.03/1.23 [1254]~P8(x12541)+P14(x12541,x12542,x12543)+~P14(x12541,x12542,x12544)+~P14(x12541,x12542,f5(x12541,x12543,x12544))
% 1.03/1.23 [1342]~P37(x13421)+~P11(a38,x13423,x13424)+~P11(x13421,f8(x13421),x13422)+P11(x13421,f14(x13421,x13422,x13423),f14(x13421,x13422,x13424))
% 1.03/1.23 [1343]~P37(x13431)+~P13(a38,x13433,x13434)+~P11(x13431,f8(x13431),x13432)+P13(x13431,f14(x13431,x13432,x13433),f14(x13431,x13432,x13434))
% 1.03/1.23 [1344]~P37(x13441)+~P13(a38,x13443,x13444)+~P13(x13441,f8(x13441),x13442)+P13(x13441,f14(x13441,x13442,x13443),f14(x13441,x13442,x13444))
% 1.03/1.23 [1360]~P42(x13601)+~P11(x13601,x13604,x13602)+~P11(x13601,x13603,f2(x13601))+P11(x13601,f9(x13601,x13602,x13603),f9(x13601,x13604,x13603))
% 1.03/1.23 [1361]~P42(x13611)+~P11(x13611,x13614,x13613)+~P11(x13611,x13612,f2(x13611))+P11(x13611,f9(x13611,x13612,x13613),f9(x13611,x13612,x13614))
% 1.03/1.23 [1362]~P42(x13621)+~P13(x13621,x13624,x13623)+~P11(x13621,x13622,f2(x13621))+P13(x13621,f9(x13621,x13622,x13623),f9(x13621,x13622,x13624))
% 1.03/1.23 [1363]~P52(x13631)+~P13(x13631,x13634,x13633)+~P13(x13631,x13632,f2(x13631))+P13(x13631,f9(x13631,x13632,x13633),f9(x13631,x13632,x13634))
% 1.03/1.23 [1364]~P52(x13641)+~P13(x13641,x13644,x13642)+~P13(x13641,x13643,f2(x13641))+P13(x13641,f9(x13641,x13642,x13643),f9(x13641,x13644,x13643))
% 1.03/1.23 [1366]~P41(x13661)+~P11(x13661,x13663,x13664)+~P11(x13661,f2(x13661),x13662)+P11(x13661,f9(x13661,x13662,x13663),f9(x13661,x13662,x13664))
% 1.03/1.23 [1367]~P44(x13671)+~P11(x13671,x13673,x13674)+~P11(x13671,f2(x13671),x13672)+P11(x13671,f9(x13671,x13672,x13673),f9(x13671,x13672,x13674))
% 1.03/1.23 [1368]~P42(x13681)+~P11(x13681,x13682,x13684)+~P11(x13681,f2(x13681),x13683)+P11(x13681,f9(x13681,x13682,x13683),f9(x13681,x13684,x13683))
% 1.03/1.23 [1369]~P44(x13691)+~P11(x13691,x13692,x13694)+~P11(x13691,f2(x13691),x13693)+P11(x13691,f9(x13691,x13692,x13693),f9(x13691,x13694,x13693))
% 1.03/1.23 [1370]~P42(x13701)+~P11(x13701,x13703,x13704)+~P11(x13701,f2(x13701),x13702)+P11(x13701,f9(x13701,x13702,x13703),f9(x13701,x13702,x13704))
% 1.03/1.23 [1371]~P42(x13711)+~P13(x13711,x13713,x13714)+~P11(x13711,f2(x13711),x13712)+P13(x13711,f9(x13711,x13712,x13713),f9(x13711,x13712,x13714))
% 1.03/1.23 [1372]~P56(x13721)+~P13(x13721,x13723,x13724)+~P13(x13721,f2(x13721),x13722)+P13(x13721,f9(x13721,x13722,x13723),f9(x13721,x13722,x13724))
% 1.03/1.23 [1373]~P54(x13731)+~P13(x13731,x13733,x13734)+~P13(x13731,f2(x13731),x13732)+P13(x13731,f9(x13731,x13732,x13733),f9(x13731,x13732,x13734))
% 1.03/1.23 [1374]~P56(x13741)+~P13(x13741,x13742,x13744)+~P13(x13741,f2(x13741),x13743)+P13(x13741,f9(x13741,x13742,x13743),f9(x13741,x13744,x13743))
% 1.03/1.23 [1375]~P37(x13751)+~P13(x13751,x13752,x13754)+~P13(x13751,f2(x13751),x13752)+P13(x13751,f14(x13751,x13752,x13753),f14(x13751,x13754,x13753))
% 1.03/1.23 [1421]~P40(x14212)+P14(x14212,x14213,x14214)+~P14(x14212,f9(x14212,x14213,x14211),f9(x14212,x14214,x14211))+E(x14211,f2(x14212))
% 1.03/1.23 [1422]~P40(x14222)+P14(x14222,x14223,x14224)+~P14(x14222,f9(x14222,x14221,x14223),f9(x14222,x14221,x14224))+E(x14221,f2(x14222))
% 1.03/1.23 [1448]P11(x14481,x14483,x14482)+~P42(x14481)+P11(x14481,x14482,x14483)+~P11(x14481,f9(x14481,x14484,x14482),f9(x14481,x14484,x14483))
% 1.03/1.23 [1449]P11(x14491,x14493,x14492)+~P42(x14491)+P11(x14491,x14492,x14493)+~P11(x14491,f9(x14491,x14492,x14494),f9(x14491,x14493,x14494))
% 1.03/1.23 [1464]~P42(x14641)+P11(x14641,x14642,x14643)+~P11(x14641,f9(x14641,x14642,x14644),f9(x14641,x14643,x14644))+P11(x14641,x14644,f2(x14641))
% 1.03/1.23 [1465]~P42(x14651)+P11(x14651,x14652,x14653)+~P11(x14651,f9(x14651,x14654,x14652),f9(x14651,x14654,x14653))+P11(x14651,x14654,f2(x14651))
% 1.03/1.23 [1466]~P42(x14661)+P11(x14661,x14662,x14663)+~P11(x14661,f9(x14661,x14664,x14663),f9(x14661,x14664,x14662))+P11(x14661,f2(x14661),x14664)
% 1.03/1.23 [1467]~P42(x14671)+P11(x14671,x14672,x14673)+~P11(x14671,f9(x14671,x14673,x14674),f9(x14671,x14672,x14674))+P11(x14671,f2(x14671),x14674)
% 1.03/1.23 [1471]~P42(x14711)+P11(x14711,f2(x14711),x14712)+~P11(x14711,f9(x14711,x14713,x14712),f9(x14711,x14714,x14712))+P11(x14711,x14712,f2(x14711))
% 1.03/1.23 [1472]~P42(x14721)+P11(x14721,f2(x14721),x14722)+~P11(x14721,f9(x14721,x14722,x14723),f9(x14721,x14722,x14724))+P11(x14721,x14722,f2(x14721))
% 1.03/1.23 [1501]~P37(x15013)+~P11(x15013,f14(x15013,x15014,x15011),f14(x15013,x15014,x15012))+P11(a38,x15011,x15012)+~P11(x15013,f8(x15013),x15014)
% 1.03/1.23 [1503]~P37(x15033)+~P13(x15033,f14(x15033,x15034,x15031),f14(x15033,x15034,x15032))+P13(a38,x15031,x15032)+~P11(x15033,f8(x15033),x15034)
% 1.03/1.23 [1504]~P42(x15041)+P11(x15041,x15042,x15043)+~P11(x15041,f9(x15041,x15044,x15043),f9(x15041,x15044,x15042))+~P11(x15041,x15044,f2(x15041))
% 1.03/1.23 [1505]~P42(x15051)+P13(x15051,x15052,x15053)+~P13(x15051,f9(x15051,x15054,x15053),f9(x15051,x15054,x15052))+~P11(x15051,x15054,f2(x15051))
% 1.03/1.23 [1506]~P42(x15061)+P11(x15061,x15062,x15063)+~P11(x15061,f9(x15061,x15064,x15062),f9(x15061,x15064,x15063))+~P11(x15061,f2(x15061),x15064)
% 1.03/1.23 [1507]~P44(x15071)+P11(x15071,x15072,x15073)+~P11(x15071,f9(x15071,x15074,x15072),f9(x15071,x15074,x15073))+~P13(x15071,f2(x15071),x15074)
% 1.03/1.23 [1508]~P46(x15081)+P11(x15081,x15082,x15083)+~P11(x15081,f9(x15081,x15084,x15082),f9(x15081,x15084,x15083))+~P13(x15081,f2(x15081),x15084)
% 1.03/1.23 [1509]~P37(x15091)+P11(x15091,x15092,x15093)+~P13(x15091,f2(x15091),x15093)+~P11(x15091,f14(x15091,x15092,x15094),f14(x15091,x15093,x15094))
% 1.03/1.23 [1510]~P44(x15101)+P11(x15101,x15102,x15103)+~P11(x15101,f9(x15101,x15102,x15104),f9(x15101,x15103,x15104))+~P13(x15101,f2(x15101),x15104)
% 1.03/1.23 [1511]~P46(x15111)+P11(x15111,x15112,x15113)+~P11(x15111,f9(x15111,x15112,x15114),f9(x15111,x15113,x15114))+~P13(x15111,f2(x15111),x15114)
% 1.03/1.23 [1512]~P42(x15121)+P13(x15121,x15122,x15123)+~P13(x15121,f9(x15121,x15124,x15122),f9(x15121,x15124,x15123))+~P11(x15121,f2(x15121),x15124)
% 1.03/1.23 [1513]~P44(x15131)+P13(x15131,x15132,x15133)+~P13(x15131,f9(x15131,x15134,x15132),f9(x15131,x15134,x15133))+~P11(x15131,f2(x15131),x15134)
% 1.03/1.23 [1514]~P44(x15141)+P13(x15141,x15142,x15143)+~P13(x15141,f9(x15141,x15142,x15144),f9(x15141,x15143,x15144))+~P11(x15141,f2(x15141),x15144)
% 1.03/1.23 [1530]~P8(x15301)+~P14(x15301,x15303,x15304)+~P14(x15301,x15303,x15302)+E(f3(x15301,f6(x15301,x15302,x15303),f6(x15301,x15304,x15303)),f6(x15301,f3(x15301,x15302,x15304),x15303))
% 1.03/1.23 [1555]~P39(x15553)+~P60(x15553)+P63(f26(x15551,f35(x15552,x15551,x15553)))+~P63(f26(x15551,f9(x15553,x15552,x15554)))
% 1.03/1.23 [1603]~P39(x16031)+~P60(x16031)+P14(x16031,x16032,f3(x16031,f35(x16032,x16033,x16031),f2(x16031)))+~P63(f26(x16033,f9(x16031,x16032,x16034)))
% 1.03/1.23 [1645]~P11(a1,x16454,x16451)+~P11(a1,f2(a1),x16453)+~P13(a1,f2(a1),x16454)+P13(a1,f2(a1),f3(a1,f9(a1,x16451,f5(a1,x16452,x16453)),x16454))
% 1.03/1.23 [1646]~P11(a1,x16461,x16464)+~P13(a1,x16464,f2(a1))+~P11(a1,f2(a1),x16463)+P13(a1,f3(a1,f9(a1,x16461,f5(a1,x16462,x16463)),x16464),f2(a1))
% 1.03/1.23 [1653]~P11(a1,x16531,x16534)+~P13(a1,x16534,f2(a1))+~P11(a1,f2(a1),x16532)+P11(a1,f9(a1,x16531,x16532),f3(a1,f9(a1,x16531,f5(a1,x16533,x16532)),x16534))
% 1.03/1.23 [1654]~P11(a1,x16544,x16541)+~P11(a1,f2(a1),x16543)+~P13(a1,f2(a1),x16544)+P11(a1,f3(a1,f9(a1,x16541,f5(a1,x16542,x16543)),x16544),f9(a1,x16541,x16543))
% 1.03/1.23 [1663]~P37(x16631)+P13(x16631,x16632,x16633)+~P13(x16631,f2(x16631),x16633)+~P13(x16631,f14(x16631,x16632,f3(a38,x16634,f8(a38))),f14(x16631,x16633,f3(a38,x16634,f8(a38))))
% 1.03/1.23 [791]~P7(x7915)+E(x7911,x7912)+~E(x7913,x7914)+~E(f4(x7915,x7913,x7914),f4(x7915,x7911,x7912))
% 1.03/1.23 [1066]~P24(x10661)+~P11(x10661,x10664,x10665)+P11(x10661,x10662,x10663)+~E(f4(x10661,x10664,x10665),f4(x10661,x10662,x10663))
% 1.03/1.23 [1068]~P24(x10681)+~P13(x10681,x10684,x10685)+P13(x10681,x10682,x10683)+~E(f4(x10681,x10684,x10685),f4(x10681,x10682,x10683))
% 1.03/1.23 [1328]~P30(x13281)+~P14(x13281,x13282,x13284)+~P13(a38,x13283,x13285)+P14(x13281,f14(x13281,x13282,x13283),f14(x13281,x13284,x13285))
% 1.03/1.23 [1331]~P26(x13311)+~P11(x13311,x13313,x13315)+~P11(x13311,x13312,x13314)+P11(x13311,f3(x13311,x13312,x13313),f3(x13311,x13314,x13315))
% 1.03/1.23 [1332]~P26(x13321)+~P11(x13321,x13323,x13325)+~P13(x13321,x13322,x13324)+P11(x13321,f3(x13321,x13322,x13323),f3(x13321,x13324,x13325))
% 1.03/1.23 [1333]~P26(x13331)+~P11(x13331,x13332,x13334)+~P13(x13331,x13333,x13335)+P11(x13331,f3(x13331,x13332,x13333),f3(x13331,x13334,x13335))
% 1.03/1.23 [1334]~P30(x13341)+~P14(x13341,x13343,x13345)+~P14(x13341,x13342,x13344)+P14(x13341,f9(x13341,x13342,x13343),f9(x13341,x13344,x13345))
% 1.03/1.23 [1335]~P25(x13351)+~P13(x13351,x13353,x13355)+~P13(x13351,x13352,x13354)+P13(x13351,f3(x13351,x13352,x13353),f3(x13351,x13354,x13355))
% 1.03/1.23 [1430]~P30(x14301)+~P14(x14301,f14(x14301,x14302,x14305),x14304)+P14(x14301,f14(x14301,x14302,x14303),x14304)+~P13(a38,x14303,x14305)
% 1.03/1.23 [1622]~P57(x16225)+E(x16221,x16222)+E(x16223,x16224)+~E(f3(x16225,f9(x16225,x16223,x16221),f9(x16225,x16224,x16222)),f3(x16225,f9(x16225,x16223,x16222),f9(x16225,x16224,x16221)))
% 1.03/1.23 [1565]~P8(x15651)+~E(f5(x15651,x15653,x15654),f5(x15651,x15656,x15654))+~E(f5(x15651,x15652,x15654),f5(x15651,x15655,x15654))+E(f5(x15651,f9(x15651,x15652,x15653),x15654),f5(x15651,f9(x15651,x15655,x15656),x15654))
% 1.03/1.23 [1566]~P8(x15661)+~E(f5(x15661,x15663,x15664),f5(x15661,x15666,x15664))+~E(f5(x15661,x15662,x15664),f5(x15661,x15665,x15664))+E(f5(x15661,f3(x15661,x15662,x15663),x15664),f5(x15661,f3(x15661,x15665,x15666),x15664))
% 1.03/1.23 [1567]~P9(x15671)+~E(f5(x15671,x15673,x15674),f5(x15671,x15676,x15674))+~E(f5(x15671,x15672,x15674),f5(x15671,x15675,x15674))+E(f5(x15671,f4(x15671,x15672,x15673),x15674),f5(x15671,f4(x15671,x15675,x15676),x15674))
% 1.03/1.23 [1159]E(x11591,x11592)+~P14(a1,x11592,x11591)+~P14(a1,x11591,x11592)+~P13(a1,f2(a1),x11592)+~P13(a1,f2(a1),x11591)
% 1.03/1.23 [816]~P38(x8162)+P13(x8162,f14(x8162,x8163,x8161),f2(x8162))+~E(x8163,f2(x8162))+~P10(a38,x8161)+E(x8161,f2(a38))
% 1.03/1.23 [997]~P38(x9972)+~P13(x9972,x9973,f2(x9972))+P13(x9972,f14(x9972,x9973,x9971),f2(x9972))+P10(a38,x9971)+E(x9971,f2(a38))
% 1.03/1.23 [1014]~P27(x10142)+~P13(x10142,f2(x10142),x10143)+~P13(x10142,f2(x10142),x10141)+~E(f3(x10142,x10143,x10141),f2(x10142))+E(x10141,f2(x10142))
% 1.03/1.23 [1015]~P27(x10152)+~P13(x10152,f2(x10152),x10153)+~P13(x10152,f2(x10152),x10151)+~E(f3(x10152,x10151,x10153),f2(x10152))+E(x10151,f2(x10152))
% 1.03/1.23 [1028]~P38(x10283)+~P11(x10283,f2(x10283),f14(x10283,x10282,x10281))+~P10(a38,x10281)+~E(x10282,f2(x10283))+E(x10281,f2(a38))
% 1.03/1.23 [1136]~P38(x11362)+~P11(x11362,f2(x11362),f14(x11362,x11363,x11361))+P11(x11362,f2(x11362),x11363)+~E(x11363,f2(x11362))+E(x11361,f2(a38))
% 1.03/1.23 [1163]~P38(x11632)+~P11(x11632,f2(x11632),f14(x11632,x11633,x11631))+P11(x11632,f2(x11632),x11633)+P10(a38,x11631)+E(x11631,f2(a38))
% 1.03/1.23 [1347]~P38(x13471)+~P13(x13471,x13472,f8(x13471))+~P13(x13471,f2(x13471),x13472)+~P13(x13471,f2(x13471),x13473)+P13(x13471,f9(x13471,x13472,x13473),x13473)
% 1.03/1.23 [1348]~P38(x13481)+~P13(x13481,x13483,f8(x13481))+~P13(x13481,f2(x13481),x13483)+~P13(x13481,f2(x13481),x13482)+P13(x13481,f9(x13481,x13482,x13483),x13482)
% 1.03/1.23 [1732]~P37(x17323)+E(x17321,x17322)+~P13(x17323,f2(x17323),x17322)+~P13(x17323,f2(x17323),x17321)+~E(f14(x17323,x17321,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))),f14(x17323,x17322,f13(a38,f3(a1,f3(a1,f3(a1,f8(a1),a10),a10),f3(a1,f3(a1,f8(a1),a10),a10)))))
% 1.03/1.23 [1468]~P37(x14681)+~P11(x14681,x14682,x14684)+~P13(x14681,f2(x14681),x14682)+P11(x14681,f14(x14681,x14682,x14683),f14(x14681,x14684,x14683))+~P11(a38,f2(a38),x14683)
% 1.03/1.23 [1473]~P37(x14731)+~P11(a38,x14734,x14733)+~P11(x14731,x14732,f8(x14731))+~P11(x14731,f2(x14731),x14732)+P11(x14731,f14(x14731,x14732,x14733),f14(x14731,x14732,x14734))
% 1.03/1.23 [1474]~P37(x14741)+~P13(a38,x14744,x14743)+~P13(x14741,x14742,f8(x14741))+~P13(x14741,f2(x14741),x14742)+P13(x14741,f14(x14741,x14742,x14743),f14(x14741,x14742,x14744))
% 1.03/1.23 [1586]~P37(x15863)+E(x15861,x15862)+~P13(x15863,f2(x15863),x15862)+~P13(x15863,f2(x15863),x15861)+~E(f14(x15863,x15861,f3(a38,x15864,f8(a38))),f14(x15863,x15862,f3(a38,x15864,f8(a38))))
% 1.03/1.23 [1643]~P39(x16432)+~P60(x16432)+~P14(x16432,x16433,f3(x16432,x16434,f2(x16432)))+~P63(f26(x16431,x16434))+P63(f26(x16431,f9(x16432,x16433,f36(x16433,x16431,x16432))))
% 1.03/1.23 [1665]P13(a1,x16651,x16652)+~P11(a1,x16653,x16654)+~P11(a1,x16653,x16655)+~P13(a1,x16654,f2(a1))+~P13(a1,f3(a1,f9(a1,x16653,x16652),x16655),f3(a1,f9(a1,x16653,x16651),x16654))
% 1.03/1.23 [1666]P13(a1,x16661,x16662)+~P11(a1,x16663,x16664)+~P11(a1,x16665,x16664)+~P13(a1,f2(a1),x16665)+~P13(a1,f3(a1,f9(a1,x16664,x16661),x16665),f3(a1,f9(a1,x16664,x16662),x16663))
% 1.03/1.23 [1442]~P57(x14424)+E(x14421,x14422)+~E(x14425,x14426)+E(x14423,f2(x14424))+~E(f3(x14424,x14425,f9(x14424,x14423,x14421)),f3(x14424,x14426,f9(x14424,x14423,x14422)))
% 1.03/1.23 [1662]~P39(x16621)+~P36(x16621)+~P14(x16621,x16622,x16625)+~P14(x16621,x16622,f3(x16621,x16623,x16626))+P14(x16621,x16622,f3(x16621,f4(x16621,x16623,f9(x16621,x16624,x16625)),x16626))
% 1.03/1.23 [1672]~P39(x16721)+~P36(x16721)+~P14(x16721,x16722,x16725)+P14(x16721,x16722,f3(x16721,x16723,x16724))+~P14(x16721,x16722,f3(x16721,f4(x16721,x16723,f9(x16721,x16726,x16725)),x16724))
% 1.03/1.23 [666]~P29(x6662)+~P49(x6662)+~P32(x6662)+~P61(x6662)+~E(f14(x6662,x6661,x6663),f2(x6662))+E(x6661,f2(x6662))
% 1.03/1.23 [667]~P29(x6672)+~P49(x6672)+~P32(x6672)+~P61(x6672)+~E(f14(x6672,x6673,x6671),f2(x6672))+~E(x6671,f2(a38))
% 1.03/1.23 [979]~P27(x9791)+~P13(x9791,f2(x9791),x9793)+~P13(x9791,f2(x9791),x9792)+~E(x9793,f2(x9791))+~E(x9792,f2(x9791))+E(f3(x9791,x9792,x9793),f2(x9791))
% 1.03/1.23 [1376]~P37(x13763)+E(x13761,x13762)+~P13(x13763,f2(x13763),x13762)+~P13(x13763,f2(x13763),x13761)+~E(f14(x13763,x13761,x13764),f14(x13763,x13762,x13764))+~P11(a38,f2(a38),x13764)
% 1.03/1.23 [1447]~P11(a1,x14471,x14473)+E(f5(a1,x14472,x14471),x14473)+E(x14471,f2(a1))+P11(a1,f2(a1),x14471)+~P13(a1,x14473,f2(a1))+~E(x14472,f3(a1,f9(a1,x14471,x14474),x14473))
% 1.03/1.23 [1495]~P11(a1,x14953,x14951)+E(f5(a1,x14952,x14951),x14953)+E(x14951,f2(a1))+~P11(a1,f2(a1),x14951)+~P13(a1,f2(a1),x14953)+~E(x14952,f3(a1,f9(a1,x14951,x14954),x14953))
% 1.03/1.23 [1541]~P44(x15411)+~P11(x15411,x15413,x15415)+~P11(x15411,x15412,x15414)+~P11(x15411,f2(x15411),x15414)+~P13(x15411,f2(x15411),x15413)+P11(x15411,f9(x15411,x15412,x15413),f9(x15411,x15414,x15415))
% 1.03/1.23 [1542]~P44(x15421)+~P11(x15421,x15423,x15425)+~P11(x15421,x15422,x15424)+~P13(x15421,f2(x15421),x15423)+~P13(x15421,f2(x15421),x15422)+P11(x15421,f9(x15421,x15422,x15423),f9(x15421,x15424,x15425))
% 1.03/1.23 [1543]~P44(x15431)+~P11(x15431,x15433,x15435)+~P13(x15431,x15432,x15434)+~P11(x15431,f2(x15431),x15432)+~P13(x15431,f2(x15431),x15433)+P11(x15431,f9(x15431,x15432,x15433),f9(x15431,x15434,x15435))
% 1.03/1.23 [1544]~P44(x15441)+~P11(x15441,x15442,x15444)+~P13(x15441,x15443,x15445)+~P11(x15441,f2(x15441),x15443)+~P13(x15441,f2(x15441),x15442)+P11(x15441,f9(x15441,x15442,x15443),f9(x15441,x15444,x15445))
% 1.03/1.23 [1545]~P56(x15451)+~P13(x15451,x15453,x15455)+~P13(x15451,x15452,x15454)+~P13(x15451,f2(x15451),x15453)+~P13(x15451,f2(x15451),x15454)+P13(x15451,f9(x15451,x15452,x15453),f9(x15451,x15454,x15455))
% 1.03/1.23 [1546]~P56(x15461)+~P13(x15461,x15463,x15465)+~P13(x15461,x15462,x15464)+~P13(x15461,f2(x15461),x15463)+~P13(x15461,f2(x15461),x15462)+P13(x15461,f9(x15461,x15462,x15463),f9(x15461,x15464,x15465))
% 1.03/1.23 [1532]~P64(x15321,x15323,x15324)+~P11(a1,x15324,x15322)+~P11(a1,x15324,f2(a1))+~P13(a1,x15322,f2(a1))+P63(f26(x15321,x15322))+~E(x15323,f3(a1,f9(a1,x15324,x15325),x15322))
% 1.03/1.23 [1533]~P64(x15331,x15333,x15334)+~P11(a1,x15332,x15334)+~P11(a1,f2(a1),x15334)+~P13(a1,f2(a1),x15332)+P63(f26(x15331,x15332))+~E(x15333,f3(a1,f9(a1,x15334,x15335),x15332))
% 1.03/1.23 [628]~P29(x6282)+~P49(x6282)+~P32(x6282)+~P61(x6282)+~E(x6283,f2(x6282))+E(f14(x6282,x6283,x6281),f2(x6282))+E(x6281,f2(a38))
% 1.03/1.23 [1562]~P11(a1,x15623,x15621)+~P11(a1,x15621,x15623)+E(f5(a1,x15622,x15621),x15623)+E(x15621,f2(a1))+~P13(a1,x15623,f2(a1))+~P13(a1,f2(a1),x15623)+~E(x15622,f3(a1,f9(a1,x15621,x15624),x15623))
% 1.03/1.23 [1647]~P47(x16471)+~P11(x16471,x16475,x16476)+~P11(x16471,x16473,x16476)+~P13(x16471,f2(x16471),x16474)+~P13(x16471,f2(x16471),x16472)+~E(f3(x16471,x16472,x16474),f8(x16471))+P11(x16471,f3(x16471,f9(x16471,x16472,x16473),f9(x16471,x16474,x16475)),x16476)
% 1.03/1.23 [1648]~P45(x16481)+~P13(x16481,x16485,x16486)+~P13(x16481,x16483,x16486)+~P13(x16481,f2(x16481),x16484)+~P13(x16481,f2(x16481),x16482)+~E(f3(x16481,x16482,x16484),f8(x16481))+P13(x16481,f3(x16481,f9(x16481,x16482,x16483),f9(x16481,x16484,x16485)),x16486)
% 1.03/1.23 [1669]~P11(a1,x16696,x16695)+~P13(a1,x16695,x16693)+P13(a1,x16691,x16692)+~P11(a1,f2(a1),x16695)+~P13(a1,f2(a1),x16694)+~P13(a1,f2(a1),f3(a1,f9(a1,x16695,x16692),x16696))+~E(f3(a1,f9(a1,x16693,x16691),x16694),f3(a1,f9(a1,x16695,x16692),x16696))
% 1.03/1.23 [1670]~P11(a1,x16704,x16703)+~P13(a1,x16705,x16703)+P13(a1,x16701,x16702)+~P11(a1,f2(a1),x16705)+~P13(a1,f2(a1),x16706)+~P11(a1,f3(a1,f9(a1,x16705,x16701),x16706),f2(a1))+~E(f3(a1,f9(a1,x16703,x16702),x16704),f3(a1,f9(a1,x16705,x16701),x16706))
% 1.03/1.23 %EqnAxiom
% 1.03/1.23 [1]E(x11,x11)
% 1.03/1.23 [2]E(x22,x21)+~E(x21,x22)
% 1.03/1.23 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.03/1.23 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 1.03/1.23 [5]~E(x51,x52)+E(f13(x51,x53),f13(x52,x53))
% 1.03/1.23 [6]~E(x61,x62)+E(f13(x63,x61),f13(x63,x62))
% 1.03/1.23 [7]~E(x71,x72)+E(f4(x71,x73,x74),f4(x72,x73,x74))
% 1.03/1.23 [8]~E(x81,x82)+E(f4(x83,x81,x84),f4(x83,x82,x84))
% 1.03/1.23 [9]~E(x91,x92)+E(f4(x93,x94,x91),f4(x93,x94,x92))
% 1.03/1.23 [10]~E(x101,x102)+E(f14(x101,x103,x104),f14(x102,x103,x104))
% 1.03/1.23 [11]~E(x111,x112)+E(f14(x113,x111,x114),f14(x113,x112,x114))
% 1.03/1.23 [12]~E(x121,x122)+E(f14(x123,x124,x121),f14(x123,x124,x122))
% 1.03/1.23 [13]~E(x131,x132)+E(f3(x131,x133,x134),f3(x132,x133,x134))
% 1.03/1.23 [14]~E(x141,x142)+E(f3(x143,x141,x144),f3(x143,x142,x144))
% 1.03/1.23 [15]~E(x151,x152)+E(f3(x153,x154,x151),f3(x153,x154,x152))
% 1.03/1.23 [16]~E(x161,x162)+E(f9(x161,x163,x164),f9(x162,x163,x164))
% 1.03/1.23 [17]~E(x171,x172)+E(f9(x173,x171,x174),f9(x173,x172,x174))
% 1.03/1.23 [18]~E(x181,x182)+E(f9(x183,x184,x181),f9(x183,x184,x182))
% 1.03/1.23 [19]~E(x191,x192)+E(f8(x191),f8(x192))
% 1.03/1.23 [20]~E(x201,x202)+E(f5(x201,x203,x204),f5(x202,x203,x204))
% 1.03/1.23 [21]~E(x211,x212)+E(f5(x213,x211,x214),f5(x213,x212,x214))
% 1.03/1.23 [22]~E(x221,x222)+E(f5(x223,x224,x221),f5(x223,x224,x222))
% 1.03/1.23 [23]~E(x231,x232)+E(f31(x231),f31(x232))
% 1.03/1.23 [24]~E(x241,x242)+E(f26(x241,x243),f26(x242,x243))
% 1.03/1.23 [25]~E(x251,x252)+E(f26(x253,x251),f26(x253,x252))
% 1.03/1.23 [26]~E(x261,x262)+E(f27(x261,x263,x264),f27(x262,x263,x264))
% 1.03/1.23 [27]~E(x271,x272)+E(f27(x273,x271,x274),f27(x273,x272,x274))
% 1.03/1.23 [28]~E(x281,x282)+E(f27(x283,x284,x281),f27(x283,x284,x282))
% 1.03/1.23 [29]~E(x291,x292)+E(f24(x291,x293,x294),f24(x292,x293,x294))
% 1.03/1.23 [30]~E(x301,x302)+E(f24(x303,x301,x304),f24(x303,x302,x304))
% 1.03/1.23 [31]~E(x311,x312)+E(f24(x313,x314,x311),f24(x313,x314,x312))
% 1.03/1.23 [32]~E(x321,x322)+E(f33(x321),f33(x322))
% 1.03/1.23 [33]~E(x331,x332)+E(f6(x331,x333,x334),f6(x332,x333,x334))
% 1.03/1.23 [34]~E(x341,x342)+E(f6(x343,x341,x344),f6(x343,x342,x344))
% 1.03/1.23 [35]~E(x351,x352)+E(f6(x353,x354,x351),f6(x353,x354,x352))
% 1.03/1.23 [36]~E(x361,x362)+E(f23(x361,x363,x364),f23(x362,x363,x364))
% 1.03/1.23 [37]~E(x371,x372)+E(f23(x373,x371,x374),f23(x373,x372,x374))
% 1.03/1.23 [38]~E(x381,x382)+E(f23(x383,x384,x381),f23(x383,x384,x382))
% 1.03/1.23 [39]~E(x391,x392)+E(f28(x391,x393,x394),f28(x392,x393,x394))
% 1.03/1.23 [40]~E(x401,x402)+E(f28(x403,x401,x404),f28(x403,x402,x404))
% 1.03/1.23 [41]~E(x411,x412)+E(f28(x413,x414,x411),f28(x413,x414,x412))
% 1.03/1.23 [42]~E(x421,x422)+E(f34(x421),f34(x422))
% 1.03/1.23 [43]~E(x431,x432)+E(f7(x431),f7(x432))
% 1.03/1.23 [44]~E(x441,x442)+E(f29(x441,x443),f29(x442,x443))
% 1.03/1.23 [45]~E(x451,x452)+E(f29(x453,x451),f29(x453,x452))
% 1.03/1.23 [46]~E(x461,x462)+E(f22(x461,x463,x464),f22(x462,x463,x464))
% 1.03/1.23 [47]~E(x471,x472)+E(f22(x473,x471,x474),f22(x473,x472,x474))
% 1.03/1.23 [48]~E(x481,x482)+E(f22(x483,x484,x481),f22(x483,x484,x482))
% 1.03/1.23 [49]~E(x491,x492)+E(f25(x491,x493,x494),f25(x492,x493,x494))
% 1.03/1.23 [50]~E(x501,x502)+E(f25(x503,x501,x504),f25(x503,x502,x504))
% 1.03/1.23 [51]~E(x511,x512)+E(f25(x513,x514,x511),f25(x513,x514,x512))
% 1.03/1.23 [52]~E(x521,x522)+E(f19(x521),f19(x522))
% 1.03/1.23 [53]~E(x531,x532)+E(f20(x531,x533),f20(x532,x533))
% 1.03/1.23 [54]~E(x541,x542)+E(f20(x543,x541),f20(x543,x542))
% 1.03/1.23 [55]~E(x551,x552)+E(f35(x551,x553,x554),f35(x552,x553,x554))
% 1.03/1.23 [56]~E(x561,x562)+E(f35(x563,x561,x564),f35(x563,x562,x564))
% 1.03/1.23 [57]~E(x571,x572)+E(f35(x573,x574,x571),f35(x573,x574,x572))
% 1.03/1.23 [58]~E(x581,x582)+E(f16(x581),f16(x582))
% 1.03/1.23 [59]~E(x591,x592)+E(f21(x591,x593),f21(x592,x593))
% 1.03/1.23 [60]~E(x601,x602)+E(f21(x603,x601),f21(x603,x602))
% 1.03/1.23 [61]~E(x611,x612)+E(f17(x611,x613),f17(x612,x613))
% 1.03/1.23 [62]~E(x621,x622)+E(f17(x623,x621),f17(x623,x622))
% 1.03/1.23 [63]~E(x631,x632)+E(f30(x631),f30(x632))
% 1.03/1.23 [64]~E(x641,x642)+E(f36(x641,x643,x644),f36(x642,x643,x644))
% 1.03/1.23 [65]~E(x651,x652)+E(f36(x653,x651,x654),f36(x653,x652,x654))
% 1.03/1.23 [66]~E(x661,x662)+E(f36(x663,x664,x661),f36(x663,x664,x662))
% 1.03/1.23 [67]~E(x671,x672)+E(f18(x671,x673),f18(x672,x673))
% 1.03/1.23 [68]~E(x681,x682)+E(f18(x683,x681),f18(x683,x682))
% 1.03/1.23 [69]~E(x691,x692)+E(f32(x691),f32(x692))
% 1.03/1.23 [70]~P1(x701)+P1(x702)+~E(x701,x702)
% 1.03/1.23 [71]P13(x712,x713,x714)+~E(x711,x712)+~P13(x711,x713,x714)
% 1.03/1.23 [72]P13(x723,x722,x724)+~E(x721,x722)+~P13(x723,x721,x724)
% 1.03/1.23 [73]P13(x733,x734,x732)+~E(x731,x732)+~P13(x733,x734,x731)
% 1.03/1.23 [74]~P38(x741)+P38(x742)+~E(x741,x742)
% 1.03/1.23 [75]~P28(x751)+P28(x752)+~E(x751,x752)
% 1.03/1.23 [76]P11(x762,x763,x764)+~E(x761,x762)+~P11(x761,x763,x764)
% 1.03/1.23 [77]P11(x773,x772,x774)+~E(x771,x772)+~P11(x773,x771,x774)
% 1.03/1.23 [78]P11(x783,x784,x782)+~E(x781,x782)+~P11(x783,x784,x781)
% 1.03/1.23 [79]~P37(x791)+P37(x792)+~E(x791,x792)
% 1.03/1.23 [80]~P2(x801)+P2(x802)+~E(x801,x802)
% 1.03/1.23 [81]P12(x812,x813)+~E(x811,x812)+~P12(x811,x813)
% 1.03/1.23 [82]P12(x823,x822)+~E(x821,x822)+~P12(x823,x821)
% 1.03/1.23 [83]P14(x832,x833,x834)+~E(x831,x832)+~P14(x831,x833,x834)
% 1.03/1.23 [84]P14(x843,x842,x844)+~E(x841,x842)+~P14(x843,x841,x844)
% 1.03/1.23 [85]P14(x853,x854,x852)+~E(x851,x852)+~P14(x853,x854,x851)
% 1.03/1.23 [86]~P30(x861)+P30(x862)+~E(x861,x862)
% 1.03/1.23 [87]~P29(x871)+P29(x872)+~E(x871,x872)
% 1.03/1.23 [88]P64(x882,x883,x884)+~E(x881,x882)+~P64(x881,x883,x884)
% 1.03/1.23 [89]P64(x893,x892,x894)+~E(x891,x892)+~P64(x893,x891,x894)
% 1.03/1.23 [90]P64(x903,x904,x902)+~E(x901,x902)+~P64(x903,x904,x901)
% 1.03/1.23 [91]~P27(x911)+P27(x912)+~E(x911,x912)
% 1.03/1.23 [92]~P63(x921)+P63(x922)+~E(x921,x922)
% 1.03/1.23 [93]~P22(x931)+P22(x932)+~E(x931,x932)
% 1.03/1.23 [94]~P26(x941)+P26(x942)+~E(x941,x942)
% 1.03/1.23 [95]~P46(x951)+P46(x952)+~E(x951,x952)
% 1.03/1.23 [96]~P43(x961)+P43(x962)+~E(x961,x962)
% 1.03/1.23 [97]~P31(x971)+P31(x972)+~E(x971,x972)
% 1.03/1.23 [98]~P56(x981)+P56(x982)+~E(x981,x982)
% 1.03/1.23 [99]~P48(x991)+P48(x992)+~E(x991,x992)
% 1.03/1.23 [100]~P39(x1001)+P39(x1002)+~E(x1001,x1002)
% 1.03/1.23 [101]~P36(x1011)+P36(x1012)+~E(x1011,x1012)
% 1.03/1.23 [102]~P49(x1021)+P49(x1022)+~E(x1021,x1022)
% 1.03/1.23 [103]P10(x1032,x1033)+~E(x1031,x1032)+~P10(x1031,x1033)
% 1.03/1.23 [104]P10(x1043,x1042)+~E(x1041,x1042)+~P10(x1043,x1041)
% 1.03/1.23 [105]~P7(x1051)+P7(x1052)+~E(x1051,x1052)
% 1.03/1.23 [106]~P42(x1061)+P42(x1062)+~E(x1061,x1062)
% 1.03/1.23 [107]~P3(x1071)+P3(x1072)+~E(x1071,x1072)
% 1.03/1.23 [108]~P8(x1081)+P8(x1082)+~E(x1081,x1082)
% 1.03/1.23 [109]~P58(x1091)+P58(x1092)+~E(x1091,x1092)
% 1.03/1.23 [110]~P61(x1101)+P61(x1102)+~E(x1101,x1102)
% 1.03/1.23 [111]~P33(x1111)+P33(x1112)+~E(x1111,x1112)
% 1.03/1.23 [112]~P24(x1121)+P24(x1122)+~E(x1121,x1122)
% 1.03/1.23 [113]~P55(x1131)+P55(x1132)+~E(x1131,x1132)
% 1.03/1.23 [114]~P40(x1141)+P40(x1142)+~E(x1141,x1142)
% 1.03/1.23 [115]~P32(x1151)+P32(x1152)+~E(x1151,x1152)
% 1.03/1.23 [116]~P44(x1161)+P44(x1162)+~E(x1161,x1162)
% 1.03/1.23 [117]~P18(x1171)+P18(x1172)+~E(x1171,x1172)
% 1.03/1.23 [118]~P52(x1181)+P52(x1182)+~E(x1181,x1182)
% 1.03/1.23 [119]~P47(x1191)+P47(x1192)+~E(x1191,x1192)
% 1.03/1.23 [120]~P59(x1201)+P59(x1202)+~E(x1201,x1202)
% 1.03/1.23 [121]~P60(x1211)+P60(x1212)+~E(x1211,x1212)
% 1.03/1.23 [122]~P53(x1221)+P53(x1222)+~E(x1221,x1222)
% 1.03/1.23 [123]~P4(x1231)+P4(x1232)+~E(x1231,x1232)
% 1.03/1.23 [124]~P54(x1241)+P54(x1242)+~E(x1241,x1242)
% 1.03/1.23 [125]~P9(x1251)+P9(x1252)+~E(x1251,x1252)
% 1.03/1.23 [126]~P57(x1261)+P57(x1262)+~E(x1261,x1262)
% 1.03/1.23 [127]~P19(x1271)+P19(x1272)+~E(x1271,x1272)
% 1.03/1.23 [128]~P25(x1281)+P25(x1282)+~E(x1281,x1282)
% 1.03/1.23 [129]~P45(x1291)+P45(x1292)+~E(x1291,x1292)
% 1.03/1.23 [130]~P34(x1301)+P34(x1302)+~E(x1301,x1302)
% 1.03/1.23 [131]~P51(x1311)+P51(x1312)+~E(x1311,x1312)
% 1.03/1.23 [132]~P35(x1321)+P35(x1322)+~E(x1321,x1322)
% 1.03/1.23 [133]~P20(x1331)+P20(x1332)+~E(x1331,x1332)
% 1.03/1.23 [134]~P50(x1341)+P50(x1342)+~E(x1341,x1342)
% 1.03/1.23 [135]~P17(x1351)+P17(x1352)+~E(x1351,x1352)
% 1.03/1.23 [136]~P41(x1361)+P41(x1362)+~E(x1361,x1362)
% 1.03/1.23 [137]~P16(x1371)+P16(x1372)+~E(x1371,x1372)
% 1.03/1.23 [138]~P6(x1381)+P6(x1382)+~E(x1381,x1382)
% 1.03/1.23 [139]~P21(x1391)+P21(x1392)+~E(x1391,x1392)
% 1.03/1.23 [140]~P62(x1401)+P62(x1402)+~E(x1401,x1402)
% 1.03/1.23 [141]~P15(x1411)+P15(x1412)+~E(x1411,x1412)
% 1.03/1.23 [142]~P5(x1421)+P5(x1422)+~E(x1421,x1422)
% 1.03/1.23 [143]~P23(x1431)+P23(x1432)+~E(x1431,x1432)
% 1.03/1.23
% 1.03/1.23 %-------------------------------------------
% 1.03/1.23 cnf(1762,plain,
% 1.03/1.23 ($false),
% 1.03/1.23 inference(scs_inference,[],[478,462,1707]),
% 1.03/1.23 ['proof']).
% 1.03/1.23 % SZS output end Proof
% 1.03/1.23 % Total time :0.080000s
%------------------------------------------------------------------------------