TSTP Solution File: SWW194+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW194+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 : n017.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 00:13:03 EDT 2023
% Result : Theorem 7.29s 7.42s
% Output : CNFRefutation 7.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW194+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 17:01:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 7.25/7.35 %-------------------------------------------
% 7.25/7.35 % File :CSE---1.6
% 7.25/7.35 % Problem :theBenchmark
% 7.25/7.35 % Transform :cnf
% 7.25/7.35 % Format :tptp:raw
% 7.25/7.35 % Command :java -jar mcs_scs.jar %d %s
% 7.25/7.35
% 7.25/7.35 % Result :Theorem 5.990000s
% 7.25/7.35 % Output :CNFRefutation 5.990000s
% 7.25/7.35 %-------------------------------------------
% 7.25/7.35 %------------------------------------------------------------------------------
% 7.25/7.35 % File : SWW194+1 : TPTP v8.1.2. Released v5.2.0.
% 7.25/7.35 % Domain : Software Verification
% 7.25/7.35 % Problem : Fundamental Theorem of Algebra 436385, 1000 axioms selected
% 7.25/7.35 % Version : Especial.
% 7.25/7.35 % English :
% 7.25/7.35
% 7.25/7.35 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 7.25/7.35 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 7.25/7.35 % Source : [Bla11]
% 7.25/7.35 % Names : fta_436385.1000.p [Bla11]
% 7.25/7.35
% 7.25/7.35 % Status : Theorem
% 7.25/7.35 % Rating : 0.33 v8.1.0, 0.39 v7.5.0, 0.41 v7.4.0, 0.43 v7.3.0, 0.38 v7.1.0, 0.35 v7.0.0, 0.33 v6.4.0, 0.42 v6.3.0, 0.33 v6.2.0, 0.36 v6.1.0, 0.47 v6.0.0, 0.35 v5.5.0, 0.59 v5.4.0, 0.61 v5.3.0, 0.63 v5.2.0
% 7.25/7.35 % Syntax : Number of formulae : 1199 ( 430 unt; 0 def)
% 7.25/7.35 % Number of atoms : 2810 ( 765 equ)
% 7.25/7.35 % Maximal formula atoms : 10 ( 2 avg)
% 7.25/7.35 % Number of connectives : 1803 ( 192 ~; 51 |; 148 &)
% 7.25/7.35 % ( 248 <=>;1164 =>; 0 <=; 0 <~>)
% 7.25/7.35 % Maximal formula depth : 13 ( 5 avg)
% 7.25/7.35 % Maximal term depth : 13 ( 2 avg)
% 7.25/7.35 % Number of predicates : 71 ( 70 usr; 0 prp; 1-3 aty)
% 7.25/7.35 % Number of functors : 37 ( 37 usr; 12 con; 0-3 aty)
% 7.25/7.35 % Number of variables : 2543 (2538 !; 5 ?)
% 7.25/7.35 % SPC : FOF_THM_RFO_SEQ
% 7.25/7.35
% 7.25/7.35 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 7.25/7.35 % 2011-03-01 11:23:48
% 7.25/7.35 %------------------------------------------------------------------------------
% 7.25/7.35 %----Relevant facts (994)
% 7.25/7.35 fof(fact_ext,axiom,
% 7.25/7.35 ! [V_g_2,V_f_2] :
% 7.25/7.35 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 7.25/7.35 => V_f_2 = V_g_2 ) ).
% 7.25/7.35
% 7.25/7.35 fof(fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096,axiom,
% 7.25/7.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(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_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 7.25/7.35
% 7.25/7.35 fof(fact__096abs_A_I2_A_K_Ay_J_A_060_061_A1_096,axiom,
% 7.25/7.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(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_y____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 7.25/7.35
% 7.25/7.35 fof(fact__0962_A_K_Ax_A_060_061_A1_096,axiom,
% 7.25/7.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 7.25/7.35
% 7.25/7.35 fof(fact__0962_A_K_Ay_A_060_061_A1_096,axiom,
% 7.25/7.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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_y____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_two__realpow__ge__one,axiom,
% 7.25/7.35 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(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)) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_four__x__squared,axiom,
% 7.25/7.35 ! [V_x] : hAPP(hAPP(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))))),hAPP(hAPP(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))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(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)))) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_power2__eq__square__number__of,axiom,
% 7.25/7.35 ! [V_w,T_b] :
% 7.25/7.35 ( ( class_Groups_Omonoid__mult(T_b)
% 7.25/7.35 & class_Int_Onumber(T_b) )
% 7.25/7.35 => hAPP(hAPP(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)))) = hAPP(hAPP(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)) ) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_abs__power2,axiom,
% 7.25/7.35 ! [V_a,T_a] :
% 7.25/7.35 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.35 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(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))))) = hAPP(hAPP(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)))) ) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_power2__abs,axiom,
% 7.25/7.35 ! [V_a,T_a] :
% 7.25/7.35 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(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)))) ) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_one__power2,axiom,
% 7.25/7.35 ! [T_a] :
% 7.25/7.35 ( class_Rings_Osemiring__1(T_a)
% 7.25/7.35 => hAPP(hAPP(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) ) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 7.25/7.35 ! [V_x,T_a] :
% 7.25/7.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(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)))) ) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_power2__eq__square,axiom,
% 7.25/7.35 ! [V_a,T_a] :
% 7.25/7.35 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.35 => hAPP(hAPP(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)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 7.25/7.35 ! [V_n,V_x,T_a] :
% 7.25/7.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
% 7.25/7.35
% 7.25/7.35 fof(fact__096_N1_A_060_061_A2_A_K_Ax_096,axiom,
% 7.25/7.35 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(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____)) ).
% 7.25/7.35
% 7.25/7.35 fof(fact_power3__eq__cube,axiom,
% 7.25/7.36 ! [V_a,T_a] :
% 7.25/7.36 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.36 => hAPP(hAPP(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)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact__096_N1_A_060_061_A2_A_K_Ay_096,axiom,
% 7.25/7.36 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(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_y____)) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_eq__number__of__Pls__Min,axiom,
% 7.25/7.36 c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 7.25/7.36 ! [V_q,V_p,V_x,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 7.25/7.36 ! [V_x,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_nat__numeral__1__eq__1,axiom,
% 7.25/7.36 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_Numeral1__eq1__nat,axiom,
% 7.25/7.36 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_power__m1__even,axiom,
% 7.25/7.36 ! [V_n,T_a] :
% 7.25/7.36 ( class_Int_Onumber__ring(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),hAPP(hAPP(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) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 7.25/7.36 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 7.25/7.36 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 7.25/7.36 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 7.25/7.36 ! [V_rx,V_ly,V_lx,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 7.25/7.36 ! [V_rx,V_ly,V_lx,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 7.25/7.36 ! [V_ry,V_rx,V_lx,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 7.25/7.36 ! [V_ry,V_rx,V_lx,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 7.25/7.36 ! [V_b,V_a,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_real__le__antisym,axiom,
% 7.25/7.36 ! [V_w,V_z] :
% 7.25/7.36 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 7.25/7.36 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 7.25/7.36 => V_z = V_w ) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_real__le__trans,axiom,
% 7.25/7.36 ! [V_k,V_j,V_i] :
% 7.25/7.36 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 7.25/7.36 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 7.25/7.36 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_real__le__linear,axiom,
% 7.25/7.36 ! [V_w,V_z] :
% 7.25/7.36 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 7.25/7.36 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_real__le__refl,axiom,
% 7.25/7.36 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_real__mult__assoc,axiom,
% 7.25/7.36 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_real__mult__commute,axiom,
% 7.25/7.36 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_power__even__eq,axiom,
% 7.25/7.36 ! [V_n,V_a,T_a] :
% 7.25/7.36 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(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)))) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 7.25/7.36 ! [V_a,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 7.25/7.36 ! [V_a,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 7.25/7.36 ! [V_q,V_y,V_x,T_a] :
% 7.25/7.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.36 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_real__mult__1,axiom,
% 7.25/7.36 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 7.25/7.36
% 7.25/7.36 fof(fact_semiring__norm_I110_J,axiom,
% 7.25/7.36 ! [T_a] :
% 7.25/7.36 ( class_Int_Onumber__ring(T_a)
% 7.25/7.36 => c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_xy,axiom,
% 7.25/7.36 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_y____),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_abs__power__minus__one,axiom,
% 7.25/7.36 ! [V_n,T_a] :
% 7.25/7.36 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.36 & class_Rings_Olinordered__idom(T_a) )
% 7.25/7.36 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_le__special_I4_J,axiom,
% 7.25/7.36 ! [V_xa_2,T_a] :
% 7.25/7.36 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.36 & class_Rings_Olinordered__idom(T_a) )
% 7.25/7.36 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))
% 7.25/7.36 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_le__special_I2_J,axiom,
% 7.25/7.36 ! [V_ya_2,T_a] :
% 7.25/7.36 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.36 & class_Rings_Olinordered__idom(T_a) )
% 7.25/7.36 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
% 7.25/7.36 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2) ) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_csqrt,axiom,
% 7.25/7.36 ! [V_z] : hAPP(hAPP(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 ).
% 7.25/7.36
% 7.25/7.36 fof(fact_abs__minus__one,axiom,
% 7.25/7.36 ! [T_a] :
% 7.25/7.36 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.36 & class_Rings_Olinordered__idom(T_a) )
% 7.25/7.36 => c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 7.25/7.36
% 7.25/7.36 fof(fact_numeral__1__eq__1,axiom,
% 7.25/7.36 ! [T_a] :
% 7.25/7.36 ( class_Int_Onumber__ring(T_a)
% 7.25/7.36 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 7.25/7.36
% 7.25/7.37 fof(fact_mult__numeral__1,axiom,
% 7.25/7.37 ! [V_a,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => hAPP(hAPP(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 ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_mult__numeral__1__right,axiom,
% 7.25/7.37 ! [V_a,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => hAPP(hAPP(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 ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_power__increasing,axiom,
% 7.25/7.37 ! [V_a,V_N,V_n,T_a] :
% 7.25/7.37 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.37 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 7.25/7.37 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.25/7.37 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_one__le__power,axiom,
% 7.25/7.37 ! [V_n,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.37 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.25/7.37 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_z,axiom,
% 7.25/7.37 v_z = c_Complex_Ocomplex_OComplex(v_x____,v_y____) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_assms,axiom,
% 7.25/7.37 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_number__of__is__id,axiom,
% 7.25/7.37 ! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k ).
% 7.25/7.37
% 7.25/7.37 fof(fact_number__of__add,axiom,
% 7.25/7.37 ! [V_w,V_v,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => 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)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 7.25/7.37 ! [V_c,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 7.25/7.37 ! [V_d,V_c,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => 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)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 7.25/7.37 ! [V_d,V_c,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => 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) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_add__number__of__eq,axiom,
% 7.25/7.37 ! [V_w,V_v,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => 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)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_times__numeral__code_I5_J,axiom,
% 7.25/7.37 ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_less__eq__number__of__int__code,axiom,
% 7.25/7.37 ! [V_l_2,V_k_2] :
% 7.25/7.37 ( 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))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_add__number__of__left,axiom,
% 7.25/7.37 ! [V_z,V_w,V_v,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => 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) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 7.25/7.37 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => 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)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 7.25/7.37 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => 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) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 7.25/7.37 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => 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)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_zle__antisym,axiom,
% 7.25/7.37 ! [V_w,V_z] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 7.25/7.37 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 7.25/7.37 => V_z = V_w ) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_zle__trans,axiom,
% 7.25/7.37 ! [V_k,V_j,V_i] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 7.25/7.37 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 7.25/7.37 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_zle__linear,axiom,
% 7.25/7.37 ! [V_w,V_z] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 7.25/7.37 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_zle__refl,axiom,
% 7.25/7.37 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I34_J,axiom,
% 7.25/7.37 ! [V_l_2,V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_less__eq__int__code_I16_J,axiom,
% 7.25/7.37 ! [V_k2_2,V_k1_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I19_J,axiom,
% 7.25/7.37 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I31_J,axiom,
% 7.25/7.37 ! [V_l_2,V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_less__eq__int__code_I13_J,axiom,
% 7.25/7.37 ! [V_k2_2,V_k1_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I24_J,axiom,
% 7.25/7.37 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_le__nat__number__of,axiom,
% 7.25/7.37 ! [V_v_H_2,V_v_2] :
% 7.25/7.37 ( 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))
% 7.25/7.37 <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
% 7.25/7.37 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 7.25/7.37 ! [V_z,V_y,V_x,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_crossproduct__noteq,axiom,
% 7.25/7.37 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 7.25/7.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 7.25/7.37 => ( ( V_a_2 != V_b_2
% 7.25/7.37 & V_c_2 != V_d_2 )
% 7.25/7.37 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 7.25/7.37 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 7.25/7.37 ! [V_b,V_m,V_a,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_crossproduct__eq,axiom,
% 7.25/7.37 ! [V_za_2,V_xa_2,V_ya_2,V_w_2,T_a] :
% 7.25/7.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 7.25/7.37 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2))
% 7.25/7.37 <=> ( V_w_2 = V_xa_2
% 7.25/7.37 | V_ya_2 = V_za_2 ) ) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_real__add__left__mono,axiom,
% 7.25/7.37 ! [V_z,V_y,V_x] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 7.25/7.37 => 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)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_real__add__mult__distrib,axiom,
% 7.25/7.37 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_right__distrib__number__of,axiom,
% 7.25/7.37 ! [V_c,V_b,V_v,T_b] :
% 7.25/7.37 ( ( class_Int_Onumber(T_b)
% 7.25/7.37 & class_Rings_Osemiring(T_b) )
% 7.25/7.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_left__distrib__number__of,axiom,
% 7.25/7.37 ! [V_v,V_b,V_a,T_b] :
% 7.25/7.37 ( ( class_Int_Onumber(T_b)
% 7.25/7.37 & class_Rings_Osemiring(T_b) )
% 7.25/7.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Oplus__class_Oplus(T_b,V_a,V_b)),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_add__numeral__0__right,axiom,
% 7.25/7.37 ! [V_a,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_add__numeral__0,axiom,
% 7.25/7.37 ! [V_a,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I22_J,axiom,
% 7.25/7.37 ! [V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I32_J,axiom,
% 7.25/7.37 ! [V_l_2,V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_less__eq__int__code_I14_J,axiom,
% 7.25/7.37 ! [V_k2_2,V_k1_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I21_J,axiom,
% 7.25/7.37 ! [V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I27_J,axiom,
% 7.25/7.37 ! [V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I30_J,axiom,
% 7.25/7.37 ! [V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin)
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I26_J,axiom,
% 7.25/7.37 ! [V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2))
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,V_k_2) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I20_J,axiom,
% 7.25/7.37 ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I23_J,axiom,
% 7.25/7.37 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_rel__simps_I28_J,axiom,
% 7.25/7.37 ! [V_k_2] :
% 7.25/7.37 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin)
% 7.25/7.37 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_add__special_I2_J,axiom,
% 7.25/7.37 ! [V_w,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => 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)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_add__special_I3_J,axiom,
% 7.25/7.37 ! [V_v,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => 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))) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_number__of__Bit1,axiom,
% 7.25/7.37 ! [V_w,T_a] :
% 7.25/7.37 ( class_Int_Onumber__ring(T_a)
% 7.25/7.37 => 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)) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 7.25/7.37 ! [V_m,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 7.25/7.37
% 7.25/7.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 7.25/7.37 ! [V_a,V_m,T_a] :
% 7.25/7.37 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.37 => c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 7.25/7.38 ! [V_m,V_a,T_a] :
% 7.25/7.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_double__number__of__Bit0,axiom,
% 7.25/7.38 ! [V_w,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_number__of__reorient,axiom,
% 7.25/7.38 ! [V_xa_2,V_w_2,T_a] :
% 7.25/7.38 ( class_Int_Onumber(T_a)
% 7.25/7.38 => ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = V_xa_2
% 7.25/7.38 <=> V_xa_2 = c_Int_Onumber__class_Onumber__of(T_a,V_w_2) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_eq__number__of,axiom,
% 7.25/7.38 ! [V_ya_2,V_xa_2,T_a] :
% 7.25/7.38 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 & class_Int_Oring__char__0(T_a) )
% 7.25/7.38 => ( c_Int_Onumber__class_Onumber__of(T_a,V_xa_2) = c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)
% 7.25/7.38 <=> V_xa_2 = V_ya_2 ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I51_J,axiom,
% 7.25/7.38 ! [V_l_2,V_k_2] :
% 7.25/7.38 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 7.25/7.38 <=> V_k_2 = V_l_2 ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__one__right,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_mult__Pls,axiom,
% 7.25/7.38 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I48_J,axiom,
% 7.25/7.38 ! [V_l_2,V_k_2] :
% 7.25/7.38 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 7.25/7.38 <=> V_k_2 = V_l_2 ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_mult__Bit0,axiom,
% 7.25/7.38 ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zpower__zpower,axiom,
% 7.25/7.38 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_mult__2__right,axiom,
% 7.25/7.38 ! [V_z,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => hAPP(hAPP(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) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_mult__2,axiom,
% 7.25/7.38 ! [V_z,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => hAPP(hAPP(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) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_one__add__one__is__two,axiom,
% 7.25/7.38 ! [T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => 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))) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 7.25/7.38 ! [V_n,V_m] :
% 7.25/7.38 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 7.25/7.38 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 7.25/7.38 | V_m = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zmult__eq__1__iff,axiom,
% 7.25/7.38 ! [V_n_2,V_m_2] :
% 7.25/7.38 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 7.25/7.38 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 7.25/7.38 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 7.25/7.38 | ( V_m_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
% 7.25/7.38 & V_n_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_le__number__of,axiom,
% 7.25/7.38 ! [V_ya_2,V_xa_2,T_a] :
% 7.25/7.38 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 & class_Rings_Olinordered__idom(T_a) )
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,V_ya_2) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_number__of__mult,axiom,
% 7.25/7.38 ! [V_w,V_v,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_arith__simps_I32_J,axiom,
% 7.25/7.38 ! [V_w,V_v,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_mult__number__of__left,axiom,
% 7.25/7.38 ! [V_z,V_w,V_v,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__commutes,axiom,
% 7.25/7.38 ! [V_n,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__mult__distrib,axiom,
% 7.25/7.38 ! [V_n,V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Ocomm__monoid__mult(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__one,axiom,
% 7.25/7.38 ! [V_n,T_a] :
% 7.25/7.38 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power2__sum,axiom,
% 7.25/7.38 ! [V_y,V_x,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I39_J,axiom,
% 7.25/7.38 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I46_J,axiom,
% 7.25/7.38 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 7.25/7.38
% 7.25/7.38 fof(fact_one__is__num__one,axiom,
% 7.25/7.38 c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I49_J,axiom,
% 7.25/7.38 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I50_J,axiom,
% 7.25/7.38 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Bit0__Pls,axiom,
% 7.25/7.38 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I38_J,axiom,
% 7.25/7.38 ! [V_l_2] :
% 7.25/7.38 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 7.25/7.38 <=> c_Int_OPls = V_l_2 ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I44_J,axiom,
% 7.25/7.38 ! [V_k_2] :
% 7.25/7.38 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 7.25/7.38 <=> V_k_2 = c_Int_OPls ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__mult,axiom,
% 7.25/7.38 ! [V_n,V_m,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__abs,axiom,
% 7.25/7.38 ! [V_n,V_a,T_a] :
% 7.25/7.38 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.38 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Bit1__Min,axiom,
% 7.25/7.38 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I43_J,axiom,
% 7.25/7.38 ! [V_l_2] :
% 7.25/7.38 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 7.25/7.38 <=> c_Int_OMin = V_l_2 ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I47_J,axiom,
% 7.25/7.38 ! [V_k_2] :
% 7.25/7.38 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 7.25/7.38 <=> V_k_2 = c_Int_OMin ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I40_J,axiom,
% 7.25/7.38 c_Int_OMin != c_Int_OPls ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I37_J,axiom,
% 7.25/7.38 c_Int_OPls != c_Int_OMin ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I42_J,axiom,
% 7.25/7.38 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_rel__simps_I45_J,axiom,
% 7.25/7.38 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sum__squared__expand,axiom,
% 7.25/7.38 ! [V_y,V_x] : hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 7.25/7.38 ~ ! [B_x,B_y] : v_z != c_Complex_Ocomplex_OComplex(B_x,B_y) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__triangle__ineq,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_order__refl,axiom,
% 7.25/7.38 ! [V_x,T_a] :
% 7.25/7.38 ( class_Orderings_Opreorder(T_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__m1__odd,axiom,
% 7.25/7.38 ! [V_n,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),c_Nat_OSuc(hAPP(hAPP(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) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__power__power,axiom,
% 7.25/7.38 ! [T_a] :
% 7.25/7.38 ( class_Power_Opower(T_a)
% 7.25/7.38 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power2__diff,axiom,
% 7.25/7.38 ! [V_y,V_x,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zero__le__even__power_H,axiom,
% 7.25/7.38 ! [V_n,V_a,T_a] :
% 7.25/7.38 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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))) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__ge__abs1,axiom,
% 7.25/7.38 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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))))))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__ge__abs2,axiom,
% 7.25/7.38 ! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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))))))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_sum__power2__ge__zero,axiom,
% 7.25/7.38 ! [V_y,V_x,T_a] :
% 7.25/7.38 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_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)))),hAPP(hAPP(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)))))) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_C_I2_J,axiom,
% 7.25/7.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_C_I1_J,axiom,
% 7.25/7.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_C_I4_J,axiom,
% 7.25/7.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_C_I3_J,axiom,
% 7.25/7.38 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_int__0__neq__1,axiom,
% 7.25/7.38 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_odd__nonzero,axiom,
% 7.25/7.38 ! [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) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_number__of__diff,axiom,
% 7.25/7.38 ! [V_w,V_v,T_a] :
% 7.25/7.38 ( class_Int_Onumber__ring(T_a)
% 7.25/7.38 => 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)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zmult__1,axiom,
% 7.25/7.38 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zmult__1__right,axiom,
% 7.25/7.38 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zmult__commute,axiom,
% 7.25/7.38 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__eq__if,axiom,
% 7.25/7.38 ! [V_n,V_m] :
% 7.25/7.38 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n )
% 7.25/7.38 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 => 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)) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zpower__zadd__distrib,axiom,
% 7.25/7.38 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zadd__zmult__distrib2,axiom,
% 7.25/7.38 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zdiff__zmult__distrib2,axiom,
% 7.25/7.38 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__Suc__0,axiom,
% 7.25/7.38 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zmult__assoc,axiom,
% 7.25/7.38 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zadd__zmult__distrib,axiom,
% 7.25/7.38 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zdiff__zmult__distrib,axiom,
% 7.25/7.38 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 7.25/7.38 ! [V_m_2,V_xa_2] :
% 7.25/7.38 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 7.25/7.38 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 | V_xa_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__zmult__eq__1,axiom,
% 7.25/7.38 ! [V_n,V_m] :
% 7.25/7.38 ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 7.25/7.38 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power_Opower_Opower__Suc,axiom,
% 7.25/7.38 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power_Opower_Opower__0,axiom,
% 7.25/7.38 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 7.25/7.38
% 7.25/7.38 fof(fact_complex__diff,axiom,
% 7.25/7.38 ! [V_d,V_c,V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zadd__assoc,axiom,
% 7.25/7.38 ! [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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Complex__eq__0,axiom,
% 7.25/7.38 ! [V_b_2,V_a_2] :
% 7.25/7.38 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 7.25/7.38 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.38 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_complex__mod__triangle__ineq2,axiom,
% 7.25/7.38 ! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zadd__left__commute,axiom,
% 7.25/7.38 ! [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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_le__iff__diff__le__0,axiom,
% 7.25/7.38 ! [V_b_2,V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zadd__commute,axiom,
% 7.25/7.38 ! [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) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zadd__0__right,axiom,
% 7.25/7.38 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zadd__0,axiom,
% 7.25/7.38 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 7.25/7.38
% 7.25/7.38 fof(fact_complex__zero__def,axiom,
% 7.25/7.38 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zero__reorient,axiom,
% 7.25/7.38 ! [V_xa_2,T_a] :
% 7.25/7.38 ( class_Groups_Ozero(T_a)
% 7.25/7.38 => ( c_Groups_Ozero__class_Ozero(T_a) = V_xa_2
% 7.25/7.38 <=> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_diff__0__right,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Ogroup__add(T_a)
% 7.25/7.38 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_diff__self,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Ogroup__add(T_a)
% 7.25/7.38 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_eq__iff__diff__eq__0,axiom,
% 7.25/7.38 ! [V_b_2,V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Oab__group__add(T_a)
% 7.25/7.38 => ( V_a_2 = V_b_2
% 7.25/7.38 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_right__minus__eq,axiom,
% 7.25/7.38 ! [V_b_2,V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Ogroup__add(T_a)
% 7.25/7.38 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.38 <=> V_a_2 = V_b_2 ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_diff__eq__diff__eq,axiom,
% 7.25/7.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Oab__group__add(T_a)
% 7.25/7.38 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 7.25/7.38 => ( V_a_2 = V_b_2
% 7.25/7.38 <=> V_c_2 = V_d_2 ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__eq__iff,axiom,
% 7.25/7.38 ! [V_ya_2,V_xa_2] :
% 7.25/7.38 ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2)
% 7.25/7.38 <=> V_xa_2 = V_ya_2 ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__eq__0__iff,axiom,
% 7.25/7.38 ! [V_xa_2] :
% 7.25/7.38 ( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.38 <=> V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__zero,axiom,
% 7.25/7.38 c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__ge__0__iff,axiom,
% 7.25/7.38 ! [V_ya_2] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__le__0__iff,axiom,
% 7.25/7.38 ! [V_xa_2] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__ge__zero,axiom,
% 7.25/7.38 ! [V_x] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__eq__zero__cancel,axiom,
% 7.25/7.38 ! [V_x] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.25/7.38 => ( c_NthRoot_Osqrt(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.38 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__le__eq__diff,axiom,
% 7.25/7.38 ! [V_ya_2,V_xa_2] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 7.25/7.38 ! [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) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__0__Suc,axiom,
% 7.25/7.38 ! [V_n,T_a] :
% 7.25/7.38 ( ( class_Power_Opower(T_a)
% 7.25/7.38 & class_Rings_Osemiring__0(T_a) )
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Suc__eq__plus1,axiom,
% 7.25/7.38 ! [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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Suc__eq__plus1__left,axiom,
% 7.25/7.38 ! [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) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_nat__one__le__power,axiom,
% 7.25/7.38 ! [V_n,V_i] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_diff__eq__diff__less__eq,axiom,
% 7.25/7.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add(T_a)
% 7.25/7.38 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__eq__0__iff,axiom,
% 7.25/7.38 ! [V_n_2,V_a_2,T_a] :
% 7.25/7.38 ( ( class_Power_Opower(T_a)
% 7.25/7.38 & class_Rings_Omult__zero(T_a)
% 7.25/7.38 & class_Rings_Ono__zero__divisors(T_a)
% 7.25/7.38 & class_Rings_Ozero__neq__one(T_a) )
% 7.25/7.38 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.38 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.38 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_diff__add__cancel,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Ogroup__add(T_a)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__diff__cancel,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Ogroup__add(T_a)
% 7.25/7.38 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__minus__commute,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__0__left,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Omonoid__add(T_a)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__0,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_double__zero__sym,axiom,
% 7.25/7.38 ! [V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Olinordered__ab__group__add(T_a)
% 7.25/7.38 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 7.25/7.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__0__right,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Omonoid__add(T_a)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add_Ocomm__neutral,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Ocomm__monoid__add(T_a)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_mult__eq__if,axiom,
% 7.25/7.38 ! [V_n,V_m] :
% 7.25/7.38 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 7.25/7.38 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__eq__0,axiom,
% 7.25/7.38 ! [V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__zero,axiom,
% 7.25/7.38 ! [T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_realpow__two__diff,axiom,
% 7.25/7.38 ! [V_y,V_x,T_a] :
% 7.25/7.38 ( class_Rings_Ocomm__ring__1(T_a)
% 7.25/7.38 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_complex__mod__triangle__sub,axiom,
% 7.25/7.38 ! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__inject__base,axiom,
% 7.25/7.38 ! [V_b,V_n,V_a,T_a] :
% 7.25/7.38 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.38 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.25/7.38 => V_a = V_b ) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__le__imp__le__base,axiom,
% 7.25/7.38 ! [V_b,V_n,V_a,T_a] :
% 7.25/7.38 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__le__mono,axiom,
% 7.25/7.38 ! [V_y,V_x] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__le__iff,axiom,
% 7.25/7.38 ! [V_ya_2,V_xa_2] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__0__left,axiom,
% 7.25/7.38 ! [V_n,T_a] :
% 7.25/7.38 ( ( class_Power_Opower(T_a)
% 7.25/7.38 & class_Rings_Osemiring__0(T_a) )
% 7.25/7.38 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 7.25/7.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_power__eq__if,axiom,
% 7.25/7.38 ! [V_p,V_m] :
% 7.25/7.38 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 7.25/7.38 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__mult,axiom,
% 7.25/7.38 ! [V_y,V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_NthRoot_Osqrt(V_y)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__power,axiom,
% 7.25/7.38 ! [V_k,V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_k)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),V_k) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__eq__1__iff,axiom,
% 7.25/7.38 ! [V_xa_2] :
% 7.25/7.38 ( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 7.25/7.38 <=> V_xa_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__one,axiom,
% 7.25/7.38 c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_diff__bin__simps_I1_J,axiom,
% 7.25/7.38 ! [V_k] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 7.25/7.38
% 7.25/7.38 fof(fact_diff__bin__simps_I7_J,axiom,
% 7.25/7.38 ! [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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Bit1__def,axiom,
% 7.25/7.38 ! [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) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__Pls__right,axiom,
% 7.25/7.38 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__Pls,axiom,
% 7.25/7.38 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__Bit0__Bit0,axiom,
% 7.25/7.38 ! [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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Bit0__def,axiom,
% 7.25/7.38 ! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zadd__left__mono,axiom,
% 7.25/7.38 ! [V_k,V_j,V_i] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 7.25/7.38 => 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)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_plus__numeral__code_I9_J,axiom,
% 7.25/7.38 ! [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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_double__eq__0__iff,axiom,
% 7.25/7.38 ! [V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Olinordered__ab__group__add(T_a)
% 7.25/7.38 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__0__iff,axiom,
% 7.25/7.38 ! [V_a_2,V_b_2,T_a] :
% 7.25/7.38 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 7.25/7.38 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
% 7.25/7.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.38 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_field__power__not__zero,axiom,
% 7.25/7.38 ! [V_n,V_a,T_a] :
% 7.25/7.38 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 7.25/7.38 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.38 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Pls__def,axiom,
% 7.25/7.38 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zero__le__zpower__abs,axiom,
% 7.25/7.38 ! [V_n,V_x] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__triangle__ineq2__sym,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__triangle__ineq2,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__triangle__ineq3,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__mult__left__cancel,axiom,
% 7.25/7.38 ! [V_b_2,V_a_2,V_c_2] :
% 7.25/7.38 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.38 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)
% 7.25/7.38 <=> V_a_2 = V_b_2 ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__mult__right__cancel,axiom,
% 7.25/7.38 ! [V_b_2,V_a_2,V_c_2] :
% 7.25/7.38 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.38 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)
% 7.25/7.38 <=> V_a_2 = V_b_2 ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__zero__not__eq__one,axiom,
% 7.25/7.38 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 7.25/7.38 ! [V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Olinordered__ab__group__add(T_a)
% 7.25/7.38 => ( 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))
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 7.25/7.38 ! [V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Olinordered__ab__group__add(T_a)
% 7.25/7.38 => ( 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))
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__nonneg__nonneg,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.25/7.38 => 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)) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__nonneg__eq__0__iff,axiom,
% 7.25/7.38 ! [V_ya_2,V_xa_2,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2)
% 7.25/7.38 => ( c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.38 <=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.38 & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__increasing,axiom,
% 7.25/7.38 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__increasing2,axiom,
% 7.25/7.38 ! [V_a,V_b,V_c,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__nonpos__nonpos,axiom,
% 7.25/7.38 ! [V_b,V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.38 => 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)) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__of__nonneg,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.38 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__le__zero__iff,axiom,
% 7.25/7.38 ! [V_a_2,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_abs__ge__zero,axiom,
% 7.25/7.38 ! [V_a,T_a] :
% 7.25/7.38 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_complex__add,axiom,
% 7.25/7.38 ! [V_d,V_c,V_b,V_a] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Suc3__eq__add__3,axiom,
% 7.25/7.38 ! [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) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__mult__self__sum__ge__zero,axiom,
% 7.25/7.38 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),V_y)))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_realpow__Suc__le__self,axiom,
% 7.25/7.38 ! [V_n,V_r,T_a] :
% 7.25/7.38 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 7.25/7.38 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r) ) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_numeral__3__eq__3,axiom,
% 7.25/7.38 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)))) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_numeral__1__eq__Suc__0,axiom,
% 7.25/7.38 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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Complex__eq__number__of,axiom,
% 7.25/7.38 ! [V_w_2,V_b_2,V_a_2] :
% 7.25/7.38 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w_2)
% 7.25/7.38 <=> ( V_a_2 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w_2)
% 7.25/7.38 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_Complex__eq__1,axiom,
% 7.25/7.38 ! [V_b_2,V_a_2] :
% 7.25/7.38 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
% 7.25/7.38 <=> ( V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 7.25/7.38 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_complex__one__def,axiom,
% 7.25/7.38 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__2__eq__Suc,axiom,
% 7.25/7.38 ! [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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_add__2__eq__Suc_H,axiom,
% 7.25/7.38 ! [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)) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__ge__one,axiom,
% 7.25/7.38 ! [V_x] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
% 7.25/7.38 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__le__1__iff,axiom,
% 7.25/7.38 ! [V_xa_2] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_real__sqrt__ge__1__iff,axiom,
% 7.25/7.38 ! [V_ya_2] :
% 7.25/7.38 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
% 7.25/7.38 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_mult__diff__mult,axiom,
% 7.25/7.38 ! [V_b,V_a,V_y,V_x,T_a] :
% 7.25/7.38 ( class_Rings_Oring(T_a)
% 7.25/7.38 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_left__diff__distrib__number__of,axiom,
% 7.25/7.38 ! [V_v,V_b,V_a,T_b] :
% 7.25/7.38 ( ( class_Int_Onumber(T_b)
% 7.25/7.38 & class_Rings_Oring(T_b) )
% 7.25/7.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a,V_b)),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Ominus__class_Ominus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 7.25/7.38
% 7.25/7.38 fof(fact_right__diff__distrib__number__of,axiom,
% 7.25/7.38 ! [V_c,V_b,V_v,T_b] :
% 7.25/7.38 ( ( class_Int_Onumber(T_b)
% 7.25/7.38 & class_Rings_Oring(T_b) )
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c)) = c_Groups_Ominus__class_Ominus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__number__of__diff1,axiom,
% 7.25/7.39 ! [V_c,V_w,V_v,T_a] :
% 7.25/7.39 ( class_Int_Onumber__ring(T_a)
% 7.25/7.39 => 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) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__diff__triangle__ineq,axiom,
% 7.25/7.39 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__triangle__ineq4,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__abs2,axiom,
% 7.25/7.39 ! [V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_numeral__2__eq__2,axiom,
% 7.25/7.39 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))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_semiring__norm_I115_J,axiom,
% 7.25/7.39 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))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_diff__bin__simps_I10_J,axiom,
% 7.25/7.39 ! [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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_diff__bin__simps_I9_J,axiom,
% 7.25/7.39 ! [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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_diff__bin__simps_I3_J,axiom,
% 7.25/7.39 ! [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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 7.25/7.39 ! [V_q,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 7.25/7.39 ! [V_q,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 7.25/7.39 ! [V_q,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power__Suc2,axiom,
% 7.25/7.39 ! [V_n,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power__Suc,axiom,
% 7.25/7.39 ! [V_n,V_a,T_a] :
% 7.25/7.39 ( class_Power_Opower(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 7.25/7.39 ! [V_q,V_p,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power__add,axiom,
% 7.25/7.39 ! [V_n,V_m,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__Bit1,axiom,
% 7.25/7.39 ! [V_l,V_k] : hAPP(hAPP(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(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),V_l) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__Bit1__Bit0,axiom,
% 7.25/7.39 ! [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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__Bit0__Bit1,axiom,
% 7.25/7.39 ! [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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_sum__squares__eq__zero__iff,axiom,
% 7.25/7.39 ! [V_ya_2,V_xa_2,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 <=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__scale__eq__noteq,axiom,
% 7.25/7.39 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 7.25/7.39 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 7.25/7.39 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 => ( ( V_a = V_b
% 7.25/7.39 & V_c != V_d )
% 7.25/7.39 => c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_complex__mult,axiom,
% 7.25/7.39 ! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power__mono,axiom,
% 7.25/7.39 ! [V_n,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__le__power,axiom,
% 7.25/7.39 ! [V_n,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_semiring__norm_I112_J,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_Int_Onumber__ring(T_a)
% 7.25/7.39 => c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_number__of__Pls,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_Int_Onumber__ring(T_a)
% 7.25/7.39 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 7.25/7.39 ! [V_x,T_a] :
% 7.25/7.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power__0,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Power_Opower(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_nat__number__of__Pls,axiom,
% 7.25/7.39 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_semiring__norm_I113_J,axiom,
% 7.25/7.39 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__is__num__zero,axiom,
% 7.25/7.39 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__two__squares__add__zero__iff,axiom,
% 7.25/7.39 ! [V_ya_2,V_xa_2] :
% 7.25/7.39 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.39 <=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.39 & V_ya_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__two__ge__zero,axiom,
% 7.25/7.39 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_complex__norm,axiom,
% 7.25/7.39 ! [V_y,V_x] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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)))))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_le__real__sqrt__sumsq,axiom,
% 7.25/7.39 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),V_y)))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__unique,axiom,
% 7.25/7.39 ! [V_x,V_y] :
% 7.25/7.39 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 7.25/7.39 => c_NthRoot_Osqrt(V_x) = V_y ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__pow2,axiom,
% 7.25/7.39 ! [V_x] :
% 7.25/7.39 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__pow2__iff,axiom,
% 7.25/7.39 ! [V_xa_2] :
% 7.25/7.39 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_xa_2)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_xa_2
% 7.25/7.39 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__squared__diff__one__factored,axiom,
% 7.25/7.39 ! [V_x,T_a] :
% 7.25/7.39 ( class_Rings_Oring__1(T_a)
% 7.25/7.39 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__sum__squares__eq__cancel2,axiom,
% 7.25/7.39 ! [V_y,V_x] :
% 7.25/7.39 ( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_y
% 7.25/7.39 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__sum__squares__eq__cancel,axiom,
% 7.25/7.39 ! [V_y,V_x] :
% 7.25/7.39 ( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_x
% 7.25/7.39 => V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_diff__bin__simps_I4_J,axiom,
% 7.25/7.39 ! [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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_diff__bin__simps_I6_J,axiom,
% 7.25/7.39 ! [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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_diff__bin__simps_I5_J,axiom,
% 7.25/7.39 ! [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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_sum__squares__le__zero__iff,axiom,
% 7.25/7.39 ! [V_ya_2,V_xa_2,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)),c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 <=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_sum__squares__ge__zero,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__ring(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_linorder__le__cases,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_Orderings_Olinorder(T_a)
% 7.25/7.39 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_le__funE,axiom,
% 7.25/7.39 ! [V_xa_2,V_g_2,V_f_2,T_a,T_b] :
% 7.25/7.39 ( class_Orderings_Oord(T_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_xt1_I6_J,axiom,
% 7.25/7.39 ! [V_z,V_x,V_y,T_a] :
% 7.25/7.39 ( class_Orderings_Oorder(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_xt1_I5_J,axiom,
% 7.25/7.39 ! [V_x,V_y,T_a] :
% 7.25/7.39 ( class_Orderings_Oorder(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.25/7.39 => V_x = V_y ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_order__trans,axiom,
% 7.25/7.39 ! [V_z,V_y,V_x,T_a] :
% 7.25/7.39 ( class_Orderings_Opreorder(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_order__antisym,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_Orderings_Oorder(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 7.25/7.39 => V_x = V_y ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_xt1_I4_J,axiom,
% 7.25/7.39 ! [V_c,V_a,V_b,T_a] :
% 7.25/7.39 ( class_Orderings_Oorder(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 7.25/7.39 => ( V_b = V_c
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_ord__le__eq__trans,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Orderings_Oord(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => ( V_b = V_c
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_xt1_I3_J,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Orderings_Oorder(T_a)
% 7.25/7.39 => ( V_a = V_b
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_ord__eq__le__trans,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Orderings_Oord(T_a)
% 7.25/7.39 => ( V_a = V_b
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_order__antisym__conv,axiom,
% 7.25/7.39 ! [V_xa_2,V_ya_2,T_a] :
% 7.25/7.39 ( class_Orderings_Oorder(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
% 7.25/7.39 <=> V_xa_2 = V_ya_2 ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_le__funD,axiom,
% 7.25/7.39 ! [V_xa_2,V_g_2,V_f_2,T_a,T_b] :
% 7.25/7.39 ( class_Orderings_Oord(T_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_order__eq__refl,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_Orderings_Opreorder(T_a)
% 7.25/7.39 => ( V_x = V_y
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_order__eq__iff,axiom,
% 7.25/7.39 ! [V_ya_2,V_xa_2,T_a] :
% 7.25/7.39 ( class_Orderings_Oorder(T_a)
% 7.25/7.39 => ( V_xa_2 = V_ya_2
% 7.25/7.39 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_linorder__linear,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_Orderings_Olinorder(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.25/7.39 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_le__fun__def,axiom,
% 7.25/7.39 ! [V_g_2,V_f_2,T_a,T_b] :
% 7.25/7.39 ( class_Orderings_Oord(T_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 7.25/7.39 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oab__semigroup__mult(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_number__of__Bit0,axiom,
% 7.25/7.39 ! [V_w,T_a] :
% 7.25/7.39 ( class_Int_Onumber__ring(T_a)
% 7.25/7.39 => 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)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oab__semigroup__add(T_a)
% 7.25/7.39 => 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)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__left__cancel,axiom,
% 7.25/7.39 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 7.25/7.39 ( class_Groups_Ocancel__semigroup__add(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
% 7.25/7.39 <=> V_b_2 = V_c_2 ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__right__cancel,axiom,
% 7.25/7.39 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 7.25/7.39 ( class_Groups_Ocancel__semigroup__add(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
% 7.25/7.39 <=> V_b_2 = V_c_2 ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__left__imp__eq,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Ocancel__semigroup__add(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 7.25/7.39 => V_b = V_c ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__imp__eq,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 7.25/7.39 => V_b = V_c ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__right__imp__eq,axiom,
% 7.25/7.39 ! [V_c,V_a,V_b,T_a] :
% 7.25/7.39 ( class_Groups_Ocancel__semigroup__add(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 7.25/7.39 => V_b = V_c ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__le__power__abs,axiom,
% 7.25/7.39 ! [V_n,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_one__reorient,axiom,
% 7.25/7.39 ! [V_xa_2,T_a] :
% 7.25/7.39 ( class_Groups_Oone(T_a)
% 7.25/7.39 => ( c_Groups_Oone__class_Oone(T_a) = V_xa_2
% 7.25/7.39 <=> V_xa_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_eq__number__of__0,axiom,
% 7.25/7.39 ! [V_v_2] :
% 7.25/7.39 ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.39 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_eq__0__number__of,axiom,
% 7.25/7.39 ! [V_v_2] :
% 7.25/7.39 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
% 7.25/7.39 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__sum__squares__ge__zero,axiom,
% 7.25/7.39 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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))))))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__idempotent,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.39 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 7.25/7.39 ! [V_n,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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))))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_complex_Oinject,axiom,
% 7.25/7.39 ! [V_real2_H_2,V_real1_H_2,V_real2_2,V_real1_2] :
% 7.25/7.39 ( c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)
% 7.25/7.39 <=> ( V_real1_2 = V_real1_H_2
% 7.25/7.39 & V_real2_2 = V_real2_H_2 ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 7.25/7.39 ! [V_ya,V_xa,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_ya),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_le__special_I3_J,axiom,
% 7.25/7.39 ! [V_xa_2,T_a] :
% 7.25/7.39 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.39 & class_Rings_Olinordered__idom(T_a) )
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,c_Int_OPls) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_le__special_I1_J,axiom,
% 7.25/7.39 ! [V_ya_2,T_a] :
% 7.25/7.39 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.39 & class_Rings_Olinordered__idom(T_a) )
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
% 7.25/7.39 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_ya_2) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power__decreasing,axiom,
% 7.25/7.39 ! [V_a,V_N,V_n,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_nat__mult__2,axiom,
% 7.25/7.39 ! [V_z] : hAPP(hAPP(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) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_nat__mult__2__right,axiom,
% 7.25/7.39 ! [V_z] : hAPP(hAPP(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) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_nat__1__add__1,axiom,
% 7.25/7.39 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))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__eq__power2,axiom,
% 7.25/7.39 ! [V_a_2,T_a] :
% 7.25/7.39 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 7.25/7.39 => ( hAPP(hAPP(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)
% 7.25/7.39 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__power2,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_Rings_Osemiring__1(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__abs,axiom,
% 7.25/7.39 ! [V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power2__eq__imp__eq,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.39 => ( hAPP(hAPP(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)))) = hAPP(hAPP(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))))
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.25/7.39 => V_x = V_y ) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power2__le__imp__le,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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)))))
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__le__power2,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_sum__power2__eq__zero__iff,axiom,
% 7.25/7.39 ! [V_ya_2,V_xa_2,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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)
% 7.25/7.39 <=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__sum__squares__triangle__ineq,axiom,
% 7.25/7.39 ! [V_d,V_b,V_c,V_a] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_b),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__sum__squares__ge2,axiom,
% 7.25/7.39 ! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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))))))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__sum__squares__ge1,axiom,
% 7.25/7.39 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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))))))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 7.25/7.39 ! [V_ya,V_xa,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_ya),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_ya),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_realpow__two__sum__zero__iff,axiom,
% 7.25/7.39 ! [V_ya_2,V_xa_2] :
% 7.25/7.39 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_ya_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)
% 7.25/7.39 <=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.39 & V_ya_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__le__imp__le__left,axiom,
% 7.25/7.39 ! [V_b,V_a,V_c,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 7.25/7.39 => ( 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))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__le__imp__le__right,axiom,
% 7.25/7.39 ! [V_b,V_c,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 7.25/7.39 => ( 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))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__mono,axiom,
% 7.25/7.39 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 7.25/7.39 => 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)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__left__mono,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => 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)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__right__mono,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => 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)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__le__cancel__left,axiom,
% 7.25/7.39 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 7.25/7.39 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_add__le__cancel__right,axiom,
% 7.25/7.39 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 7.25/7.39 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult_Ocomm__neutral,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Groups_Ocomm__monoid__mult(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__1__right,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__1,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Groups_Ocomm__monoid__mult(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__1__left,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__le__D1,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__ge__self,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__add__abs,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.25/7.39 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 7.25/7.39 ! [V_n,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(hAPP(hAPP(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))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power__odd__eq,axiom,
% 7.25/7.39 ! [V_n,V_a,T_a] :
% 7.25/7.39 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(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))))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_sum__power2__le__zero__iff,axiom,
% 7.25/7.39 ! [V_ya_2,V_xa_2,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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))
% 7.25/7.39 <=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 & V_ya_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_even__power__le__0__imp__0,axiom,
% 7.25/7.39 ! [V_k,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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))
% 7.25/7.39 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 7.25/7.39 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)))) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__diff__triangle__ineq,axiom,
% 7.25/7.39 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_convex__bound__le,axiom,
% 7.25/7.39 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__semiring__1(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__number__of,axiom,
% 7.25/7.39 ! [V_w,T_a] :
% 7.25/7.39 ( ( class_Int_Onumber__ring(T_a)
% 7.25/7.39 & class_RealVector_Oreal__normed__algebra__1(T_a) )
% 7.25/7.39 => c_RealVector_Onorm__class_Onorm(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__triangle__ineq3,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__power__ineq,axiom,
% 7.25/7.39 ! [V_n,V_x,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__triangle__ineq4,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_complex__i__not__one,axiom,
% 7.25/7.39 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_complex__i__not__number__of,axiom,
% 7.25/7.39 ! [V_w] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_complex__i__not__zero,axiom,
% 7.25/7.39 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_real__norm__def,axiom,
% 7.25/7.39 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_i__squared,axiom,
% 7.25/7.39 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_Complex__eq__i,axiom,
% 7.25/7.39 ! [V_ya_2,V_xa_2] :
% 7.25/7.39 ( c_Complex_Ocomplex_OComplex(V_xa_2,V_ya_2) = c_Complex_Oii
% 7.25/7.39 <=> ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.39 & V_ya_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_i__def,axiom,
% 7.25/7.39 c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 7.25/7.39 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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__zero__left,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Rings_Omult__zero(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult_Ozero__left,axiom,
% 7.25/7.39 ! [V_b,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__left_Ozero,axiom,
% 7.25/7.39 ! [V_y,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__zero__right,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Rings_Omult__zero(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult_Ozero__right,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__right_Ozero,axiom,
% 7.25/7.39 ! [V_x,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__eq__0__iff,axiom,
% 7.25/7.39 ! [V_b_2,V_a_2,T_a] :
% 7.25/7.39 ( class_Rings_Oring__no__zero__divisors(T_a)
% 7.25/7.39 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_no__zero__divisors,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Ono__zero__divisors(T_a)
% 7.25/7.39 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_divisors__zero,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Ono__zero__divisors(T_a)
% 7.25/7.39 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_one__neq__zero,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_Rings_Ozero__neq__one(T_a)
% 7.25/7.39 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__neq__one,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_Rings_Ozero__neq__one(T_a)
% 7.25/7.39 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult_Oadd__right,axiom,
% 7.25/7.39 ! [V_b_H,V_b,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__right_Oadd,axiom,
% 7.25/7.39 ! [V_y,V_x,V_xa,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_comm__semiring__class_Odistrib,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Ocomm__semiring(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult_Oadd__left,axiom,
% 7.25/7.39 ! [V_b,V_a_H,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__left_Oadd,axiom,
% 7.25/7.39 ! [V_ya,V_y,V_x,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_combine__common__factor,axiom,
% 7.25/7.39 ! [V_c,V_b,V_e,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Osemiring(T_a)
% 7.25/7.39 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult_Odiff__right,axiom,
% 7.25/7.39 ! [V_b_H,V_b,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__right_Odiff,axiom,
% 7.25/7.39 ! [V_y,V_x,V_xa,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult_Odiff__left,axiom,
% 7.25/7.39 ! [V_b,V_a_H,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__left_Odiff,axiom,
% 7.25/7.39 ! [V_ya,V_y,V_x,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__eq__zero,axiom,
% 7.25/7.39 ! [V_xa_2,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => ( c_RealVector_Onorm__class_Onorm(T_a,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 7.25/7.39 <=> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__zero,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__mult,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__mult__self,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__one,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__minus__commute,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__ge__zero,axiom,
% 7.25/7.39 ! [V_x,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 7.25/7.39 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)) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 7.25/7.39 ! [V_y,V_x] :
% 7.25/7.39 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 7.25/7.39 => 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)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 7.25/7.39 ! [V_y,V_x] :
% 7.25/7.39 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_abs__norm__cancel,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 7.25/7.39 ! [V_n,V_x] :
% 7.25/7.39 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power2__i,axiom,
% 7.25/7.39 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__le__square,axiom,
% 7.25/7.39 ! [V_a,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__ring(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__le__mult__iff,axiom,
% 7.25/7.39 ! [V_b_2,V_a_2,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))
% 7.25/7.39 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 7.25/7.39 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__le__0__iff,axiom,
% 7.25/7.39 ! [V_b_2,V_a_2,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 7.25/7.39 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__nonneg__nonneg,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__cancel__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__nonneg__nonpos,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__cancel__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__nonneg__nonpos2,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__cancel__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__nonpos__nonneg,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__cancel__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__nonpos__nonpos,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__ring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__right__mono,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__left__mono,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_comm__mult__left__mono,axiom,
% 7.25/7.39 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__comm__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__right__mono__neg,axiom,
% 7.25/7.39 ! [V_c,V_a,V_b,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__ring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__left__mono__neg,axiom,
% 7.25/7.39 ! [V_c,V_a,V_b,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__ring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__mono_H,axiom,
% 7.25/7.39 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__mono,axiom,
% 7.25/7.39 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__semiring(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_split__mult__pos__le,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__ring(T_a)
% 7.25/7.39 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 7.25/7.39 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_split__mult__neg__le,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_Rings_Oordered__cancel__semiring(T_a)
% 7.25/7.39 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 7.25/7.39 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.39 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_not__one__le__zero,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.39 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_zero__le__one,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__semidom(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult_Oprod__diff__prod,axiom,
% 7.25/7.39 ! [V_b,V_a,V_y,V_x,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.39 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_eq__add__iff2,axiom,
% 7.25/7.39 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 7.25/7.39 ( class_Rings_Oring(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
% 7.25/7.39 <=> V_c_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_eq__add__iff1,axiom,
% 7.25/7.39 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 7.25/7.39 ( class_Rings_Oring(T_a)
% 7.25/7.39 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
% 7.25/7.39 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2) = V_d_2 ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_power__eq__0__iff__number__of,axiom,
% 7.25/7.39 ! [V_w_2,V_a_2,T_a] :
% 7.25/7.39 ( ( class_Power_Opower(T_a)
% 7.25/7.39 & class_Rings_Omult__zero(T_a)
% 7.25/7.39 & class_Rings_Ono__zero__divisors(T_a)
% 7.25/7.39 & class_Rings_Ozero__neq__one(T_a) )
% 7.25/7.39 => ( hAPP(hAPP(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)
% 7.25/7.39 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.39 & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__le__zero__iff,axiom,
% 7.25/7.39 ! [V_xa_2,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 7.25/7.39 <=> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__diff__ineq,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__triangle__ineq2,axiom,
% 7.25/7.39 ! [V_b,V_a,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.39 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__mult,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 7.25/7.39 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__one,axiom,
% 7.25/7.39 ! [T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 7.25/7.39 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_norm__power,axiom,
% 7.25/7.39 ! [V_n,V_x,T_a] :
% 7.25/7.39 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 7.25/7.39 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ) ).
% 7.25/7.39
% 7.25/7.39 fof(fact_mult__right__le__one__le,axiom,
% 7.25/7.39 ! [V_y,V_x,T_a] :
% 7.25/7.39 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.25/7.39 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__left__le__one__le,axiom,
% 7.25/7.40 ! [V_y,V_x,T_a] :
% 7.25/7.40 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__add__iff2,axiom,
% 7.25/7.40 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 7.25/7.40 ( class_Rings_Oordered__ring(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__add__iff1,axiom,
% 7.25/7.40 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 7.25/7.40 ( class_Rings_Oordered__ring(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2),V_d_2) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_abs__mult__pos,axiom,
% 7.25/7.40 ! [V_y,V_x,T_a] :
% 7.25/7.40 ( class_Rings_Olinordered__idom(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.25/7.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_abs__eq__mult,axiom,
% 7.25/7.40 ! [V_b,V_a,T_a] :
% 7.25/7.40 ( class_Rings_Oordered__ring__abs(T_a)
% 7.25/7.40 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.25/7.40 | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
% 7.25/7.40 & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.25/7.40 | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 7.25/7.40 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_power__0__left__number__of,axiom,
% 7.25/7.40 ! [V_w,T_a] :
% 7.25/7.40 ( ( class_Power_Opower(T_a)
% 7.25/7.40 & class_Rings_Osemiring__0(T_a) )
% 7.25/7.40 => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a) )
% 7.25/7.40 & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_norm__mult__ineq,axiom,
% 7.25/7.40 ! [V_y,V_x,T_a] :
% 7.25/7.40 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 7.25/7.40 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)))) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_norm__triangle__ineq,axiom,
% 7.25/7.40 ! [V_y,V_x,T_a] :
% 7.25/7.40 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_realpow__num__eq__if,axiom,
% 7.25/7.40 ! [V_m,V_n,T_a] :
% 7.25/7.40 ( class_Power_Opower(T_a)
% 7.25/7.40 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 7.25/7.40 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_number__of1,axiom,
% 7.25/7.40 ! [V_n] :
% 7.25/7.40 ( 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))
% 7.25/7.40 => ( 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)))
% 7.25/7.40 & 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))) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_lemma__realpow__diff,axiom,
% 7.25/7.40 ! [V_y,V_n,V_p,T_a] :
% 7.25/7.40 ( class_Groups_Omonoid__mult(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
% 7.25/7.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le0,axiom,
% 7.25/7.40 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_norm__ratiotest__lemma,axiom,
% 7.25/7.40 ! [V_y,V_x,V_c,T_a] :
% 7.25/7.40 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
% 7.25/7.40 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_n__not__Suc__n,axiom,
% 7.25/7.40 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__n__not__n,axiom,
% 7.25/7.40 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat_Oinject,axiom,
% 7.25/7.40 ! [V_nat_H_2,V_nat_2] :
% 7.25/7.40 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 7.25/7.40 <=> V_nat_2 = V_nat_H_2 ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__inject,axiom,
% 7.25/7.40 ! [V_y,V_x] :
% 7.25/7.40 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 7.25/7.40 => V_x = V_y ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__add__commute,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__add__left__commute,axiom,
% 7.25/7.40 ! [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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__add__assoc,axiom,
% 7.25/7.40 ! [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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__add__left__cancel,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_k_2] :
% 7.25/7.40 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
% 7.25/7.40 <=> V_m_2 = V_n_2 ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__add__right__cancel,axiom,
% 7.25/7.40 ! [V_n_2,V_k_2,V_m_2] :
% 7.25/7.40 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
% 7.25/7.40 <=> V_m_2 = V_n_2 ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__refl,axiom,
% 7.25/7.40 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__le__linear,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.25/7.40 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_eq__imp__le,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( V_m = V_n
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__trans,axiom,
% 7.25/7.40 ! [V_k,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__antisym,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 7.25/7.40 => V_m = V_n ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__mult__commute,axiom,
% 7.25/7.40 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__mult__assoc,axiom,
% 7.25/7.40 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__commute,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Zero__not__Suc,axiom,
% 7.25/7.40 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat_Osimps_I2_J,axiom,
% 7.25/7.40 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__not__Zero,axiom,
% 7.25/7.40 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat_Osimps_I3_J,axiom,
% 7.25/7.40 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Zero__neq__Suc,axiom,
% 7.25/7.40 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__neq__Zero,axiom,
% 7.25/7.40 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_plus__nat_Oadd__0,axiom,
% 7.25/7.40 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Nat_Oadd__0__right,axiom,
% 7.25/7.40 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__is__0,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__eq__self__zero,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 7.25/7.40 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 7.25/7.40 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__0__eq,axiom,
% 7.25/7.40 ! [V_n_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 7.25/7.40 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__Suc__shift,axiom,
% 7.25/7.40 ! [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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__Suc,axiom,
% 7.25/7.40 ! [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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__Suc__right,axiom,
% 7.25/7.40 ! [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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__n__not__le__n,axiom,
% 7.25/7.40 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_not__less__eq__eq,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__Suc__eq,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 7.25/7.40 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 7.25/7.40 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__le__mono,axiom,
% 7.25/7.40 ! [V_m_2,V_n_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__SucI,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__SucE,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 7.25/7.40 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.25/7.40 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__leD,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__0,axiom,
% 7.25/7.40 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__0__right,axiom,
% 7.25/7.40 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__is__0,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__cancel1,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_k_2] :
% 7.25/7.40 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 7.25/7.40 <=> ( V_m_2 = V_n_2
% 7.25/7.40 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__cancel2,axiom,
% 7.25/7.40 ! [V_n_2,V_k_2,V_m_2] :
% 7.25/7.40 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
% 7.25/7.40 <=> ( V_m_2 = V_n_2
% 7.25/7.40 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diffs0__imp__equal,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 => V_m = V_n ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__self__eq__0,axiom,
% 7.25/7.40 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_minus__nat_Odiff__0,axiom,
% 7.25/7.40 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__0__eq__0,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__mult__cancel1,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_k_2] :
% 7.25/7.40 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
% 7.25/7.40 <=> V_m_2 = V_n_2 ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__add2,axiom,
% 7.25/7.40 ! [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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__add1,axiom,
% 7.25/7.40 ! [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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__Suc__ex__iff,axiom,
% 7.25/7.40 ! [V_l_2,V_k_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 7.25/7.40 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__iff__add,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 7.25/7.40 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__add__left__cancel__le,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_k_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_trans__le__add1,axiom,
% 7.25/7.40 ! [V_m,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_trans__le__add2,axiom,
% 7.25/7.40 ! [V_m,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__le__mono1,axiom,
% 7.25/7.40 ! [V_k,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__le__mono,axiom,
% 7.25/7.40 ! [V_l,V_k,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 7.25/7.40 => 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)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__leD2,axiom,
% 7.25/7.40 ! [V_n,V_k,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__leD1,axiom,
% 7.25/7.40 ! [V_n,V_k,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__leE,axiom,
% 7.25/7.40 ! [V_n,V_k,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 7.25/7.40 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.25/7.40 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__Suc__Suc,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__diff__diff,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__mult__distrib2,axiom,
% 7.25/7.40 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__mult__distrib,axiom,
% 7.25/7.40 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__square,axiom,
% 7.25/7.40 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__cube,axiom,
% 7.25/7.40 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__le__mono1,axiom,
% 7.25/7.40 ! [V_k,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__le__mono2,axiom,
% 7.25/7.40 ! [V_k,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__le__mono,axiom,
% 7.25/7.40 ! [V_l,V_k,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__add__inverse2,axiom,
% 7.25/7.40 ! [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 ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__add__inverse,axiom,
% 7.25/7.40 ! [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 ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__diff__left,axiom,
% 7.25/7.40 ! [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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__cancel,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__cancel2,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__le__self,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__le__mono2,axiom,
% 7.25/7.40 ! [V_l,V_n,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.25/7.40 => 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__le__mono,axiom,
% 7.25/7.40 ! [V_l,V_n,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.25/7.40 => 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__diff__cancel,axiom,
% 7.25/7.40 ! [V_n,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
% 7.25/7.40 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_eq__diff__iff,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_k_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 7.25/7.40 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
% 7.25/7.40 <=> V_m_2 = V_n_2 ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Nat_Odiff__diff__eq,axiom,
% 7.25/7.40 ! [V_n,V_m,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 7.25/7.40 => 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) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__diff__iff,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_k_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__mult__distrib2,axiom,
% 7.25/7.40 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__mult__distrib,axiom,
% 7.25/7.40 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__mult__1,axiom,
% 7.25/7.40 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__1__eq__mult__iff,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 7.25/7.40 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 7.25/7.40 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__mult__1__right,axiom,
% 7.25/7.40 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__mult__eq__1__iff,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 7.25/7.40 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 7.25/7.40 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__is__1,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 7.25/7.40 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 7.25/7.40 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 7.25/7.40 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_one__is__add,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
% 7.25/7.40 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 7.25/7.40 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 7.25/7.40 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__eq__1__iff,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 7.25/7.40 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 7.25/7.40 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_One__nat__def,axiom,
% 7.25/7.40 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__add__0,axiom,
% 7.25/7.40 ! [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) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__is__0__eq_H,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.25/7.40 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__is__0__eq,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__Suc__right,axiom,
% 7.25/7.40 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__Suc,axiom,
% 7.25/7.40 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__mult__le__cancel1,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_k_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Suc__diff__le,axiom,
% 7.25/7.40 ! [V_m,V_n] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 7.25/7.40 => 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__eq__self__implies__10,axiom,
% 7.25/7.40 ! [V_n,V_m] :
% 7.25/7.40 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 7.25/7.40 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 7.25/7.40 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__add__assoc2,axiom,
% 7.25/7.40 ! [V_i,V_j,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 7.25/7.40 => 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) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__diff__assoc2,axiom,
% 7.25/7.40 ! [V_i,V_j,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 7.25/7.40 => 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) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__add__assoc,axiom,
% 7.25/7.40 ! [V_i,V_j,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 7.25/7.40 => 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__imp__diff__is__add,axiom,
% 7.25/7.40 ! [V_k_2,V_j_2,V_i_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 7.25/7.40 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 7.25/7.40 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__add__diff__inverse2,axiom,
% 7.25/7.40 ! [V_m,V_n] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 7.25/7.40 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__diff__conv2,axiom,
% 7.25/7.40 ! [V_i_2,V_j_2,V_k_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
% 7.25/7.40 => ( 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))
% 7.25/7.40 <=> 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) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__diff__assoc,axiom,
% 7.25/7.40 ! [V_i,V_j,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 7.25/7.40 => 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) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__add__diff__inverse,axiom,
% 7.25/7.40 ! [V_m,V_n] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 7.25/7.40 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__add__diff,axiom,
% 7.25/7.40 ! [V_m,V_n,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 7.25/7.40 => 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_le__diff__conv,axiom,
% 7.25/7.40 ! [V_i_2,V_k_2,V_j_2] :
% 7.25/7.40 ( 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)
% 7.25/7.40 <=> 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__diff__right,axiom,
% 7.25/7.40 ! [V_i,V_j,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 7.25/7.40 => 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) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__Suc__1,axiom,
% 7.25/7.40 ! [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 ).
% 7.25/7.40
% 7.25/7.40 fof(fact_one__le__mult__iff,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
% 7.25/7.40 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
% 7.25/7.40 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_number__of2,axiom,
% 7.25/7.40 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)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__Suc__diff__eq2,axiom,
% 7.25/7.40 ! [V_m,V_j,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 7.25/7.40 => 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__Suc__diff__eq1,axiom,
% 7.25/7.40 ! [V_m,V_j,V_k] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 7.25/7.40 => 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)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_rabs__ratiotest__lemma,axiom,
% 7.25/7.40 ! [V_y,V_x,V_c] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
% 7.25/7.40 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_complex_Osize_I1_J,axiom,
% 7.25/7.40 ! [V_real2,V_real1] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__le__add__iff1,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__diff__add__eq1,axiom,
% 7.25/7.40 ! [V_n,V_m,V_u,V_i,V_j] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
% 7.25/7.40 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__eq__add__iff1,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
% 7.25/7.40 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
% 7.25/7.40 <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_n_2 ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_k_2] :
% 7.25/7.40 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 7.25/7.40 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.25/7.40 | V_m_2 = V_n_2 ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_left__add__mult__distrib,axiom,
% 7.25/7.40 ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__eq__add__iff2,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 7.25/7.40 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
% 7.25/7.40 <=> V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__diff__add__eq2,axiom,
% 7.25/7.40 ! [V_n,V_m,V_u,V_j,V_i] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 7.25/7.40 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nat__le__add__iff2,axiom,
% 7.25/7.40 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
% 7.25/7.40 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_cos__x__y__le__one,axiom,
% 7.25/7.40 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_complex_Osize_I2_J,axiom,
% 7.25/7.40 ! [V_real2,V_real1] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_complex_Osimps_I2_J,axiom,
% 7.25/7.40 ! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__zero__left,axiom,
% 7.25/7.40 ! [V_a,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide_Ozero,axiom,
% 7.25/7.40 ! [V_y,T_a] :
% 7.25/7.40 ( class_RealVector_Oreal__normed__field(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__zero,axiom,
% 7.25/7.40 ! [V_a,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__divide__distrib,axiom,
% 7.25/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide_Odiff,axiom,
% 7.25/7.40 ! [V_ya,V_y,V_x,T_a] :
% 7.25/7.40 ( class_RealVector_Oreal__normed__field(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya) = c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_times__divide__eq__right,axiom,
% 7.25/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_add__divide__distrib,axiom,
% 7.25/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide_Oadd,axiom,
% 7.25/7.40 ! [V_ya,V_y,V_x,T_a] :
% 7.25/7.40 ( class_RealVector_Oreal__normed__field(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__1,axiom,
% 7.25/7.40 ! [V_a,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_power__divide,axiom,
% 7.25/7.40 ! [V_n,V_b,V_a,T_a] :
% 7.25/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_real__divide__square__eq,axiom,
% 7.25/7.40 ! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_real__sqrt__divide,axiom,
% 7.25/7.40 ! [V_y,V_x] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nonzero__norm__divide,axiom,
% 7.25/7.40 ! [V_a,V_b,T_a] :
% 7.25/7.40 ( class_RealVector_Oreal__normed__field(T_a)
% 7.25/7.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_norm__divide,axiom,
% 7.25/7.40 ! [V_b,V_a,T_a] :
% 7.25/7.40 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 & class_RealVector_Oreal__normed__field(T_a) )
% 7.25/7.40 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_eq__divide__imp,axiom,
% 7.25/7.40 ! [V_b,V_a,V_c,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 7.25/7.40 => V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__eq__imp,axiom,
% 7.25/7.40 ! [V_a,V_b,V_c,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nonzero__divide__eq__eq,axiom,
% 7.25/7.40 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
% 7.25/7.40 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nonzero__eq__divide__eq,axiom,
% 7.25/7.40 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
% 7.25/7.40 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__self__if,axiom,
% 7.25/7.40 ! [V_a,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 7.25/7.40 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 7.25/7.40 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__self,axiom,
% 7.25/7.40 ! [V_a,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_right__inverse__eq,axiom,
% 7.25/7.40 ! [V_a_2,V_b_2,T_a] :
% 7.25/7.40 ( class_Rings_Odivision__ring(T_a)
% 7.25/7.40 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 7.25/7.40 <=> V_a_2 = V_b_2 ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_nonzero__power__divide,axiom,
% 7.25/7.40 ! [V_n,V_a,V_b,T_a] :
% 7.25/7.40 ( class_Fields_Ofield(T_a)
% 7.25/7.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_power__one__over,axiom,
% 7.25/7.40 ! [V_n,V_a,T_a] :
% 7.25/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)),V_n) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_real__0__le__divide__iff,axiom,
% 7.25/7.40 ! [V_ya_2,V_xa_2] :
% 7.25/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_xa_2,V_ya_2))
% 7.25/7.40 <=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 7.25/7.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2) )
% 7.25/7.40 & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)
% 7.25/7.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_ya_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__eq__eq__number__of1,axiom,
% 7.25/7.40 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 7.25/7.40 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 & class_Int_Onumber(T_a) )
% 7.25/7.40 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_a_2
% 7.25/7.40 <=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) )
% 7.25/7.40 & ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__eq__eq__number__of,axiom,
% 7.25/7.40 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 7.25/7.40 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 & class_Int_Onumber(T_a) )
% 7.25/7.40 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = c_Int_Onumber__class_Onumber__of(T_a,V_w_2)
% 7.25/7.40 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2) )
% 7.25/7.40 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_eq__divide__eq__number__of,axiom,
% 7.25/7.40 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 7.25/7.40 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 & class_Int_Onumber(T_a) )
% 7.25/7.40 => ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
% 7.25/7.40 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2) = V_b_2 )
% 7.25/7.40 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_eq__divide__eq__number__of1,axiom,
% 7.25/7.40 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 7.25/7.40 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 & class_Int_Onumber(T_a) )
% 7.25/7.40 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.25/7.40 <=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_b_2 )
% 7.25/7.40 & ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__Numeral0,axiom,
% 7.25/7.40 ! [V_x,T_a] :
% 7.25/7.40 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 & class_Int_Onumber__ring(T_a) )
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__Numeral1,axiom,
% 7.25/7.40 ! [V_x,T_a] :
% 7.25/7.40 ( ( class_Fields_Ofield(T_a)
% 7.25/7.40 & class_Int_Onumber__ring(T_a) )
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__numeral__1,axiom,
% 7.25/7.40 ! [V_a,T_a] :
% 7.25/7.40 ( ( class_Fields_Ofield(T_a)
% 7.25/7.40 & class_Int_Onumber__ring(T_a) )
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_power__diff,axiom,
% 7.25/7.40 ! [V_m,V_n,V_a,T_a] :
% 7.25/7.40 ( class_Fields_Ofield(T_a)
% 7.25/7.40 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 7.25/7.40 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_real__average__minus__second,axiom,
% 7.25/7.40 ! [V_a,V_b] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_real__average__minus__first,axiom,
% 7.25/7.40 ! [V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_b),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_a),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_real__sum__of__halves,axiom,
% 7.25/7.40 ! [V_x] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x ).
% 7.25/7.40
% 7.25/7.40 fof(fact_Deriv_Oadd__diff__add,axiom,
% 7.25/7.40 ! [V_d,V_b,V_c,V_a,T_a] :
% 7.25/7.40 ( class_Groups_Oab__group__add(T_a)
% 7.25/7.40 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_lemma__MVT,axiom,
% 7.25/7.40 ! [V_b_2,V_a_2,V_f_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_b_2),hAPP(V_f_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_a_2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_b_2),hAPP(V_f_2,V_a_2)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_b_2)) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_DERIV__mult__lemma,axiom,
% 7.25/7.40 ! [V_h,V_d,V_c,V_b,V_a,T_a] :
% 7.25/7.40 ( class_RealVector_Oreal__field(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)),V_h) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d),V_h)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h)),V_d)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_eq__divide__2__times__iff,axiom,
% 7.25/7.40 ! [V_za_2,V_ya_2,V_xa_2] :
% 7.25/7.40 ( V_xa_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_ya_2,hAPP(hAPP(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_za_2))
% 7.25/7.40 <=> hAPP(hAPP(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_xa_2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_ya_2,V_za_2) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__divide__eq__iff,axiom,
% 7.25/7.40 ! [V_y,V_x,V_z,T_a] :
% 7.25/7.40 ( class_Fields_Ofield(T_a)
% 7.25/7.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__diff__eq__iff,axiom,
% 7.25/7.40 ! [V_y,V_x,V_z,T_a] :
% 7.25/7.40 ( class_Fields_Ofield(T_a)
% 7.25/7.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_diff__frac__eq,axiom,
% 7.25/7.40 ! [V_w,V_x,V_z,V_y,T_a] :
% 7.25/7.40 ( class_Fields_Ofield(T_a)
% 7.25/7.40 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_times__divide__times__eq,axiom,
% 7.25/7.40 ! [V_w,V_z,V_y,V_x,T_a] :
% 7.25/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_abs__divide,axiom,
% 7.25/7.40 ! [V_b,V_a,T_a] :
% 7.25/7.40 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.25/7.40 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_zero__le__divide__iff,axiom,
% 7.25/7.40 ! [V_b_2,V_a_2,T_a] :
% 7.25/7.40 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
% 7.25/7.40 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 7.25/7.40 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 7.25/7.40 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.40 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__le__0__iff,axiom,
% 7.25/7.40 ! [V_b_2,V_a_2,T_a] :
% 7.25/7.40 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.40 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 7.25/7.40 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 7.25/7.40 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.40 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__right__mono,axiom,
% 7.25/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.40 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__right__mono__neg,axiom,
% 7.25/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.25/7.40 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.25/7.40 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 7.25/7.40 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_eq__divide__eq,axiom,
% 7.25/7.40 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 7.25/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
% 7.25/7.40 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 )
% 7.25/7.40 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_divide__eq__eq,axiom,
% 7.25/7.40 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 7.25/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = V_a_2
% 7.25/7.40 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) )
% 7.25/7.40 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__divide__mult__cancel__right,axiom,
% 7.25/7.40 ! [V_b,V_a,V_c,T_a] :
% 7.25/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_mult__divide__mult__cancel__left,axiom,
% 7.25/7.40 ! [V_b,V_a,V_c,T_a] :
% 7.25/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.25/7.40 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 7.25/7.40 => c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 7.25/7.40
% 7.25/7.40 fof(fact_frac__eq__eq,axiom,
% 7.29/7.40 ! [V_w_2,V_xa_2,V_za_2,V_ya_2,T_a] :
% 7.29/7.40 ( class_Fields_Ofield(T_a)
% 7.29/7.40 => ( V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => ( V_za_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => ( c_Rings_Oinverse__class_Odivide(T_a,V_xa_2,V_ya_2) = c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_za_2)
% 7.29/7.40 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_za_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2) ) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_nonzero__abs__divide,axiom,
% 7.29/7.40 ! [V_a,V_b,T_a] :
% 7.29/7.40 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__frac__eq,axiom,
% 7.29/7.40 ! [V_w,V_x,V_z,V_y,T_a] :
% 7.29/7.40 ( class_Fields_Ofield(T_a)
% 7.29/7.40 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_divide__add__eq__iff,axiom,
% 7.29/7.40 ! [V_y,V_x,V_z,T_a] :
% 7.29/7.40 ( class_Fields_Ofield(T_a)
% 7.29/7.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__frac__num,axiom,
% 7.29/7.40 ! [V_z,V_x,V_y,T_a] :
% 7.29/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.29/7.40 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__divide__eq__iff,axiom,
% 7.29/7.40 ! [V_y,V_x,V_z,T_a] :
% 7.29/7.40 ( class_Fields_Ofield(T_a)
% 7.29/7.40 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__num__frac,axiom,
% 7.29/7.40 ! [V_x,V_z,V_y,T_a] :
% 7.29/7.40 ( class_Fields_Ofield__inverse__zero(T_a)
% 7.29/7.40 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.40 => c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_arctan__half,axiom,
% 7.29/7.40 ! [V_x] : c_Transcendental_Oarctan(V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(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)))))))))) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_lemma__sqrt__hcomplex__capprox,axiom,
% 7.29/7.40 ! [V_y,V_x,V_u] :
% 7.29/7.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_real__sqrt__sum__squares__less,axiom,
% 7.29/7.40 ! [V_y,V_u,V_x] :
% 7.29/7.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 7.29/7.40 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__strict__left__mono__neg,axiom,
% 7.29/7.40 ! [V_c,V_a,V_b,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__strict__right__mono__neg,axiom,
% 7.29/7.40 ! [V_c,V_a,V_b,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_comm__mult__strict__left__mono,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__strict__left__mono,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__strict__right__mono,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__neg__neg,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__neg__pos,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__less__cancel__left__neg,axiom,
% 7.29/7.40 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_zero__less__mult__pos2,axiom,
% 7.29/7.40 ! [V_a,V_b,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_zero__less__mult__pos,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__pos__neg2,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__pos__neg,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__pos__pos,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__less__cancel__left__pos,axiom,
% 7.29/7.40 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__less__cancel__left__disj,axiom,
% 7.29/7.40 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 7.29/7.40 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.40 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 7.29/7.40 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_mult__less__cancel__right__disj,axiom,
% 7.29/7.40 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
% 7.29/7.40 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.40 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 7.29/7.40 | ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_not__square__less__zero,axiom,
% 7.29/7.40 ! [V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__ring(T_a)
% 7.29/7.40 => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__neg__neg,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 => 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)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__pos__pos,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.29/7.40 => 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)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 7.29/7.40 ! [V_a_2,T_a] :
% 7.29/7.40 ( class_Groups_Olinordered__ab__group__add(T_a)
% 7.29/7.40 => ( 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))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 7.29/7.40 ! [V_a_2,T_a] :
% 7.29/7.40 ( class_Groups_Olinordered__ab__group__add(T_a)
% 7.29/7.40 => ( 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))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_even__less__0__iff,axiom,
% 7.29/7.40 ! [V_a_2,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.40 => ( 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))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_pos__add__strict,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_arctan__zero__zero,axiom,
% 7.29/7.40 c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_arctan__monotone_H,axiom,
% 7.29/7.40 ! [V_y,V_x] :
% 7.29/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 7.29/7.40 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_arctan__monotone,axiom,
% 7.29/7.40 ! [V_y,V_x] :
% 7.29/7.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_real__sqrt__less__mono,axiom,
% 7.29/7.40 ! [V_y,V_x] :
% 7.29/7.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y)) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_real__sqrt__less__iff,axiom,
% 7.29/7.40 ! [V_ya_2,V_xa_2] :
% 7.29/7.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_less__special_I3_J,axiom,
% 7.29/7.40 ! [V_xa_2,T_a] :
% 7.29/7.40 ( ( class_Int_Onumber__ring(T_a)
% 7.29/7.40 & class_Rings_Olinordered__idom(T_a) )
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OPls) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_less__special_I1_J,axiom,
% 7.29/7.40 ! [V_ya_2,T_a] :
% 7.29/7.40 ( ( class_Int_Onumber__ring(T_a)
% 7.29/7.40 & class_Rings_Olinordered__idom(T_a) )
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_ya_2) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_power__strict__decreasing,axiom,
% 7.29/7.40 ! [V_a,V_N,V_n,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_one__less__power,axiom,
% 7.29/7.40 ! [V_n,V_a,T_a] :
% 7.29/7.40 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_order__less__irrefl,axiom,
% 7.29/7.40 ! [V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Opreorder(T_a)
% 7.29/7.40 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_linorder__neq__iff,axiom,
% 7.29/7.40 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.40 ( class_Orderings_Olinorder(T_a)
% 7.29/7.40 => ( V_xa_2 != V_ya_2
% 7.29/7.40 <=> ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.40 | c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_not__less__iff__gr__or__eq,axiom,
% 7.29/7.40 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.40 ( class_Orderings_Olinorder(T_a)
% 7.29/7.40 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.40 <=> ( c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
% 7.29/7.40 | V_xa_2 = V_ya_2 ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_linorder__less__linear,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Olinorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 | V_x = V_y
% 7.29/7.40 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_linorder__antisym__conv3,axiom,
% 7.29/7.40 ! [V_xa_2,V_ya_2,T_a] :
% 7.29/7.40 ( class_Orderings_Olinorder(T_a)
% 7.29/7.40 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
% 7.29/7.40 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.40 <=> V_xa_2 = V_ya_2 ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_linorder__neqE,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Olinorder(T_a)
% 7.29/7.40 => ( V_x != V_y
% 7.29/7.40 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_less__imp__neq,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Oorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => V_x != V_y ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_order__less__not__sym,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Opreorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_order__less__imp__not__less,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Opreorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_order__less__imp__not__eq,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Oorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => V_x != V_y ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_order__less__imp__not__eq2,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Oorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => V_y != V_x ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_order__less__asym_H,axiom,
% 7.29/7.40 ! [V_b,V_a,T_a] :
% 7.29/7.40 ( class_Orderings_Opreorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.40 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_xt1_I9_J,axiom,
% 7.29/7.40 ! [V_a,V_b,T_a] :
% 7.29/7.40 ( class_Orderings_Oorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 7.29/7.40 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_ord__eq__less__trans,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.40 ( class_Orderings_Oord(T_a)
% 7.29/7.40 => ( V_a = V_b
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_xt1_I1_J,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.40 ( class_Orderings_Oorder(T_a)
% 7.29/7.40 => ( V_a = V_b
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_ord__less__eq__trans,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.40 ( class_Orderings_Oord(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.40 => ( V_b = V_c
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_xt1_I2_J,axiom,
% 7.29/7.40 ! [V_c,V_a,V_b,T_a] :
% 7.29/7.40 ( class_Orderings_Oorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 7.29/7.40 => ( V_b = V_c
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_order__less__trans,axiom,
% 7.29/7.40 ! [V_z,V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Opreorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_xt1_I10_J,axiom,
% 7.29/7.40 ! [V_z,V_x,V_y,T_a] :
% 7.29/7.40 ( class_Orderings_Oorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_order__less__asym,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Opreorder(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_linorder__cases,axiom,
% 7.29/7.40 ! [V_y,V_x,T_a] :
% 7.29/7.40 ( class_Orderings_Olinorder(T_a)
% 7.29/7.40 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.40 => ( V_x != V_y
% 7.29/7.40 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_less__eq__real__def,axiom,
% 7.29/7.40 ! [V_ya_2,V_xa_2] :
% 7.29/7.40 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
% 7.29/7.40 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)
% 7.29/7.40 | V_xa_2 = V_ya_2 ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_real__less__def,axiom,
% 7.29/7.40 ! [V_ya_2,V_xa_2] :
% 7.29/7.40 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)
% 7.29/7.40 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
% 7.29/7.40 & V_xa_2 != V_ya_2 ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_diff__eq__diff__less,axiom,
% 7.29/7.40 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 7.29/7.40 ( class_Groups_Oordered__ab__group__add(T_a)
% 7.29/7.40 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) ) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__less__cancel__right,axiom,
% 7.29/7.40 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 7.29/7.40 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__less__cancel__left,axiom,
% 7.29/7.40 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.40 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 7.29/7.40 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__strict__right__mono,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.40 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 7.29/7.40 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.40 => 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)) ) ) ).
% 7.29/7.40
% 7.29/7.40 fof(fact_add__strict__left__mono,axiom,
% 7.29/7.40 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => 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)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__strict__mono,axiom,
% 7.29/7.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 7.29/7.41 => 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)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__less__imp__less__right,axiom,
% 7.29/7.41 ! [V_b,V_c,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 7.29/7.41 => ( 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))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__less__imp__less__left,axiom,
% 7.29/7.41 ! [V_b,V_a,V_c,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 7.29/7.41 => ( 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))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_xt1_I8_J,axiom,
% 7.29/7.41 ! [V_z,V_x,V_y,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_order__le__less__trans,axiom,
% 7.29/7.41 ! [V_z,V_y,V_x,T_a] :
% 7.29/7.41 ( class_Orderings_Opreorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_xt1_I7_J,axiom,
% 7.29/7.41 ! [V_z,V_x,V_y,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_order__less__le__trans,axiom,
% 7.29/7.41 ! [V_z,V_y,V_x,T_a] :
% 7.29/7.41 ( class_Orderings_Opreorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_xt1_I11_J,axiom,
% 7.29/7.41 ! [V_a,V_b,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 7.29/7.41 => ( V_a != V_b
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_order__le__neq__trans,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.29/7.41 => ( V_a != V_b
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_order__le__imp__less__or__eq,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.41 | V_x = V_y ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_linorder__antisym__conv2,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Orderings_Olinorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 <=> V_xa_2 = V_ya_2 ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_order__less__imp__le,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Orderings_Opreorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_leD,axiom,
% 7.29/7.41 ! [V_x,V_y,T_a] :
% 7.29/7.41 ( class_Orderings_Olinorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 7.29/7.41 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_xt1_I12_J,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( V_a != V_b
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_order__neq__le__trans,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( V_a != V_b
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_linorder__antisym__conv1,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Orderings_Olinorder(T_a)
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 <=> V_xa_2 = V_ya_2 ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__leE,axiom,
% 7.29/7.41 ! [V_x,V_y,T_a] :
% 7.29/7.41 ( class_Orderings_Olinorder(T_a)
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_leI,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Orderings_Olinorder(T_a)
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_order__le__less,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 | V_xa_2 = V_ya_2 ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__le__not__le,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Orderings_Opreorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_order__less__le,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Orderings_Oorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 & V_xa_2 != V_ya_2 ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_linorder__le__less__linear,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Orderings_Olinorder(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.29/7.41 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_linorder__not__le,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Orderings_Olinorder(T_a)
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_linorder__not__less,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Orderings_Olinorder(T_a)
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__strict__increasing,axiom,
% 7.29/7.41 ! [V_a,V_N,V_n,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__less__imp__less__exp,axiom,
% 7.29/7.41 ! [V_n,V_m,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__strict__increasing__iff,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,V_b_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_linorder__neqE__linordered__idom,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.41 => ( V_x != V_y
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__number__of,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( ( class_Int_Onumber__ring(T_a)
% 7.29/7.41 & class_Rings_Olinordered__idom(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__special_I4_J,axiom,
% 7.29/7.41 ! [V_xa_2,T_a] :
% 7.29/7.41 ( ( class_Int_Onumber__ring(T_a)
% 7.29/7.41 & class_Rings_Olinordered__idom(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__special_I2_J,axiom,
% 7.29/7.41 ! [V_ya_2,T_a] :
% 7.29/7.41 ( ( class_Int_Onumber__ring(T_a)
% 7.29/7.41 & class_Rings_Olinordered__idom(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__strict__mono,axiom,
% 7.29/7.41 ! [V_n,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__le__less__mono,axiom,
% 7.29/7.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 7.29/7.41 => 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)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__less__le__mono,axiom,
% 7.29/7.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 7.29/7.41 => 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)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_le__number__of__eq__not__less,axiom,
% 7.29/7.41 ! [V_w_2,V_v_2,T_a] :
% 7.29/7.41 ( ( class_Int_Onumber(T_a)
% 7.29/7.41 & class_Orderings_Olinorder(T_a) )
% 7.29/7.41 => ( 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))
% 7.29/7.41 <=> ~ 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)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zero__less__one,axiom,
% 7.29/7.41 ! [T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__one__less__zero,axiom,
% 7.29/7.41 ! [T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__iff__diff__less__0,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__ab__group__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__1__mult,axiom,
% 7.29/7.41 ! [V_n,V_m,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zero__less__power,axiom,
% 7.29/7.41 ! [V_n,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__add__one,axiom,
% 7.29/7.41 ! [V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => 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))) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__strict__right__mono__neg,axiom,
% 7.29/7.41 ! [V_c,V_a,V_b,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__strict__right__mono,axiom,
% 7.29/7.41 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__neg__neg,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__neg__pos,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__pos__neg,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__pos__pos,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__less__0__iff,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 7.29/7.41 & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 7.29/7.41 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zero__less__divide__iff,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 7.29/7.41 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 7.29/7.41 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__inject__exp,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
% 7.29/7.41 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
% 7.29/7.41 <=> V_m_2 = V_n_2 ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_abs__not__less__zero,axiom,
% 7.29/7.41 ! [V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.29/7.41 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zero__less__abs__iff,axiom,
% 7.29/7.41 ! [V_a_2,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
% 7.29/7.41 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_abs__of__pos,axiom,
% 7.29/7.41 ! [V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_abs__mult__less,axiom,
% 7.29/7.41 ! [V_d,V_b,V_c,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__mult__less__mono2,axiom,
% 7.29/7.41 ! [V_y,V_x,V_z] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__mult__order,axiom,
% 7.29/7.41 ! [V_y,V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__mult__less__iff1,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,V_za_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_za_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__real__square__gt__zero,axiom,
% 7.29/7.41 ! [V_xa_2] :
% 7.29/7.41 ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2))
% 7.29/7.41 <=> V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_norm__not__less__zero,axiom,
% 7.29/7.41 ! [V_x,T_a] :
% 7.29/7.41 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.29/7.41 => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__gt__0__iff,axiom,
% 7.29/7.41 ! [V_ya_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__lt__0__iff,axiom,
% 7.29/7.41 ! [V_xa_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__not__eq__zero,axiom,
% 7.29/7.41 ! [V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.29/7.41 => c_NthRoot_Osqrt(V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__gt__zero,axiom,
% 7.29/7.41 ! [V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__lt__1__iff,axiom,
% 7.29/7.41 ! [V_xa_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__gt__1__iff,axiom,
% 7.29/7.41 ! [V_ya_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__le__cancel__left__pos,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__le__cancel__left__neg,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__strict__mono,axiom,
% 7.29/7.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__strict__mono_H,axiom,
% 7.29/7.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__less__le__imp__less,axiom,
% 7.29/7.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__le__less__imp__less,axiom,
% 7.29/7.41 ! [V_d,V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__right__less__imp__less,axiom,
% 7.29/7.41 ! [V_b,V_c,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__less__imp__less__right,axiom,
% 7.29/7.41 ! [V_b,V_c,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__left__less__imp__less,axiom,
% 7.29/7.41 ! [V_b,V_a,V_c,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__less__imp__less__left,axiom,
% 7.29/7.41 ! [V_b,V_a,V_c,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__right__le__imp__le,axiom,
% 7.29/7.41 ! [V_b,V_c,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__left__le__imp__le,axiom,
% 7.29/7.41 ! [V_b,V_a,V_c,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__nonpos__neg,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => 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)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__neg__nonpos,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => 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)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__strict__increasing2,axiom,
% 7.29/7.41 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__strict__increasing,axiom,
% 7.29/7.41 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__nonneg__pos,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.29/7.41 => 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)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__pos__nonneg,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.29/7.41 => 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)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__sum__squares__lt__zero,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__ring(T_a)
% 7.29/7.41 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_sum__squares__gt__zero__iff,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__ring__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)))
% 7.29/7.41 <=> ( V_xa_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.41 | V_ya_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__less__imp__less__base,axiom,
% 7.29/7.41 ! [V_b,V_n,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zero__less__two,axiom,
% 7.29/7.41 ! [T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => 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))) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__nonneg__pos,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__nonneg__neg,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_frac__less2,axiom,
% 7.29/7.41 ! [V_z,V_w,V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_frac__less,axiom,
% 7.29/7.41 ! [V_z,V_w,V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_frac__le,axiom,
% 7.29/7.41 ! [V_z,V_w,V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__nonpos__pos,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__nonpos__neg,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__add__iff2,axiom,
% 7.29/7.41 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 7.29/7.41 ( class_Rings_Oordered__ring(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__add__iff1,axiom,
% 7.29/7.41 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 7.29/7.41 ( class_Rings_Oordered__ring(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2),V_d_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__divide__eq,axiom,
% 7.29/7.41 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__less__eq,axiom,
% 7.29/7.41 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_pos__less__divide__eq,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_pos__divide__less__eq,axiom,
% 7.29/7.41 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__imp__div__pos__less,axiom,
% 7.29/7.41 ! [V_z,V_x,V_y,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__imp__less__div__pos,axiom,
% 7.29/7.41 ! [V_x,V_z,V_y,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_neg__less__divide__eq,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_neg__divide__less__eq,axiom,
% 7.29/7.41 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__strict__left__mono,axiom,
% 7.29/7.41 ! [V_c,V_a,V_b,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__strict__left__mono__neg,axiom,
% 7.29/7.41 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__gt1__lemma,axiom,
% 7.29/7.41 ! [V_n,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__less__power__Suc,axiom,
% 7.29/7.41 ! [V_n,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__half__sum,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_gt__half__sum,axiom,
% 7.29/7.41 ! [V_b,V_a,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__gt1,axiom,
% 7.29/7.41 ! [V_n,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_abs__diff__less__iff,axiom,
% 7.29/7.41 ! [V_r_2,V_a_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_xa_2,V_a_2)),V_r_2)
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_r_2),V_xa_2)
% 7.29/7.41 & c_Orderings_Oord__class_Oless(T_a,V_xa_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_r_2)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_abs__div__pos,axiom,
% 7.29/7.41 ! [V_x,V_y,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zero__less__norm__iff,axiom,
% 7.29/7.41 ! [V_xa_2,T_a] :
% 7.29/7.41 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_xa_2))
% 7.29/7.41 <=> V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__mult__le__cancel__iff1,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,V_za_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_za_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__mult__le__cancel__iff2,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,V_za_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_ya_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_norm__mult__less,axiom,
% 7.29/7.41 ! [V_s,V_y,V_r,V_x,T_a] :
% 7.29/7.41 ( class_RealVector_Oreal__normed__algebra(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_norm__add__less,axiom,
% 7.29/7.41 ! [V_s,V_y,V_r,V_x,T_a] :
% 7.29/7.41 ( class_RealVector_Oreal__normed__vector(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_abs__add__one__not__less__self,axiom,
% 7.29/7.41 ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_arctan__add,axiom,
% 7.29/7.41 ! [V_y,V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 7.29/7.41 => c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) = c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)))) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__left__mono__neg,axiom,
% 7.29/7.41 ! [V_c,V_b,V_a,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__left__mono,axiom,
% 7.29/7.41 ! [V_c,V_a,V_b,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_neg__divide__le__eq,axiom,
% 7.29/7.41 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_neg__le__divide__eq,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__imp__le__div__pos,axiom,
% 7.29/7.41 ! [V_x,V_z,V_y,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__imp__div__pos__le,axiom,
% 7.29/7.41 ! [V_z,V_x,V_y,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_pos__divide__le__eq,axiom,
% 7.29/7.41 ! [V_a_2,V_b_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_pos__le__divide__eq,axiom,
% 7.29/7.41 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__le__eq,axiom,
% 7.29/7.41 ! [V_a_2,V_c_2,V_b_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_le__divide__eq,axiom,
% 7.29/7.41 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 7.29/7.41 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__Suc__less,axiom,
% 7.29/7.41 ! [V_n,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__less__eq__number__of1,axiom,
% 7.29/7.41 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_a_2)
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__less__eq__number__of,axiom,
% 7.29/7.41 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2)) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__divide__eq__number__of,axiom,
% 7.29/7.41 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2)) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__divide__eq__number__of1,axiom,
% 7.29/7.41 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__Suc__less__one,axiom,
% 7.29/7.41 ! [V_n,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__increasing__iff,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,V_b_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_xa_2,V_ya_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power__le__imp__le__exp,axiom,
% 7.29/7.41 ! [V_n,V_m,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_abs__add__one__gt__zero,axiom,
% 7.29/7.41 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_convex__bound__lt,axiom,
% 7.29/7.41 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 7.29/7.41 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__le__eq__number__of1,axiom,
% 7.29/7.41 ! [V_a_2,V_w_2,V_b_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_a_2)
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_divide__le__eq__number__of,axiom,
% 7.29/7.41 ! [V_w_2,V_c_2,V_b_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2)) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_le__divide__eq__number__of,axiom,
% 7.29/7.41 ! [V_c_2,V_b_2,V_w_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2)) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_le__divide__eq__number__of1,axiom,
% 7.29/7.41 ! [V_w_2,V_b_2,V_a_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) )
% 7.29/7.41 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_half__gt__zero__iff,axiom,
% 7.29/7.41 ! [V_r_2,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber__ring(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_half__gt__zero,axiom,
% 7.29/7.41 ! [V_r,T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber__ring(T_a) )
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power2__less__0,axiom,
% 7.29/7.41 ! [V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.41 => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zero__less__power2,axiom,
% 7.29/7.41 ! [V_a_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 7.29/7.41 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__two__gt__zero,axiom,
% 7.29/7.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__less__half__sum,axiom,
% 7.29/7.41 ! [V_y,V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__gt__half__sum,axiom,
% 7.29/7.41 ! [V_y,V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__two__gt__one,axiom,
% 7.29/7.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_power2__less__imp__less,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__semidom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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)))))
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_half,axiom,
% 7.29/7.41 ! [T_a] :
% 7.29/7.41 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 7.29/7.41 & class_Int_Onumber__ring(T_a) )
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__sum__power2__lt__zero,axiom,
% 7.29/7.41 ! [V_y,V_x,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.41 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_sum__power2__gt__zero__iff,axiom,
% 7.29/7.41 ! [V_ya_2,V_xa_2,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 7.29/7.41 <=> ( V_xa_2 != c_Groups_Ozero__class_Ozero(T_a)
% 7.29/7.41 | V_ya_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_real__sqrt__pow2__gt__zero,axiom,
% 7.29/7.41 ! [V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_lemma__real__divide__sqrt__less,axiom,
% 7.29/7.41 ! [V_u] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__one__imp__sqr__less__one,axiom,
% 7.29/7.41 ! [V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_odd__power__less__zero,axiom,
% 7.29/7.41 ! [V_n,V_a,T_a] :
% 7.29/7.41 ( class_Rings_Olinordered__idom(T_a)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_machin,axiom,
% 7.29/7.41 c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(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_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))))))))) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_complex_Orecs,axiom,
% 7.29/7.41 ! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_natceiling__add__one,axiom,
% 7.29/7.41 ! [V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 7.29/7.41 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__zeroE,axiom,
% 7.29/7.41 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_Suc__mono,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_lessI,axiom,
% 7.29/7.41 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zero__less__Suc,axiom,
% 7.29/7.41 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__lessD1,axiom,
% 7.29/7.41 ! [V_k,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__add__eq__less,axiom,
% 7.29/7.41 ! [V_n,V_m,V_l,V_k] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 7.29/7.41 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__less__mono,axiom,
% 7.29/7.41 ! [V_l,V_k,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 7.29/7.41 => 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)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__less__mono1,axiom,
% 7.29/7.41 ! [V_k,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 7.29/7.41 => 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)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_trans__less__add2,axiom,
% 7.29/7.41 ! [V_m,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_trans__less__add1,axiom,
% 7.29/7.41 ! [V_m,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_nat__add__left__cancel__less,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2,V_k_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__add__less2,axiom,
% 7.29/7.41 ! [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) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__add__less1,axiom,
% 7.29/7.41 ! [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) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_pi__not__less__zero,axiom,
% 7.29/7.41 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Opi,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__less0,axiom,
% 7.29/7.41 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_pi__gt__zero,axiom,
% 7.29/7.41 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_neq0__conv,axiom,
% 7.29/7.41 ! [V_n_2] :
% 7.29/7.41 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__nat__zero__code,axiom,
% 7.29/7.41 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_gr__implies__not0,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__imp__diff__less,axiom,
% 7.29/7.41 ! [V_n,V_k,V_j] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_diff__less__mono2,axiom,
% 7.29/7.41 ! [V_l,V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
% 7.29/7.41 => 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)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_gr0I,axiom,
% 7.29/7.41 ! [V_n] :
% 7.29/7.41 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_nat__less__le,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 & V_m_2 != V_n_2 ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_le__eq__less__or__eq,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 | V_m_2 = V_n_2 ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__imp__le__nat,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_le__neq__implies__less,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => ( V_m != V_n
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__or__eq__imp__le,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 | V_m = V_n )
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__not__refl,axiom,
% 7.29/7.41 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_nat__neq__iff,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( V_m_2 != V_n_2
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_linorder__neqE__nat,axiom,
% 7.29/7.41 ! [V_y,V_x] :
% 7.29/7.41 ( V_x != V_y
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__irrefl__nat,axiom,
% 7.29/7.41 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__not__refl2,axiom,
% 7.29/7.41 ! [V_m,V_n] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 7.29/7.41 => V_m != V_n ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__not__refl3,axiom,
% 7.29/7.41 ! [V_t,V_s] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 7.29/7.41 => V_s != V_t ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_nat__less__cases,axiom,
% 7.29/7.41 ! [V_P_2,V_n_2,V_m_2] :
% 7.29/7.41 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 7.29/7.41 => ( ( V_m_2 = V_n_2
% 7.29/7.41 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 7.29/7.41 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 7.29/7.41 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 7.29/7.41 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_Suc__less__SucD,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_Suc__lessD,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__SucE,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 7.29/7.41 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => V_m = V_n ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__trans__Suc,axiom,
% 7.29/7.41 ! [V_k,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_Suc__lessI,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => ( c_Nat_OSuc(V_m) != V_n
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__SucI,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__antisym,axiom,
% 7.29/7.41 ! [V_m,V_n] :
% 7.29/7.41 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 7.29/7.41 => V_m = V_n ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__less__less__Suc__eq,axiom,
% 7.29/7.41 ! [V_m_2,V_n_2] :
% 7.29/7.41 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 7.29/7.41 <=> V_n_2 = V_m_2 ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_Suc__less__eq,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__Suc__eq,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 | V_m_2 = V_n_2 ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_not__less__eq,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_rel__simps_I7_J,axiom,
% 7.29/7.41 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zless__linear,axiom,
% 7.29/7.41 ! [V_y,V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 7.29/7.41 | V_x = V_y
% 7.29/7.41 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__number__of__int__code,axiom,
% 7.29/7.41 ! [V_l_2,V_k_2] :
% 7.29/7.41 ( 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))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zadd__strict__right__mono,axiom,
% 7.29/7.41 ! [V_k,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 7.29/7.41 => 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)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_zless__le,axiom,
% 7.29/7.41 ! [V_w_2,V_za_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_w_2)
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_w_2)
% 7.29/7.41 & V_za_2 != V_w_2 ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__int__code_I13_J,axiom,
% 7.29/7.41 ! [V_k2_2,V_k1_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_rel__simps_I14_J,axiom,
% 7.29/7.41 ! [V_l_2,V_k_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_rel__simps_I2_J,axiom,
% 7.29/7.41 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__int__code_I16_J,axiom,
% 7.29/7.41 ! [V_k2_2,V_k1_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_rel__simps_I17_J,axiom,
% 7.29/7.41 ! [V_l_2,V_k_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__nat__number__of,axiom,
% 7.29/7.41 ! [V_v_H_2,V_v_2] :
% 7.29/7.41 ( 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))
% 7.29/7.41 <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) )
% 7.29/7.41 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__fun__def,axiom,
% 7.29/7.41 ! [V_g_2,V_f_2,T_a,T_b] :
% 7.29/7.41 ( class_Orderings_Oord(T_b)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 7.29/7.41 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__0__number__of,axiom,
% 7.29/7.41 ! [V_v_2] :
% 7.29/7.41 ( 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))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_pi__ge__zero,axiom,
% 7.29/7.41 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_pi__neq__zero,axiom,
% 7.29/7.41 c_Transcendental_Opi != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_bin__less__0__simps_I4_J,axiom,
% 7.29/7.41 ! [V_w_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_rel__simps_I12_J,axiom,
% 7.29/7.41 ! [V_k_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_bin__less__0__simps_I1_J,axiom,
% 7.29/7.41 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__int__code_I15_J,axiom,
% 7.29/7.41 ! [V_k2_2,V_k1_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_rel__simps_I16_J,axiom,
% 7.29/7.41 ! [V_l_2,V_k_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_bin__less__0__simps_I3_J,axiom,
% 7.29/7.41 ! [V_w_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__Suc__eq__0__disj,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 7.29/7.41 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.29/7.41 | ? [B_j] :
% 7.29/7.41 ( V_m_2 = c_Nat_OSuc(B_j)
% 7.29/7.41 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2) ) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__Suc0,axiom,
% 7.29/7.41 ! [V_n_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 7.29/7.41 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_gr0__conv__Suc,axiom,
% 7.29/7.41 ! [V_n_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 7.29/7.41 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 7.29/7.41 ! [V_x] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 7.29/7.41 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 7.29/7.41 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_rel__simps_I10_J,axiom,
% 7.29/7.41 ! [V_k_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_rel__simps_I4_J,axiom,
% 7.29/7.41 ! [V_k_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_add__gr__0,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 7.29/7.41 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__add__Suc1,axiom,
% 7.29/7.41 ! [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))) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__add__Suc2,axiom,
% 7.29/7.41 ! [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))) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__iff__Suc__add,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_Suc__le__lessD,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_le__less__Suc__eq,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
% 7.29/7.41 <=> V_n_2 = V_m_2 ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_Suc__leI,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_le__imp__less__Suc,axiom,
% 7.29/7.41 ! [V_n,V_m] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_Suc__le__eq,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__Suc__eq__le,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_less__eq__Suc__le,axiom,
% 7.29/7.41 ! [V_m_2,V_n_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 7.29/7.41 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_int__0__less__1,axiom,
% 7.29/7.41 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_nat__0__less__mult__iff,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 7.29/7.41 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__less__cancel1,axiom,
% 7.29/7.41 ! [V_n_2,V_m_2,V_k_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 7.29/7.41 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__less__cancel2,axiom,
% 7.29/7.41 ! [V_n_2,V_k_2,V_m_2] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
% 7.29/7.41 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 7.29/7.41 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__less__mono1,axiom,
% 7.29/7.41 ! [V_k,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ) ).
% 7.29/7.41
% 7.29/7.41 fof(fact_mult__less__mono2,axiom,
% 7.29/7.41 ! [V_k,V_j,V_i] :
% 7.29/7.41 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 7.29/7.41 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 7.29/7.41 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ) ).
% 7.29/7.41
% 7.29/7.41 %----Arity declarations (204)
% 7.29/7.41 fof(arity_fun__Orderings_Opreorder,axiom,
% 7.29/7.41 ! [T_2,T_1] :
% 7.29/7.41 ( class_Orderings_Opreorder(T_1)
% 7.29/7.41 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(arity_fun__Orderings_Oorder,axiom,
% 7.29/7.41 ! [T_2,T_1] :
% 7.29/7.41 ( class_Orderings_Oorder(T_1)
% 7.29/7.41 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(arity_fun__Orderings_Oord,axiom,
% 7.29/7.41 ! [T_2,T_1] :
% 7.29/7.41 ( class_Orderings_Oord(T_1)
% 7.29/7.41 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 7.29/7.41
% 7.29/7.41 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.29/7.41 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 7.29/7.41
% 7.29/7.41 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 7.29/7.41 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 7.29/7.41
% 7.29/7.41 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 7.29/7.41 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 7.29/7.41
% 7.29/7.41 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 7.29/7.41 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 7.29/7.41
% 7.29/7.41 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 7.29/7.42 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 7.29/7.42 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 7.29/7.42 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 7.29/7.42 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 7.29/7.42 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 7.29/7.42 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 7.29/7.42 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 7.29/7.42 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 7.29/7.42 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 7.29/7.42 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 7.29/7.42 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 7.29/7.42 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 7.29/7.42 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 7.29/7.42 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 7.29/7.42 class_Orderings_Opreorder(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 7.29/7.42 class_Orderings_Olinorder(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 7.29/7.42 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 7.29/7.42 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 7.29/7.42 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 7.29/7.42 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 7.29/7.42 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 7.29/7.42 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 7.29/7.42 class_Rings_Omult__zero(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 7.29/7.42 class_Orderings_Oorder(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 7.29/7.42 class_Int_Oring__char__0(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 7.29/7.42 class_Int_Onumber__ring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 7.29/7.42 class_Rings_Osemiring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 7.29/7.42 class_Orderings_Oord(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 7.29/7.42 class_Rings_Oring__1(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Power_Opower,axiom,
% 7.29/7.42 class_Power_Opower(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 7.29/7.42 class_Groups_Ozero(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Rings_Oring,axiom,
% 7.29/7.42 class_Rings_Oring(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Int_Onumber,axiom,
% 7.29/7.42 class_Int_Onumber(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Int__Oint__Groups_Oone,axiom,
% 7.29/7.42 class_Groups_Oone(tc_Int_Oint) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.29/7.42 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 7.29/7.42 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 7.29/7.42 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 7.29/7.42 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 7.29/7.42 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 7.29/7.42 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 7.29/7.42 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 7.29/7.42 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 7.29/7.42 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 7.29/7.42 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 7.29/7.42 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 7.29/7.42 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 7.29/7.42 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 7.29/7.42 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 7.29/7.42 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 7.29/7.42 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 7.29/7.42 class_Orderings_Oorder(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 7.29/7.42 class_Rings_Osemiring(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 7.29/7.42 class_Orderings_Oord(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Power_Opower,axiom,
% 7.29/7.42 class_Power_Opower(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 7.29/7.42 class_Groups_Ozero(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 7.29/7.42 class_Int_Onumber(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 7.29/7.42 class_Groups_Oone(tc_Nat_Onat) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 7.29/7.42 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 7.29/7.42 class_Orderings_Oorder(tc_HOL_Obool) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 7.29/7.42 class_Orderings_Oord(tc_HOL_Obool) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.29/7.42 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 7.29/7.42 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 7.29/7.42 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 7.29/7.42 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 7.29/7.42 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 7.29/7.42 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 7.29/7.42 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 7.29/7.42 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 7.29/7.42 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 7.29/7.42 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 7.29/7.42 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 7.29/7.42 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 7.29/7.42 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 7.29/7.42 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 7.29/7.42 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 7.29/7.42 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 7.29/7.42 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 7.29/7.42 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 7.29/7.42 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__RealVector_Oreal__field,axiom,
% 7.29/7.42 class_RealVector_Oreal__field(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 7.29/7.42 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 7.29/7.42 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 7.29/7.42 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 7.29/7.42 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 7.29/7.42 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 7.29/7.42 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 7.29/7.42 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 7.29/7.42 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 7.29/7.42 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 7.29/7.42 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
% 7.29/7.42 class_Rings_Osemiring__1(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 7.29/7.42 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 7.29/7.42 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 7.29/7.42 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 7.29/7.42 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 7.29/7.42 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
% 7.29/7.42 class_Int_Onumber__ring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 7.29/7.42 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 7.29/7.42 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 7.29/7.42 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 7.29/7.42 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 7.29/7.42 class_Power_Opower(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 7.29/7.42 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 7.29/7.42 class_Rings_Oring(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Int_Onumber,axiom,
% 7.29/7.42 class_Int_Onumber(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 7.29/7.42 class_Groups_Oone(tc_RealDef_Oreal) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 7.29/7.42 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 7.29/7.42 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
% 7.29/7.42 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 7.29/7.42 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 7.29/7.42 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 7.29/7.42 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 7.29/7.42 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 7.29/7.42 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 7.29/7.42 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 7.29/7.42 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
% 7.29/7.42 class_RealVector_Oreal__field(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 7.29/7.42 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 7.29/7.42 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 7.29/7.42 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 7.29/7.42 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 7.29/7.42 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 7.29/7.42 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 7.29/7.42 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
% 7.29/7.42 class_Rings_Osemiring__1(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 7.29/7.42 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 7.29/7.42 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 7.29/7.42 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 7.29/7.42 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
% 7.29/7.42 class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 7.29/7.42 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 7.29/7.42 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 7.29/7.42 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 7.29/7.42 class_Power_Opower(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 7.29/7.42 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 7.29/7.42 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
% 7.29/7.42 class_Int_Onumber(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 7.29/7.42 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 7.29/7.42
% 7.29/7.42 %----Conjectures (1)
% 7.29/7.42 fof(conj_0,conjecture,
% 7.29/7.42 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 7.29/7.42
% 7.29/7.42 %------------------------------------------------------------------------------
% 7.29/7.42 %-------------------------------------------
% 7.29/7.42 % Proof found
% 7.29/7.42 % SZS status Theorem for theBenchmark
% 7.29/7.42 % SZS output start Proof
% 7.29/7.42 %ClaNum:1771(EqnAxiom:133)
% 7.29/7.42 %VarNum:8871(SingletonVarNum:2940)
% 7.29/7.42 %MaxLitNum:7
% 7.29/7.42 %MaxfuncDepth:14
% 7.29/7.42 %SharedTerms:383
% 7.29/7.42 %goalClause: 560
% 7.29/7.42 %singleGoalClaCount:1
% 7.29/7.42 [135]P1(a38)
% 7.29/7.42 [136]P1(a39)
% 7.29/7.42 [137]P1(a1)
% 7.29/7.42 [138]P1(a16)
% 7.29/7.42 [139]P18(a38)
% 7.29/7.42 [140]P18(a39)
% 7.29/7.42 [141]P18(a1)
% 7.29/7.42 [142]P18(a16)
% 7.29/7.42 [143]P27(a38)
% 7.29/7.42 [144]P27(a1)
% 7.29/7.42 [145]P47(a38)
% 7.29/7.42 [146]P47(a39)
% 7.29/7.42 [147]P47(a1)
% 7.29/7.42 [148]P47(a16)
% 7.29/7.42 [149]P28(a38)
% 7.29/7.42 [150]P28(a39)
% 7.29/7.42 [151]P28(a1)
% 7.29/7.42 [152]P28(a16)
% 7.29/7.42 [153]P29(a38)
% 7.29/7.42 [154]P29(a1)
% 7.29/7.42 [155]P29(a16)
% 7.29/7.42 [156]P48(a38)
% 7.29/7.42 [157]P48(a39)
% 7.29/7.42 [158]P48(a1)
% 7.29/7.42 [159]P68(a38)
% 7.29/7.42 [160]P68(a39)
% 7.29/7.42 [161]P68(a1)
% 7.29/7.42 [162]P68(a16)
% 7.29/7.42 [163]P51(a38)
% 7.29/7.42 [164]P51(a39)
% 7.29/7.42 [165]P51(a1)
% 7.29/7.42 [166]P51(a16)
% 7.29/7.42 [167]P30(a38)
% 7.29/7.42 [168]P30(a1)
% 7.29/7.42 [169]P30(a16)
% 7.29/7.42 [170]P2(a38)
% 7.29/7.42 [171]P2(a39)
% 7.29/7.42 [172]P2(a1)
% 7.29/7.42 [173]P2(a16)
% 7.29/7.42 [174]P19(a38)
% 7.29/7.42 [175]P19(a1)
% 7.29/7.42 [176]P31(a38)
% 7.29/7.42 [177]P31(a39)
% 7.29/7.42 [178]P31(a1)
% 7.29/7.42 [179]P31(a37)
% 7.29/7.42 [180]P35(a38)
% 7.29/7.42 [181]P35(a39)
% 7.29/7.42 [182]P35(a1)
% 7.29/7.42 [183]P35(a16)
% 7.29/7.42 [184]P20(a38)
% 7.29/7.42 [185]P20(a1)
% 7.29/7.42 [186]P22(a38)
% 7.29/7.42 [187]P22(a39)
% 7.29/7.42 [188]P22(a1)
% 7.29/7.42 [189]P22(a16)
% 7.29/7.42 [190]P15(a38)
% 7.29/7.42 [191]P15(a1)
% 7.29/7.42 [192]P15(a16)
% 7.29/7.42 [193]P3(a38)
% 7.29/7.42 [194]P3(a1)
% 7.29/7.42 [195]P3(a16)
% 7.29/7.42 [196]P67(a38)
% 7.29/7.42 [197]P67(a39)
% 7.29/7.42 [198]P67(a1)
% 7.29/7.42 [199]P67(a16)
% 7.29/7.42 [200]P52(a38)
% 7.29/7.42 [201]P52(a39)
% 7.29/7.42 [202]P52(a1)
% 7.29/7.42 [203]P52(a16)
% 7.29/7.42 [204]P57(a38)
% 7.29/7.42 [205]P57(a39)
% 7.29/7.42 [206]P57(a1)
% 7.29/7.42 [207]P57(a16)
% 7.29/7.42 [208]P69(a38)
% 7.29/7.42 [209]P69(a39)
% 7.29/7.42 [210]P69(a1)
% 7.29/7.42 [211]P69(a16)
% 7.29/7.42 [212]P16(a38)
% 7.29/7.42 [213]P16(a39)
% 7.29/7.42 [214]P16(a1)
% 7.29/7.42 [215]P16(a16)
% 7.29/7.42 [216]P10(a38)
% 7.29/7.42 [217]P10(a39)
% 7.29/7.42 [218]P10(a1)
% 7.29/7.42 [219]P10(a16)
% 7.29/7.42 [220]P17(a38)
% 7.29/7.42 [221]P17(a1)
% 7.29/7.42 [222]P36(a38)
% 7.29/7.42 [223]P36(a1)
% 7.29/7.42 [224]P36(a16)
% 7.29/7.42 [225]P58(a38)
% 7.29/7.42 [226]P58(a1)
% 7.29/7.42 [227]P58(a16)
% 7.29/7.42 [228]P23(a38)
% 7.29/7.42 [229]P23(a39)
% 7.29/7.42 [230]P23(a1)
% 7.29/7.42 [231]P59(a38)
% 7.29/7.42 [232]P59(a1)
% 7.29/7.42 [233]P59(a16)
% 7.29/7.42 [234]P49(a38)
% 7.29/7.42 [235]P49(a1)
% 7.29/7.42 [236]P65(a38)
% 7.29/7.42 [237]P65(a1)
% 7.29/7.42 [238]P65(a16)
% 7.29/7.42 [239]P50(a38)
% 7.29/7.42 [240]P50(a1)
% 7.29/7.42 [241]P32(a38)
% 7.29/7.42 [242]P32(a39)
% 7.29/7.42 [243]P32(a1)
% 7.29/7.42 [244]P33(a38)
% 7.29/7.42 [245]P33(a39)
% 7.29/7.42 [246]P33(a1)
% 7.29/7.42 [247]P33(a37)
% 7.29/7.42 [248]P34(a38)
% 7.29/7.42 [249]P34(a39)
% 7.29/7.42 [250]P34(a1)
% 7.29/7.42 [251]P34(a37)
% 7.29/7.42 [252]P11(a38)
% 7.29/7.42 [253]P11(a39)
% 7.29/7.42 [254]P11(a1)
% 7.29/7.42 [255]P11(a16)
% 7.29/7.42 [256]P12(a38)
% 7.29/7.42 [257]P12(a39)
% 7.29/7.42 [258]P12(a1)
% 7.29/7.42 [259]P12(a16)
% 7.29/7.42 [260]P13(a38)
% 7.29/7.42 [261]P13(a39)
% 7.29/7.42 [262]P13(a1)
% 7.29/7.42 [263]P13(a16)
% 7.29/7.42 [264]P14(a38)
% 7.29/7.42 [265]P14(a39)
% 7.29/7.42 [266]P14(a1)
% 7.29/7.42 [267]P14(a16)
% 7.29/7.42 [268]P21(a38)
% 7.29/7.42 [269]P21(a39)
% 7.29/7.42 [270]P21(a1)
% 7.29/7.42 [271]P21(a16)
% 7.29/7.42 [272]P24(a38)
% 7.29/7.42 [273]P24(a39)
% 7.29/7.42 [274]P24(a1)
% 7.29/7.42 [275]P25(a38)
% 7.29/7.42 [276]P25(a39)
% 7.29/7.42 [277]P25(a1)
% 7.29/7.42 [278]P37(a38)
% 7.29/7.42 [279]P37(a16)
% 7.29/7.42 [280]P53(a38)
% 7.29/7.42 [281]P53(a1)
% 7.29/7.42 [282]P38(a38)
% 7.29/7.42 [283]P38(a16)
% 7.29/7.42 [284]P39(a38)
% 7.29/7.42 [285]P39(a16)
% 7.29/7.42 [286]P66(a38)
% 7.29/7.42 [287]P66(a1)
% 7.29/7.42 [288]P66(a16)
% 7.29/7.42 [289]P43(a38)
% 7.29/7.42 [290]P43(a39)
% 7.29/7.42 [291]P43(a1)
% 7.29/7.42 [292]P43(a16)
% 7.29/7.42 [293]P60(a38)
% 7.29/7.42 [294]P60(a39)
% 7.29/7.42 [295]P60(a1)
% 7.29/7.42 [296]P61(a38)
% 7.29/7.42 [297]P61(a1)
% 7.29/7.42 [298]P63(a38)
% 7.29/7.42 [299]P63(a39)
% 7.29/7.42 [300]P63(a1)
% 7.29/7.42 [301]P62(a38)
% 7.29/7.42 [302]P62(a39)
% 7.29/7.42 [303]P62(a1)
% 7.29/7.42 [304]P41(a38)
% 7.29/7.42 [305]P41(a16)
% 7.29/7.42 [306]P64(a38)
% 7.29/7.42 [307]P64(a1)
% 7.29/7.42 [308]P44(a38)
% 7.29/7.42 [309]P44(a16)
% 7.29/7.42 [310]P42(a38)
% 7.29/7.42 [311]P42(a16)
% 7.29/7.42 [312]P45(a38)
% 7.29/7.42 [313]P45(a16)
% 7.29/7.42 [314]P4(a38)
% 7.29/7.42 [315]P4(a16)
% 7.29/7.42 [316]P5(a38)
% 7.29/7.42 [317]P5(a16)
% 7.29/7.42 [318]P40(a38)
% 7.29/7.42 [319]P40(a16)
% 7.29/7.42 [320]P8(a38)
% 7.29/7.42 [321]P9(a38)
% 7.29/7.42 [322]P46(a38)
% 7.29/7.42 [323]P46(a39)
% 7.29/7.42 [324]P46(a1)
% 7.29/7.42 [325]P55(a38)
% 7.29/7.42 [326]P55(a39)
% 7.29/7.42 [327]P55(a1)
% 7.29/7.42 [328]P26(a38)
% 7.29/7.42 [329]P26(a39)
% 7.29/7.42 [330]P26(a1)
% 7.29/7.42 [331]P54(a38)
% 7.29/7.42 [332]P54(a39)
% 7.29/7.42 [333]P54(a1)
% 7.29/7.42 [334]P56(a38)
% 7.29/7.42 [335]P56(a1)
% 7.29/7.42 [355]P6(a1,a15,a14)
% 7.29/7.42 [523]~E(a15,a14)
% 7.29/7.42 [531]~P6(a1,a14,a15)
% 7.29/7.42 [532]~P7(a1,a14,a14)
% 7.29/7.42 [533]~P7(a1,a15,a15)
% 7.29/7.42 [134]E(f2(a1),a14)
% 7.29/7.42 [339]E(f4(a40,a42),a43)
% 7.29/7.42 [340]E(f4(a26,a29),a43)
% 7.29/7.42 [343]E(f18(a1,a14),f2(a1))
% 7.29/7.42 [344]E(f18(a39,a14),f2(a39))
% 7.29/7.42 [345]E(f21(a16,a43),f3(a38))
% 7.29/7.42 [370]P6(a38,f2(a38),a27)
% 7.29/7.42 [371]P7(a38,f2(a38),a27)
% 7.29/7.42 [382]P6(a1,f2(a1),f3(a1))
% 7.29/7.42 [384]P7(a1,f2(a1),f3(a1))
% 7.29/7.42 [386]P6(a1,f2(a1),f18(a1,a14))
% 7.29/7.42 [524]~E(f3(a16),a5)
% 7.29/7.42 [525]~E(f2(a16),a5)
% 7.29/7.42 [526]~E(f2(a38),a27)
% 7.29/7.42 [527]~E(f3(a38),f2(a38))
% 7.29/7.42 [528]~E(f3(a1),f2(a1))
% 7.29/7.42 [530]~E(f18(a1,a15),f18(a1,a14))
% 7.29/7.42 [538]~P7(a38,a27,f2(a38))
% 7.29/7.42 [539]~P7(a1,a14,f2(a1))
% 7.29/7.42 [336]E(f17(f3(a38)),f3(a38))
% 7.29/7.42 [337]E(f17(f2(a38)),f2(a38))
% 7.29/7.42 [338]E(f20(f2(a38)),f2(a38))
% 7.29/7.42 [346]E(f4(f2(a38),f3(a38)),a5)
% 7.29/7.42 [347]E(f4(f3(a38),f2(a38)),f3(a16))
% 7.29/7.42 [348]E(f4(f2(a38),f2(a38)),f2(a16))
% 7.29/7.42 [415]P6(a38,f3(a38),f21(a16,f13(a16,a43,a5)))
% 7.29/7.42 [416]P6(a38,f3(a38),f21(a16,f11(a16,a43,a5)))
% 7.29/7.42 [363]E(f30(f30(f12(a16),a5),a5),f18(a16,a15))
% 7.29/7.42 [403]E(f13(a1,f13(a1,f3(a1),a15),a15),a15)
% 7.29/7.42 [418]P6(a38,f3(a38),f21(a16,f13(a16,a43,f3(a16))))
% 7.29/7.42 [419]P6(a38,f3(a38),f21(a16,f11(a16,a43,f3(a16))))
% 7.29/7.42 [438]E(f18(a1,f13(a1,f13(a1,f3(a1),a14),a14)),f3(a1))
% 7.29/7.42 [439]E(f18(a39,f13(a1,f13(a1,f3(a1),a14),a14)),f3(a39))
% 7.29/7.42 [451]E(f18(a39,f13(a1,f13(a1,f3(a1),a14),a14)),f13(a39,f2(a39),f3(a39)))
% 7.29/7.42 [479]E(f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a39,f3(a39),f3(a39)))
% 7.29/7.42 [481]E(f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a39,f13(a39,f2(a39),f3(a39)),f3(a39)))
% 7.29/7.42 [482]E(f18(a39,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a39,f13(a39,f13(a39,f2(a39),f3(a39)),f3(a39)),f3(a39)))
% 7.29/7.42 [484]P6(a1,f2(a1),f18(a1,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))
% 7.29/7.42 [489]P6(a1,f2(a1),f18(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))
% 7.29/7.42 [483]E(f30(f30(f22(a16),a5),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f18(a16,a15))
% 7.29/7.42 [491]P6(a38,f2(a38),f17(f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.42 [492]P7(a38,f3(a38),f17(f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.42 [493]P7(a38,f2(a38),f17(f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.42 [560]~P6(a38,f30(f30(f22(a38),f9(a38,f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),a40))),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),f3(a38)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.42 [499]P6(a38,f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),a40),f3(a38))
% 7.29/7.42 [500]P6(a38,f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),a42),f3(a38))
% 7.29/7.42 [502]P6(a38,f18(a38,a15),f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),a40))
% 7.29/7.42 [503]P6(a38,f18(a38,a15),f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),a42))
% 7.29/7.42 [504]E(f13(a38,f30(f30(f22(a38),a40),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),a42),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f3(a38))
% 7.29/7.42 [506]P6(a38,f9(a38,f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),a40)),f3(a38))
% 7.29/7.42 [507]P6(a38,f9(a38,f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),a42)),f3(a38))
% 7.29/7.42 [521]E(f11(a38,f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f20(f25(a38,f3(a38),f18(a38,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))),f20(f25(a38,f3(a38),f18(a38,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14)))))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14)))))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14)))))))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14)))))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14)))))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))))),f13(a1,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14)))))))))))),f25(a38,a27,f18(a38,f13(a1,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))
% 7.29/7.42 [364]P6(a38,x3641,x3641)
% 7.29/7.42 [365]P6(a39,x3651,x3651)
% 7.29/7.42 [366]P6(a1,x3661,x3661)
% 7.29/7.42 [537]~P7(a39,x5371,x5371)
% 7.29/7.42 [341]E(f18(a1,x3411),x3411)
% 7.29/7.42 [349]E(f9(a38,x3491),f21(a38,x3491))
% 7.29/7.42 [360]E(f13(a1,x3601,a14),x3601)
% 7.29/7.42 [361]E(f11(a1,x3611,a14),x3611)
% 7.29/7.42 [362]E(f13(a1,a14,x3621),x3621)
% 7.29/7.42 [373]E(f11(a39,x3731,x3731),f2(a39))
% 7.29/7.42 [375]P6(a39,f2(a39),x3751)
% 7.29/7.42 [529]~E(f18(a16,x5291),a5)
% 7.29/7.42 [535]~E(f13(a1,x5351,x5351),a15)
% 7.29/7.42 [542]~P7(a39,x5421,f2(a39))
% 7.29/7.42 [357]E(f30(f30(f12(a39),x3571),f3(a39)),x3571)
% 7.29/7.42 [358]E(f30(f30(f12(a1),x3581),f3(a1)),x3581)
% 7.29/7.42 [359]E(f30(f30(f12(a39),x3591),f2(a39)),f2(a39))
% 7.29/7.42 [376]E(f13(a39,x3761,f2(a39)),x3761)
% 7.29/7.42 [377]E(f13(a1,x3771,f2(a1)),x3771)
% 7.29/7.42 [378]E(f11(a39,x3781,f2(a39)),x3781)
% 7.29/7.42 [379]E(f13(a39,f2(a39),x3791),x3791)
% 7.29/7.42 [380]E(f13(a1,f2(a1),x3801),x3801)
% 7.29/7.42 [381]E(f11(a39,f2(a39),x3811),f2(a39))
% 7.29/7.42 [406]P7(a39,x4061,f13(a39,x4061,f3(a39)))
% 7.29/7.42 [407]P7(a39,f2(a39),f13(a39,x4071,f3(a39)))
% 7.29/7.42 [410]P7(a38,f2(a38),f13(a38,f3(a38),f9(a38,x4101)))
% 7.29/7.42 [453]E(f13(a1,f11(a1,a14,x4531),f11(a1,a14,x4531)),f11(a1,a14,f13(a1,x4531,x4531)))
% 7.29/7.42 [463]E(f13(a1,f13(a1,f3(a1),f11(a1,a15,x4631)),f11(a1,a15,x4631)),f11(a1,a15,f13(a1,x4631,x4631)))
% 7.29/7.42 [544]~E(f13(a39,x5441,f3(a39)),x5441)
% 7.29/7.42 [550]~E(f13(a39,x5501,f3(a39)),f2(a39))
% 7.29/7.42 [555]~P6(a39,f13(a39,x5551,f3(a39)),x5551)
% 7.29/7.42 [557]~P7(a38,f13(a38,f9(a38,x5571),f3(a38)),x5571)
% 7.29/7.42 [352]E(f30(f30(f12(a1),a14),x3521),a14)
% 7.29/7.42 [367]E(f30(f30(f12(a38),f3(a38)),x3671),x3671)
% 7.29/7.42 [368]E(f30(f30(f12(a39),f3(a39)),x3681),x3681)
% 7.29/7.42 [369]E(f30(f30(f12(a1),f3(a1)),x3691),x3691)
% 7.29/7.42 [372]E(f30(f30(f12(a39),f2(a39)),x3721),f2(a39))
% 7.29/7.42 [396]P6(a39,x3961,f30(f30(f12(a39),x3961),x3961))
% 7.29/7.42 [554]~E(f13(a1,f13(a1,f3(a1),x5541),x5541),a14)
% 7.29/7.42 [556]~E(f13(a1,f13(a1,f3(a1),x5561),x5561),f2(a1))
% 7.29/7.42 [392]E(f17(f30(f30(f12(a38),x3921),x3921)),f9(a38,x3921))
% 7.29/7.42 [431]P6(a39,x4311,f30(f30(f12(a39),x4311),f30(f30(f12(a39),x4311),x4311)))
% 7.29/7.42 [440]E(f30(f30(f22(a39),f13(a39,f2(a39),f3(a39))),x4401),f13(a39,f2(a39),f3(a39)))
% 7.29/7.42 [464]E(f11(a1,a15,f13(a1,f13(a1,f3(a1),x4641),x4641)),f13(a1,f11(a1,a15,x4641),f11(a1,a15,x4641)))
% 7.29/7.42 [468]E(f13(a1,f13(a1,f3(a1),f11(a1,a15,x4681)),f11(a1,a15,x4681)),f11(a1,a14,f13(a1,f13(a1,f3(a1),x4681),x4681)))
% 7.29/7.43 [485]E(f30(f30(f22(a16),f10(x4851)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x4851)
% 7.29/7.43 [486]E(f30(f30(f12(a39),x4861),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f13(a39,x4861,x4861))
% 7.29/7.43 [487]E(f13(a39,x4871,f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f13(a39,f13(a39,x4871,f3(a39)),f3(a39)))
% 7.29/7.43 [488]E(f13(a39,f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))),x4881),f13(a39,f13(a39,x4881,f3(a39)),f3(a39)))
% 7.29/7.43 [490]E(f13(a39,f18(a39,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14))),x4901),f13(a39,f13(a39,f13(a39,x4901,f3(a39)),f3(a39)),f3(a39)))
% 7.29/7.43 [494]E(f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x4941),f13(a39,x4941,x4941))
% 7.29/7.43 [495]E(f17(f30(f30(f22(a38),x4951),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f9(a38,x4951))
% 7.29/7.43 [501]P6(a38,f3(a38),f30(f30(f22(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x5011))
% 7.29/7.43 [505]E(f13(a38,f25(a38,x5051,f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f25(a38,x5051,f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),x5051)
% 7.29/7.43 [514]E(f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f30(f30(f22(a38),x5141),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f30(f30(f22(a38),f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x5141)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [517]E(f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f20(f25(a38,x5171,f13(a38,f3(a38),f17(f13(a38,f3(a38),f30(f30(f22(a38),x5171),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))))),f20(x5171))
% 7.29/7.43 [390]E(f13(a39,x3901,x3902),f13(a39,x3902,x3901))
% 7.29/7.43 [391]E(f13(a1,x3911,x3912),f13(a1,x3912,x3911))
% 7.29/7.43 [398]P6(a39,x3981,f13(a39,x3982,x3981))
% 7.29/7.43 [399]P6(a39,x3991,f13(a39,x3991,x3992))
% 7.29/7.43 [400]P6(a39,f11(a39,x4001,x4002),x4001)
% 7.29/7.43 [551]~P7(a39,f13(a39,x5511,x5512),x5512)
% 7.29/7.43 [552]~P7(a39,f13(a39,x5521,x5522),x5521)
% 7.29/7.43 [350]E(f6(f4(x3501,x3502)),f2(a39))
% 7.29/7.43 [351]E(f19(a16,f4(x3511,x3512)),f2(a39))
% 7.29/7.43 [401]E(f11(a39,f13(a39,x4011,x4012),x4012),x4011)
% 7.29/7.43 [402]E(f11(a39,f13(a39,x4021,x4022),x4021),x4022)
% 7.29/7.43 [405]E(f11(a39,x4051,f13(a39,x4051,x4052)),f2(a39))
% 7.29/7.43 [409]E(f25(a38,f17(x4091),f17(x4092)),f17(f25(a38,x4091,x4092)))
% 7.29/7.43 [411]E(f13(a1,f18(a1,x4111),f18(a1,x4112)),f18(a1,f13(a1,x4111,x4112)))
% 7.29/7.43 [445]P7(a39,x4451,f13(a39,f13(a39,x4452,x4451),f3(a39)))
% 7.29/7.43 [446]P7(a39,x4461,f13(a39,f13(a39,x4461,x4462),f3(a39)))
% 7.29/7.43 [461]E(f13(a1,f13(a1,x4611,x4611),f13(a1,x4612,x4612)),f13(a1,f13(a1,x4611,x4612),f13(a1,x4611,x4612)))
% 7.29/7.43 [462]E(f11(a1,f13(a1,x4621,x4621),f13(a1,x4622,x4622)),f13(a1,f11(a1,x4621,x4622),f11(a1,x4621,x4622)))
% 7.29/7.43 [466]P6(a38,f21(a16,x4661),f13(a38,f21(a16,f13(a16,x4661,x4662)),f21(a16,x4662)))
% 7.29/7.43 [467]P6(a38,f11(a38,f21(a16,f13(a16,x4671,x4672)),f21(a16,x4671)),f21(a16,x4672))
% 7.29/7.43 [471]E(f13(a1,f13(a1,f13(a1,f3(a1),x4711),x4711),f13(a1,x4712,x4712)),f13(a1,f13(a1,f3(a1),f13(a1,x4711,x4712)),f13(a1,x4711,x4712)))
% 7.29/7.43 [472]E(f11(a1,f13(a1,f13(a1,f3(a1),x4721),x4721),f13(a1,x4722,x4722)),f13(a1,f13(a1,f3(a1),f11(a1,x4721,x4722)),f11(a1,x4721,x4722)))
% 7.29/7.43 [387]E(f30(f30(f12(a38),x3871),x3872),f30(f30(f12(a38),x3872),x3871))
% 7.29/7.43 [388]E(f30(f30(f12(a39),x3881),x3882),f30(f30(f12(a39),x3882),x3881))
% 7.29/7.43 [389]E(f30(f30(f12(a1),x3891),x3892),f30(f30(f12(a1),x3892),x3891))
% 7.29/7.43 [413]P6(a1,f2(a1),f30(f30(f22(a1),f9(a1,x4131)),x4132))
% 7.29/7.43 [430]E(f13(a39,f13(a39,x4301,f3(a39)),x4302),f13(a39,f13(a39,x4301,x4302),f3(a39)))
% 7.29/7.43 [432]E(f11(a39,f11(a39,x4321,f3(a39)),x4322),f11(a39,x4321,f13(a39,x4322,f3(a39))))
% 7.29/7.43 [433]E(f13(a39,f13(a39,x4331,f3(a39)),x4332),f13(a39,x4331,f13(a39,x4332,f3(a39))))
% 7.29/7.43 [559]~E(f13(a1,x5591,x5591),f13(a1,f13(a1,f3(a1),x5592),x5592))
% 7.29/7.43 [397]E(f17(f30(f30(f22(a38),x3971),x3972)),f30(f30(f22(a38),f17(x3971)),x3972))
% 7.29/7.43 [404]E(f30(f30(f12(a38),f17(x4041)),f17(x4042)),f17(f30(f30(f12(a38),x4041),x4042)))
% 7.29/7.43 [412]E(f30(f30(f12(a1),f18(a1,x4121)),f18(a1,x4122)),f18(a1,f30(f30(f12(a1),x4121),x4122)))
% 7.29/7.43 [417]E(f25(a38,f30(f30(f12(a38),x4171),x4172),f30(f30(f12(a38),x4171),x4171)),f25(a38,x4172,x4171))
% 7.29/7.43 [420]E(f30(f30(f12(a39),x4201),f13(a39,x4202,f3(a39))),f13(a39,x4201,f30(f30(f12(a39),x4201),x4202)))
% 7.29/7.43 [452]E(f30(f30(f12(a39),f13(a39,x4521,f3(a39))),x4522),f13(a39,x4522,f30(f30(f12(a39),x4521),x4522)))
% 7.29/7.43 [470]E(f13(a1,f13(a1,x4701,x4701),f13(a1,f13(a1,f3(a1),x4702),x4702)),f13(a1,f13(a1,f3(a1),f13(a1,x4701,x4702)),f13(a1,x4701,x4702)))
% 7.29/7.43 [473]E(f11(a1,f13(a1,f13(a1,f3(a1),x4731),x4731),f13(a1,f13(a1,f3(a1),x4732),x4732)),f13(a1,f11(a1,x4731,x4732),f11(a1,x4731,x4732)))
% 7.29/7.43 [475]P6(a38,x4751,f17(f13(a38,f30(f30(f12(a38),x4751),x4751),f30(f30(f12(a38),x4752),x4752))))
% 7.29/7.43 [476]P6(a38,f2(a38),f17(f13(a38,f30(f30(f12(a38),x4761),x4761),f30(f30(f12(a38),x4762),x4762))))
% 7.29/7.43 [478]E(f13(a1,f13(a1,f30(f30(f12(a1),x4781),x4782),f30(f30(f12(a1),x4781),x4782)),x4782),f30(f30(f12(a1),f13(a1,f13(a1,f3(a1),x4781),x4781)),x4782))
% 7.29/7.43 [497]E(f11(a38,f25(a38,f13(a38,x4971,x4972),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x4972),f25(a38,f11(a38,x4971,x4972),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [498]E(f11(a38,f25(a38,f13(a38,x4981,x4982),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x4981),f25(a38,f11(a38,x4982,x4981),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [508]E(f17(f13(a38,f30(f30(f22(a38),x5081),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5082),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),f21(a16,f4(x5081,x5082)))
% 7.29/7.43 [509]P6(a38,x5091,f17(f13(a38,f30(f30(f22(a38),x5092),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5091),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))
% 7.29/7.43 [510]P6(a38,x5101,f17(f13(a38,f30(f30(f22(a38),x5101),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5102),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))
% 7.29/7.43 [511]P6(a38,f2(a38),f17(f13(a38,f30(f30(f22(a38),x5111),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5112),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))
% 7.29/7.43 [512]P6(a38,f9(a38,x5121),f17(f13(a38,f30(f30(f22(a38),x5122),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5121),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))
% 7.29/7.43 [513]P6(a38,f9(a38,x5131),f17(f13(a38,f30(f30(f22(a38),x5131),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5132),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))
% 7.29/7.43 [515]E(f13(a38,f13(a38,f30(f30(f22(a38),x5151),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5152),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f30(f30(f12(a38),f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x5151)),x5152)),f30(f30(f22(a38),f13(a38,x5151,x5152)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [516]P6(a38,f9(a38,f25(a38,x5161,f17(f13(a38,f30(f30(f22(a38),x5161),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5162),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))),f3(a38))
% 7.29/7.43 [421]E(f13(a39,x4211,f13(a39,x4212,x4213)),f13(a39,x4212,f13(a39,x4211,x4213)))
% 7.29/7.43 [422]E(f13(a1,x4221,f13(a1,x4222,x4223)),f13(a1,x4222,f13(a1,x4221,x4223)))
% 7.29/7.43 [423]E(f13(a39,f13(a39,x4231,x4232),x4233),f13(a39,x4231,f13(a39,x4232,x4233)))
% 7.29/7.43 [424]E(f13(a1,f13(a1,x4241,x4242),x4243),f13(a1,x4241,f13(a1,x4242,x4243)))
% 7.29/7.43 [425]E(f11(a39,f11(a39,x4251,x4252),x4253),f11(a39,x4251,f13(a39,x4252,x4253)))
% 7.29/7.43 [426]E(f11(a39,f11(a39,x4261,x4262),x4263),f11(a39,f11(a39,x4261,x4263),x4262))
% 7.29/7.43 [427]E(f11(a39,f13(a39,x4271,x4272),f13(a39,x4273,x4272)),f11(a39,x4271,x4273))
% 7.29/7.43 [428]E(f11(a39,f13(a39,x4281,x4282),f13(a39,x4281,x4283)),f11(a39,x4282,x4283))
% 7.29/7.43 [465]E(f11(a39,f11(a39,f13(a39,x4651,f3(a39)),x4652),f13(a39,x4653,f3(a39))),f11(a39,f11(a39,x4651,x4652),x4653))
% 7.29/7.43 [447]E(f13(a39,f30(f30(f12(a39),x4471),x4472),f30(f30(f12(a39),x4471),x4473)),f30(f30(f12(a39),x4471),f13(a39,x4472,x4473)))
% 7.29/7.43 [448]E(f11(a39,f30(f30(f12(a39),x4481),x4482),f30(f30(f12(a39),x4481),x4483)),f30(f30(f12(a39),x4481),f11(a39,x4482,x4483)))
% 7.29/7.43 [449]E(f13(a1,f30(f30(f12(a1),x4491),x4492),f30(f30(f12(a1),x4491),x4493)),f30(f30(f12(a1),x4491),f13(a1,x4492,x4493)))
% 7.29/7.43 [450]E(f11(a1,f30(f30(f12(a1),x4501),x4502),f30(f30(f12(a1),x4501),x4503)),f30(f30(f12(a1),x4501),f11(a1,x4502,x4503)))
% 7.29/7.43 [454]E(f30(f30(f12(a1),f30(f30(f22(a1),x4541),x4542)),f30(f30(f22(a1),x4541),x4543)),f30(f30(f22(a1),x4541),f13(a39,x4542,x4543)))
% 7.29/7.43 [455]E(f13(a38,f30(f30(f12(a38),x4551),x4552),f30(f30(f12(a38),x4553),x4552)),f30(f30(f12(a38),f13(a38,x4551,x4553)),x4552))
% 7.29/7.43 [456]E(f13(a39,f30(f30(f12(a39),x4561),x4562),f30(f30(f12(a39),x4563),x4562)),f30(f30(f12(a39),f13(a39,x4561,x4563)),x4562))
% 7.29/7.43 [457]E(f11(a39,f30(f30(f12(a39),x4571),x4572),f30(f30(f12(a39),x4573),x4572)),f30(f30(f12(a39),f11(a39,x4571,x4573)),x4572))
% 7.29/7.43 [458]E(f13(a1,f30(f30(f12(a1),x4581),x4582),f30(f30(f12(a1),x4583),x4582)),f30(f30(f12(a1),f13(a1,x4581,x4583)),x4582))
% 7.29/7.43 [460]E(f11(a1,f30(f30(f12(a1),x4601),x4602),f30(f30(f12(a1),x4603),x4602)),f30(f30(f12(a1),f11(a1,x4601,x4603)),x4602))
% 7.29/7.43 [441]E(f30(f30(f12(a38),f30(f30(f12(a38),x4411),x4412)),x4413),f30(f30(f12(a38),x4411),f30(f30(f12(a38),x4412),x4413)))
% 7.29/7.43 [442]E(f30(f30(f12(a39),f30(f30(f12(a39),x4421),x4422)),x4423),f30(f30(f12(a39),x4421),f30(f30(f12(a39),x4422),x4423)))
% 7.29/7.43 [443]E(f30(f30(f12(a1),f30(f30(f12(a1),x4431),x4432)),x4433),f30(f30(f12(a1),x4431),f30(f30(f12(a1),x4432),x4433)))
% 7.29/7.43 [444]E(f30(f30(f22(a1),f30(f30(f22(a1),x4441),x4442)),x4443),f30(f30(f22(a1),x4441),f30(f30(f12(a39),x4442),x4443)))
% 7.29/7.43 [496]E(f11(a38,f30(x4961,x4962),f30(f30(f12(a38),f25(a38,f11(a38,f30(x4961,x4963),f30(x4961,x4962)),f11(a38,x4963,x4962))),x4962)),f11(a38,f30(x4961,x4963),f30(f30(f12(a38),f25(a38,f11(a38,f30(x4961,x4963),f30(x4961,x4962)),f11(a38,x4963,x4962))),x4963)))
% 7.29/7.43 [394]E(f7(x3941,x3942,f4(x3943,x3944)),f30(f30(x3942,x3943),x3944))
% 7.29/7.43 [395]E(f8(x3951,x3952,f4(x3953,x3954)),f30(f30(x3952,x3953),x3954))
% 7.29/7.43 [414]E(f30(f30(f23(x4141,x4142,x4143),x4144),f2(a39)),x4142)
% 7.29/7.43 [435]E(f4(f13(a38,x4351,x4352),f13(a38,x4353,x4354)),f13(a16,f4(x4351,x4353),f4(x4352,x4354)))
% 7.29/7.43 [436]E(f4(f11(a38,x4361,x4362),f11(a38,x4363,x4364)),f11(a16,f4(x4361,x4363),f4(x4362,x4364)))
% 7.29/7.43 [474]E(f13(a39,f30(f30(f12(a39),x4741),x4742),f13(a39,f30(f30(f12(a39),x4743),x4742),x4744)),f13(a39,f30(f30(f12(a39),f13(a39,x4741,x4743)),x4742),x4744))
% 7.29/7.43 [477]E(f4(f11(a38,f30(f30(f12(a38),x4771),x4772),f30(f30(f12(a38),x4773),x4774)),f13(a38,f30(f30(f12(a38),x4771),x4774),f30(f30(f12(a38),x4773),x4772))),f30(f30(f12(a16),f4(x4771,x4773)),f4(x4772,x4774)))
% 7.29/7.43 [520]E(f30(f30(f22(a38),f17(f30(f30(f12(a38),f13(a38,f30(f30(f22(a38),x5201),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5202),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),f13(a38,f30(f30(f22(a38),x5203),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5204),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f12(a38),f13(a38,f30(f30(f22(a38),x5201),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5202),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),f13(a38,f30(f30(f22(a38),x5203),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5204),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))))
% 7.29/7.43 [518]P6(a38,f17(f13(a38,f30(f30(f22(a38),f13(a38,x5181,x5182)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),f13(a38,x5183,x5184)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),f13(a38,f17(f13(a38,f30(f30(f22(a38),x5181),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5183),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),f17(f13(a38,f30(f30(f22(a38),x5182),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5184),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))))
% 7.29/7.43 [519]P6(a38,f2(a38),f17(f30(f30(f12(a38),f13(a38,f30(f30(f22(a38),x5191),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5192),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),f13(a38,f30(f30(f22(a38),x5193),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x5194),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))))
% 7.29/7.43 [469]E(f30(f30(f23(x4691,x4692,x4693),x4694),f13(a39,x4695,f3(a39))),f30(f30(x4693,x4694),f30(f30(f23(x4691,x4692,x4693),x4694),x4695)))
% 7.29/7.43 [561]~E(x5611,f3(a38))+E(f17(x5611),f3(a38))
% 7.29/7.43 [562]~E(x5621,f2(a38))+E(f17(x5621),f2(a38))
% 7.29/7.43 [563]~E(f17(x5631),f3(a38))+E(x5631,f3(a38))
% 7.29/7.43 [564]~E(f17(x5641),f2(a38))+E(x5641,f2(a38))
% 7.29/7.43 [567]~P69(x5671)+~E(f3(x5671),f2(x5671))
% 7.29/7.43 [569]~P29(x5691)+E(f18(x5691,a14),f2(x5691))
% 7.29/7.43 [600]~E(a14,x6001)+E(f13(a1,x6001,x6001),a14)
% 7.29/7.43 [601]~E(x6011,a14)+E(f13(a1,x6011,x6011),a14)
% 7.29/7.43 [609]E(x6091,f2(a39))+P7(a39,f2(a39),x6091)
% 7.29/7.43 [656]~P48(x6561)+P6(x6561,f2(x6561),f3(x6561))
% 7.29/7.43 [657]~P48(x6571)+P7(x6571,f2(x6571),f3(x6571))
% 7.29/7.43 [663]P6(a1,x6631,a14)+~E(f18(a39,x6631),f2(a39))
% 7.29/7.43 [678]E(x6781,a14)+~E(f13(a1,x6781,x6781),a14)
% 7.29/7.43 [679]E(a14,x6791)+~E(f13(a1,x6791,x6791),a14)
% 7.29/7.43 [699]E(x6991,f2(a39))+~P6(a39,x6991,f2(a39))
% 7.29/7.43 [711]~P6(a1,x7111,a14)+E(f18(a39,x7111),f2(a39))
% 7.29/7.43 [725]~E(f17(x7251),f2(a38))+~P7(a38,f2(a38),x7251)
% 7.29/7.43 [748]~P48(x7481)+~P6(x7481,f3(x7481),f2(x7481))
% 7.29/7.43 [749]~P48(x7491)+~P7(x7491,f3(x7491),f2(x7491))
% 7.29/7.43 [829]~P6(a38,x8291,f3(a38))+P6(a38,f17(x8291),f3(a38))
% 7.29/7.43 [830]~P6(a38,x8301,f2(a38))+P6(a38,f17(x8301),f2(a38))
% 7.29/7.43 [831]~P7(a38,x8311,f3(a38))+P7(a38,f17(x8311),f3(a38))
% 7.29/7.43 [832]~P7(a38,x8321,f2(a38))+P7(a38,f17(x8321),f2(a38))
% 7.29/7.43 [834]~P6(a38,f3(a38),x8341)+P6(a38,f3(a38),f17(x8341))
% 7.29/7.43 [836]~P6(a38,f2(a38),x8361)+P6(a38,f2(a38),f17(x8361))
% 7.29/7.43 [837]~P7(a38,f3(a38),x8371)+P7(a38,f3(a38),f17(x8371))
% 7.29/7.43 [839]~P7(a38,f2(a38),x8391)+P7(a38,f2(a38),f17(x8391))
% 7.29/7.43 [852]~P6(a38,f17(x8521),f3(a38))+P6(a38,x8521,f3(a38))
% 7.29/7.43 [853]~P6(a38,f17(x8531),f2(a38))+P6(a38,x8531,f2(a38))
% 7.29/7.43 [854]~P7(a38,f17(x8541),f3(a38))+P7(a38,x8541,f3(a38))
% 7.29/7.43 [855]~P7(a38,f17(x8551),f2(a38))+P7(a38,x8551,f2(a38))
% 7.29/7.43 [856]~P6(a38,f3(a38),f17(x8561))+P6(a38,f3(a38),x8561)
% 7.29/7.43 [857]~P6(a38,f2(a38),f17(x8571))+P6(a38,f2(a38),x8571)
% 7.29/7.43 [858]~P7(a38,f3(a38),f17(x8581))+P7(a38,f3(a38),x8581)
% 7.29/7.43 [859]~P7(a38,f2(a38),f17(x8591))+P7(a38,f2(a38),x8591)
% 7.29/7.43 [865]~P7(a1,a14,x8651)+P7(a39,f2(a39),f18(a39,x8651))
% 7.29/7.43 [882]P7(a1,a14,x8821)+~P7(a39,f2(a39),f18(a39,x8821))
% 7.29/7.43 [979]~P6(a1,a14,x9791)+P6(a1,a14,f13(a1,x9791,x9791))
% 7.29/7.43 [980]~P7(a1,a14,x9801)+P7(a1,a14,f13(a1,x9801,x9801))
% 7.29/7.43 [981]~P6(a1,x9811,a14)+P6(a1,f13(a1,x9811,x9811),a14)
% 7.29/7.43 [982]~P6(a1,x9821,a15)+P6(a1,f13(a1,x9821,x9821),a15)
% 7.29/7.43 [983]~P7(a1,x9831,a14)+P7(a1,f13(a1,x9831,x9831),a14)
% 7.29/7.43 [1022]~P7(a1,x10221,f2(a1))+P7(a1,f13(a1,x10221,x10221),f2(a1))
% 7.29/7.43 [1061]P6(a1,x10611,a14)+~P6(a1,f13(a1,x10611,x10611),a14)
% 7.29/7.43 [1062]P6(a1,x10621,a15)+~P6(a1,f13(a1,x10621,x10621),a15)
% 7.29/7.43 [1063]P7(a1,x10631,a14)+~P7(a1,f13(a1,x10631,x10631),a14)
% 7.29/7.43 [1064]P6(a1,a14,x10641)+~P6(a1,a14,f13(a1,x10641,x10641))
% 7.29/7.43 [1065]P7(a1,a14,x10651)+~P7(a1,a14,f13(a1,x10651,x10651))
% 7.29/7.43 [1081]P7(a1,x10811,f2(a1))+~P7(a1,f13(a1,x10811,x10811),f2(a1))
% 7.29/7.43 [575]~P38(x5751)+E(f21(x5751,f3(x5751)),f3(a38))
% 7.29/7.43 [576]~P37(x5761)+E(f21(x5761,f2(x5761)),f2(a38))
% 7.29/7.43 [581]~P27(x5811)+E(f9(x5811,f3(x5811)),f3(x5811))
% 7.29/7.43 [582]~P19(x5821)+E(f9(x5821,f2(x5821)),f2(x5821))
% 7.29/7.43 [669]~P35(x6691)+E(f23(x6691,f3(x6691),f12(x6691)),f22(x6691))
% 7.29/7.43 [840]~P7(a39,f2(a39),x8401)+E(f13(a39,f31(x8401),f3(a39)),x8401)
% 7.29/7.43 [927]~P48(x9271)+P7(x9271,f2(x9271),f13(x9271,f3(x9271),f3(x9271)))
% 7.29/7.43 [1043]E(x10431,f2(a39))+~P7(a39,x10431,f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [1268]~P6(a1,f2(a1),f18(a1,x12681))+P6(a1,f2(a1),f18(a1,f13(a1,x12681,x12681)))
% 7.29/7.43 [814]E(x8141,f2(a38))+P7(a38,f2(a38),f30(f30(f12(a38),x8141),x8141))
% 7.29/7.43 [868]~E(a15,x8681)+E(f13(a1,f13(a1,f3(a1),x8681),x8681),a15)
% 7.29/7.43 [869]~E(x8691,a15)+E(f13(a1,f13(a1,f3(a1),x8691),x8691),a15)
% 7.29/7.43 [978]~E(x9781,f2(a38))+~P7(a38,f2(a38),f30(f30(f12(a38),x9781),x9781))
% 7.29/7.43 [1030]E(x10301,a15)+~E(f13(a1,f13(a1,f3(a1),x10301),x10301),a15)
% 7.29/7.43 [1031]E(a15,x10311)+~E(f13(a1,f13(a1,f3(a1),x10311),x10311),a15)
% 7.29/7.43 [1038]~P6(a38,f2(a38),x10381)+E(f24(f13(a38,x10381,f3(a38))),f13(a39,f24(x10381),f3(a39)))
% 7.29/7.43 [1339]~P6(a1,a14,x13391)+P6(a1,a14,f13(a1,f13(a1,f3(a1),x13391),x13391))
% 7.29/7.43 [1340]~P6(a1,a15,x13401)+P6(a1,a15,f13(a1,f13(a1,f3(a1),x13401),x13401))
% 7.29/7.43 [1341]~P6(a1,x13411,a15)+P6(a1,f13(a1,f13(a1,f3(a1),x13411),x13411),a15)
% 7.29/7.43 [1342]~P7(a1,x13421,a14)+P7(a1,f13(a1,f13(a1,f3(a1),x13421),x13421),a14)
% 7.29/7.43 [1359]~P7(a1,x13591,f2(a1))+P7(a1,f13(a1,f13(a1,f3(a1),x13591),x13591),f2(a1))
% 7.29/7.43 [1536]P6(a1,x15361,a15)+~P6(a1,f13(a1,f13(a1,f3(a1),x15361),x15361),a15)
% 7.29/7.43 [1537]P7(a1,x15371,a14)+~P7(a1,f13(a1,f13(a1,f3(a1),x15371),x15371),a14)
% 7.29/7.43 [1538]P6(a1,a14,x15381)+~P6(a1,a14,f13(a1,f13(a1,f3(a1),x15381),x15381))
% 7.29/7.43 [1539]P6(a1,a15,x15391)+~P6(a1,a15,f13(a1,f13(a1,f3(a1),x15391),x15391))
% 7.29/7.43 [1541]P7(a1,x15411,f2(a1))+~P7(a1,f13(a1,f13(a1,f3(a1),x15411),x15411),f2(a1))
% 7.29/7.43 [1132]~P29(x11321)+E(f18(x11321,f13(a1,f13(a1,f3(a1),a14),a14)),f3(x11321))
% 7.29/7.43 [1641]~P6(a1,f2(a1),f18(a1,x16411))+P6(a1,f2(a1),f18(a1,f13(a1,f13(a1,f3(a1),x16411),x16411)))
% 7.29/7.43 [1686]~P29(x16861)+E(f13(x16861,f3(x16861),f3(x16861)),f18(x16861,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))
% 7.29/7.43 [1707]~P47(x17071)+E(f30(f30(f22(x17071),f3(x17071)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f3(x17071))
% 7.29/7.43 [1708]~P47(x17081)+E(f30(f30(f22(x17081),f2(x17081)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f2(x17081))
% 7.29/7.43 [1713]~P6(a38,f2(a38),x17131)+E(f30(f30(f22(a38),f17(x17131)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17131)
% 7.29/7.43 [1718]P6(a38,f2(a38),x17181)+~E(f30(f30(f22(a38),f17(x17181)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17181)
% 7.29/7.43 [1726]~P7(a38,f2(a38),x17261)+P7(a38,f2(a38),f30(f30(f22(a38),f17(x17261)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [1727]~P7(a38,f9(a38,x17271),f3(a38))+P7(a38,f30(f30(f22(a38),x17271),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f3(a38))
% 7.29/7.43 [1739]~P7(a38,f2(a38),x17391)+P7(a38,f25(a38,x17391,f17(f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),x17391)
% 7.29/7.43 [602]~E(x6021,x6022)+P6(a38,x6021,x6022)
% 7.29/7.43 [605]~E(x6051,x6052)+P6(a39,x6051,x6052)
% 7.29/7.43 [615]~P31(x6151)+P6(x6151,x6152,x6152)
% 7.29/7.43 [684]~E(x6841,x6842)+~P7(a38,x6841,x6842)
% 7.29/7.43 [689]~E(x6891,x6892)+~P7(a39,x6891,x6892)
% 7.29/7.43 [690]~E(x6901,x6902)+~P7(a1,x6901,x6902)
% 7.29/7.43 [705]~P7(x7051,x7052,x7052)+~P31(x7051)
% 7.29/7.43 [737]P6(a38,x7372,x7371)+P6(a38,x7371,x7372)
% 7.29/7.43 [738]P6(a39,x7382,x7381)+P6(a39,x7381,x7382)
% 7.29/7.43 [739]P6(a1,x7392,x7391)+P6(a1,x7391,x7392)
% 7.29/7.43 [780]~P7(a38,x7801,x7802)+P6(a38,x7801,x7802)
% 7.29/7.43 [784]~P7(a39,x7841,x7842)+P6(a39,x7841,x7842)
% 7.29/7.43 [785]~P7(a1,x7851,x7852)+P6(a1,x7851,x7852)
% 7.29/7.43 [565]E(x5651,x5652)+~E(f17(x5651),f17(x5652))
% 7.29/7.43 [571]E(x5711,f3(a38))+~E(f4(x5712,x5711),a5)
% 7.29/7.43 [572]E(x5721,f2(a38))+~E(f4(x5721,x5722),a5)
% 7.29/7.43 [577]E(x5771,f3(a38))+~E(f4(x5771,x5772),f3(a16))
% 7.29/7.43 [578]E(x5781,f2(a38))+~E(f4(x5782,x5781),f3(a16))
% 7.29/7.43 [579]E(x5791,f2(a38))+~E(f4(x5792,x5791),f2(a16))
% 7.29/7.43 [580]E(x5801,f2(a38))+~E(f4(x5801,x5802),f2(a16))
% 7.29/7.43 [585]~P31(x5852)+P31(f41(x5851,x5852))
% 7.29/7.43 [586]~P33(x5862)+P33(f41(x5861,x5862))
% 7.29/7.43 [587]~P34(x5872)+P34(f41(x5871,x5872))
% 7.29/7.43 [607]E(f13(a39,x6071,x6072),x6072)+~E(x6071,f2(a39))
% 7.29/7.43 [623]~P15(x6231)+E(f11(x6231,x6232,x6232),f2(x6231))
% 7.29/7.43 [691]~P19(x6911)+P6(x6911,x6912,f9(x6911,x6912))
% 7.29/7.43 [692]~E(f13(a39,x6922,x6921),x6922)+E(x6921,f2(a39))
% 7.29/7.43 [694]~P37(x6941)+P6(a38,f2(a38),f21(x6941,x6942))
% 7.29/7.43 [696]~P7(a39,x6962,x6961)+~E(x6961,f2(a39))
% 7.29/7.43 [697]E(x6971,f2(a39))+~E(f13(a39,x6972,x6971),f2(a39))
% 7.29/7.43 [698]E(x6981,f2(a39))+~E(f13(a39,x6981,x6982),f2(a39))
% 7.29/7.43 [706]~P19(x7061)+P6(x7061,f2(x7061),f9(x7061,x7062))
% 7.29/7.43 [778]~P37(x7781)+~P7(a38,f21(x7781,x7782),f2(a38))
% 7.29/7.43 [789]~P6(a39,x7891,x7892)+E(f11(a39,x7891,x7892),f2(a39))
% 7.29/7.43 [796]P6(a39,x7961,x7962)+~E(f11(a39,x7961,x7962),f2(a39))
% 7.29/7.43 [798]~P19(x7981)+~P7(x7981,f9(x7981,x7982),f2(x7981))
% 7.29/7.43 [809]~P6(a38,x8091,x8092)+P6(a38,f17(x8091),f17(x8092))
% 7.29/7.43 [810]~P6(a38,x8101,x8102)+P6(a38,f20(x8101),f20(x8102))
% 7.29/7.43 [812]~P7(a38,x8121,x8122)+P7(a38,f17(x8121),f17(x8122))
% 7.29/7.43 [813]~P7(a38,x8131,x8132)+P7(a38,f20(x8131),f20(x8132))
% 7.29/7.43 [862]P6(a38,x8621,x8622)+~P6(a38,f17(x8621),f17(x8622))
% 7.29/7.43 [863]P7(a38,x8631,x8632)+~P7(a38,f17(x8631),f17(x8632))
% 7.29/7.43 [873]E(x8731,x8732)+~E(f13(a1,x8731,x8731),f13(a1,x8732,x8732))
% 7.29/7.43 [899]~P6(a1,x8991,a14)+P6(a39,f18(a39,x8991),f18(a39,x8992))
% 7.29/7.43 [915]~P6(a1,x9151,x9152)+P6(a39,f18(a39,x9151),f18(a39,x9152))
% 7.29/7.43 [916]~P6(a1,x9161,x9162)+P6(a1,f18(a1,x9161),f18(a1,x9162))
% 7.29/7.43 [917]~P7(a1,x9171,x9172)+P7(a1,f18(a1,x9171),f18(a1,x9172))
% 7.29/7.43 [936]P6(a1,x9361,x9362)+~P6(a1,f18(a1,x9361),f18(a1,x9362))
% 7.29/7.43 [937]P7(a1,x9371,x9372)+~P7(a39,f18(a39,x9371),f18(a39,x9372))
% 7.29/7.43 [938]P7(a1,x9381,x9382)+~P7(a1,f18(a1,x9381),f18(a1,x9382))
% 7.29/7.43 [1008]~P6(a38,x10081,x10082)+P6(a38,f11(a38,x10081,x10082),f2(a38))
% 7.29/7.43 [1079]P6(a38,x10791,x10792)+~P6(a38,f11(a38,x10791,x10792),f2(a38))
% 7.29/7.43 [1144]~P6(a1,x11441,x11442)+P6(a1,f13(a1,x11441,x11441),f13(a1,x11442,x11442))
% 7.29/7.43 [1149]~P7(a1,x11491,x11492)+P7(a1,f13(a1,x11491,x11491),f13(a1,x11492,x11492))
% 7.29/7.43 [1354]P6(a1,x13541,x13542)+~P6(a1,f13(a1,x13541,x13541),f13(a1,x13542,x13542))
% 7.29/7.43 [1357]P7(a1,x13571,x13572)+~P7(a1,f13(a1,x13571,x13571),f13(a1,x13572,x13572))
% 7.29/7.43 [606]~P37(x6061)+E(f9(a38,f21(x6061,x6062)),f21(x6061,x6062))
% 7.29/7.43 [614]~P19(x6141)+E(f9(x6141,f9(x6141,x6142)),f9(x6141,x6142))
% 7.29/7.43 [617]~P1(x6171)+E(f30(f30(f22(x6171),x6172),f3(a39)),x6172)
% 7.29/7.43 [618]~P28(x6181)+E(f30(f30(f22(x6181),x6182),f3(a39)),x6182)
% 7.29/7.43 [624]~P1(x6241)+E(f30(f30(f12(x6241),x6242),f3(x6241)),x6242)
% 7.29/7.43 [625]~P28(x6251)+E(f30(f30(f12(x6251),x6252),f3(x6251)),x6252)
% 7.29/7.43 [626]~P2(x6261)+E(f30(f30(f12(x6261),x6262),f3(x6261)),x6262)
% 7.29/7.43 [627]~P28(x6271)+E(f30(f30(f22(x6271),x6272),f2(a39)),f3(x6271))
% 7.29/7.43 [628]~P35(x6281)+E(f30(f30(f22(x6281),x6282),f2(a39)),f3(x6281))
% 7.29/7.43 [630]~P28(x6301)+E(f13(x6301,x6302,f2(x6301)),x6302)
% 7.29/7.43 [631]~P16(x6311)+E(f13(x6311,x6312,f2(x6311)),x6312)
% 7.29/7.43 [632]~P10(x6321)+E(f13(x6321,x6322,f2(x6321)),x6322)
% 7.29/7.43 [633]~P15(x6331)+E(f11(x6331,x6332,f2(x6331)),x6332)
% 7.29/7.43 [634]~P44(x6341)+E(f25(x6341,x6342,f3(x6341)),x6342)
% 7.29/7.43 [635]~P28(x6351)+E(f13(x6351,f2(x6351),x6352),x6352)
% 7.29/7.43 [636]~P16(x6361)+E(f13(x6361,f2(x6361),x6362),x6362)
% 7.29/7.43 [637]~P10(x6371)+E(f13(x6371,f2(x6371),x6372),x6372)
% 7.29/7.43 [641]~P28(x6411)+E(f30(f30(f12(x6411),x6412),f2(x6411)),f2(x6411))
% 7.29/7.43 [642]~P52(x6421)+E(f30(f30(f12(x6421),x6422),f2(x6421)),f2(x6421))
% 7.29/7.43 [644]~P39(x6441)+E(f30(f30(f12(x6441),x6442),f2(x6441)),f2(x6441))
% 7.29/7.43 [648]~P45(x6481)+E(f25(x6481,x6482,f2(x6481)),f2(x6481))
% 7.29/7.43 [649]~P44(x6491)+E(f25(x6491,f2(x6491),x6492),f2(x6491))
% 7.29/7.43 [650]~P42(x6501)+E(f25(x6501,f2(x6501),x6502),f2(x6501))
% 7.29/7.43 [680]~P29(x6801)+E(f13(x6801,x6802,f18(x6801,a14)),x6802)
% 7.29/7.43 [681]~P29(x6811)+E(f13(x6811,f18(x6811,a14),x6812),x6812)
% 7.29/7.43 [773]E(x7731,x7732)+~E(f30(x7731,f28(x7732,x7731)),f30(x7732,f28(x7732,x7731)))
% 7.29/7.43 [800]P7(a39,f2(a39),x8001)+~E(x8001,f13(a39,x8002,f3(a39)))
% 7.29/7.43 [866]~P6(a39,x8661,x8662)+E(f13(a39,x8661,f32(x8662,x8661)),x8662)
% 7.29/7.43 [867]~P6(a39,x8671,x8672)+E(f13(a39,x8671,f34(x8672,x8671)),x8672)
% 7.29/7.43 [870]~E(x8701,x8702)+P7(a39,x8701,f13(a39,x8702,f3(a39)))
% 7.29/7.43 [874]~E(x8741,f2(a39))+P7(a39,x8741,f13(a39,x8742,f3(a39)))
% 7.29/7.43 [906]~P48(x9061)+P7(x9061,x9062,f13(x9061,x9062,f3(x9061)))
% 7.29/7.43 [944]P7(a39,x9441,x9442)+P7(a39,x9442,f13(a39,x9441,f3(a39)))
% 7.29/7.43 [945]P6(a39,x9451,x9452)+P6(a39,f13(a39,x9452,f3(a39)),x9451)
% 7.29/7.43 [1005]~P6(a39,x10051,x10052)+E(f13(a39,x10051,f11(a39,x10052,x10051)),x10052)
% 7.29/7.43 [1006]~P6(a39,x10062,x10061)+E(f11(a39,x10061,f11(a39,x10061,x10062)),x10062)
% 7.29/7.43 [1007]~P6(a39,x10072,x10071)+E(f13(a39,f11(a39,x10071,x10072),x10072),x10071)
% 7.29/7.43 [1012]~P6(a39,x10121,x10122)+P7(a39,x10121,f13(a39,x10122,f3(a39)))
% 7.29/7.43 [1017]~P7(a39,x10171,x10172)+P6(a39,f13(a39,x10171,f3(a39)),x10172)
% 7.29/7.43 [1068]~P7(a39,x10681,x10682)+E(f13(a39,f13(a39,x10681,f36(x10682,x10681)),f3(a39)),x10682)
% 7.29/7.43 [1082]P6(a39,x10821,x10822)+~P7(a39,x10821,f13(a39,x10822,f3(a39)))
% 7.29/7.43 [1086]P7(a39,x10861,x10862)+~P6(a39,f13(a39,x10861,f3(a39)),x10862)
% 7.29/7.43 [1133]~P7(a39,x11331,x11332)+~P7(a39,x11332,f13(a39,x11331,f3(a39)))
% 7.29/7.43 [1134]~P6(a39,x11341,x11342)+~P6(a39,f13(a39,x11342,f3(a39)),x11341)
% 7.29/7.43 [1219]~P29(x12191)+E(f13(x12191,f13(x12191,f2(x12191),f18(x12191,x12192)),f18(x12191,x12192)),f18(x12191,f13(a1,x12192,x12192)))
% 7.29/7.43 [1292]E(x12921,f2(a39))+E(f13(a39,f13(a39,f11(a39,x12921,f3(a39)),x12922),f3(a39)),f13(a39,x12921,x12922))
% 7.29/7.43 [1358]~P29(x13581)+E(f30(f30(f12(x13581),f13(x13581,f3(x13581),f3(x13581))),f18(x13581,x13582)),f18(x13581,f13(a1,x13582,x13582)))
% 7.29/7.43 [1362]P6(a39,x13621,x13622)+~P6(a39,f13(a39,x13621,f3(a39)),f13(a39,x13622,f3(a39)))
% 7.29/7.43 [1364]P7(a39,x13641,x13642)+~P7(a39,f13(a39,x13641,f3(a39)),f13(a39,x13642,f3(a39)))
% 7.29/7.43 [594]~E(x5942,f2(a39))+E(f30(f30(f12(a39),x5941),x5942),f2(a39))
% 7.29/7.43 [596]~E(x5961,f2(a39))+E(f30(f30(f12(a39),x5961),x5962),f2(a39))
% 7.29/7.43 [597]~E(x5972,f2(a39))+E(f30(f30(f22(a39),x5971),x5972),f3(a39))
% 7.29/7.43 [653]~P1(x6531)+E(f30(f30(f12(x6531),f3(x6531)),x6532),x6532)
% 7.29/7.43 [654]~P28(x6541)+E(f30(f30(f12(x6541),f3(x6541)),x6542),x6542)
% 7.29/7.43 [655]~P2(x6551)+E(f30(f30(f12(x6551),f3(x6551)),x6552),x6552)
% 7.29/7.43 [664]~P28(x6641)+E(f30(f30(f12(x6641),f2(x6641)),x6642),f2(x6641))
% 7.29/7.43 [665]~P52(x6651)+E(f30(f30(f12(x6651),f2(x6651)),x6652),f2(x6651))
% 7.29/7.43 [667]~P39(x6671)+E(f30(f30(f12(x6671),f2(x6671)),x6672),f2(x6671))
% 7.29/7.43 [668]~P1(x6681)+E(f30(f30(f22(x6681),f3(x6681)),x6682),f3(x6681))
% 7.29/7.43 [674]E(x6741,f3(a39))+~E(f30(f30(f12(a39),x6742),x6741),f3(a39))
% 7.29/7.43 [675]E(x6751,f3(a39))+~E(f30(f30(f12(a39),x6751),x6752),f3(a39))
% 7.29/7.43 [746]~E(x7462,f2(a39))+E(f30(f30(f22(a39),x7461),x7462),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [880]~P50(x8801)+P6(x8801,f2(x8801),f30(f30(f12(x8801),x8802),x8802))
% 7.29/7.43 [924]~P27(x9241)+E(f30(f30(f12(x9241),f9(x9241,x9242)),f9(x9241,x9242)),f30(f30(f12(x9241),x9242),x9242))
% 7.29/7.43 [928]~E(x9281,f13(a39,f2(a39),f3(a39)))+E(f30(f30(f22(a39),x9281),x9282),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [953]E(x9531,f13(a39,f2(a39),f3(a39)))+~E(f30(f30(f12(a39),x9532),x9531),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [954]E(x9541,f13(a39,f2(a39),f3(a39)))+~E(f30(f30(f12(a39),x9541),x9542),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [975]~P6(a1,f2(a1),x9751)+P6(a1,f2(a1),f30(f30(f22(a1),x9751),x9752))
% 7.29/7.43 [1036]~P50(x10361)+~P7(x10361,f30(f30(f12(x10361),x10362),x10362),f2(x10361))
% 7.29/7.43 [1053]P7(a39,f2(a39),x10531)+~P7(a39,f2(a39),f30(f30(f12(a39),x10532),x10531))
% 7.29/7.43 [1054]P7(a39,f2(a39),x10541)+~P7(a39,f2(a39),f30(f30(f12(a39),x10541),x10542))
% 7.29/7.43 [1411]E(x14111,x14112)+~E(f13(a1,f13(a1,f3(a1),x14111),x14111),f13(a1,f13(a1,f3(a1),x14112),x14112))
% 7.29/7.43 [1437]~P6(a39,f13(a39,f2(a39),f3(a39)),x14371)+P6(a39,f13(a39,f2(a39),f3(a39)),f30(f30(f22(a39),x14371),x14372))
% 7.29/7.43 [1474]~P6(a1,x14741,x14742)+P6(a1,f13(a1,x14741,x14741),f13(a1,f13(a1,f3(a1),x14742),x14742))
% 7.29/7.43 [1476]~P7(a1,x14761,x14762)+P7(a1,f13(a1,f13(a1,f3(a1),x14761),x14761),f13(a1,x14762,x14762))
% 7.29/7.43 [1506]P6(a39,f13(a39,f2(a39),f3(a39)),x15061)+~P6(a39,f13(a39,f2(a39),f3(a39)),f30(f30(f12(a39),x15062),x15061))
% 7.29/7.43 [1507]P6(a39,f13(a39,f2(a39),f3(a39)),x15071)+~P6(a39,f13(a39,f2(a39),f3(a39)),f30(f30(f12(a39),x15071),x15072))
% 7.29/7.43 [1508]~P65(x15081)+E(f30(f30(f12(x15081),f13(x15081,x15082,f3(x15081))),f11(x15081,x15082,f3(x15081))),f11(x15081,f30(f30(f12(x15081),x15082),x15082),f3(x15081)))
% 7.29/7.43 [1619]~P6(a1,x16191,x16192)+P6(a1,f13(a1,f13(a1,f3(a1),x16191),x16191),f13(a1,f13(a1,f3(a1),x16192),x16192))
% 7.29/7.43 [1621]~P7(a1,x16211,x16212)+P7(a1,f13(a1,f13(a1,f3(a1),x16211),x16211),f13(a1,f13(a1,f3(a1),x16212),x16212))
% 7.29/7.43 [1624]P6(a1,x16241,x16242)+~P6(a1,f13(a1,x16241,x16241),f13(a1,f13(a1,f3(a1),x16242),x16242))
% 7.29/7.43 [1626]P7(a1,x16261,x16262)+~P7(a1,f13(a1,f13(a1,f3(a1),x16261),x16261),f13(a1,x16262,x16262))
% 7.29/7.43 [1670]P6(a1,x16701,x16702)+~P6(a1,f13(a1,f13(a1,f3(a1),x16701),x16701),f13(a1,f13(a1,f3(a1),x16702),x16702))
% 7.29/7.43 [1672]P7(a1,x16721,x16722)+~P7(a1,f13(a1,f13(a1,f3(a1),x16721),x16721),f13(a1,f13(a1,f3(a1),x16722),x16722))
% 7.29/7.43 [1751]~P29(x17511)+E(f30(f30(f22(x17511),f18(x17511,a15)),f13(a39,f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17512),f3(a39))),f18(x17511,a15))
% 7.29/7.43 [900]E(f9(a1,x9001),f3(a1))+~E(f9(a1,f30(f30(f12(a1),x9001),x9002)),f3(a1))
% 7.29/7.43 [1216]E(x12161,f2(a38))+~E(f13(a38,f30(f30(f12(a38),x12162),x12162),f30(f30(f12(a38),x12161),x12161)),f2(a38))
% 7.29/7.43 [1217]E(x12171,f2(a38))+~E(f13(a38,f30(f30(f12(a38),x12171),x12171),f30(f30(f12(a38),x12172),x12172)),f2(a38))
% 7.29/7.43 [1218]~P28(x12181)+E(f13(x12181,x12182,x12182),f30(f30(f12(x12181),f13(x12181,f3(x12181),f3(x12181))),x12182))
% 7.29/7.43 [1256]E(x12561,f2(a39))+E(f30(f30(f12(a39),x12562),f30(f30(f22(a39),x12562),f11(a39,x12561,f3(a39)))),f30(f30(f22(a39),x12562),x12561))
% 7.29/7.43 [1517]~P29(x15171)+E(f13(x15171,f13(x15171,f3(x15171),f18(x15171,x15172)),f18(x15171,x15172)),f18(x15171,f13(a1,f13(a1,f3(a1),x15172),x15172)))
% 7.29/7.43 [1531]E(x15311,f2(a39))+E(f13(a39,x15312,f30(f30(f12(a39),f11(a39,x15311,f3(a39))),x15312)),f30(f30(f12(a39),x15311),x15312))
% 7.29/7.43 [1574]~P29(x15741)+E(f30(f30(f12(x15741),x15742),f18(x15741,f13(a1,f13(a1,f3(a1),a14),a14))),x15742)
% 7.29/7.43 [1639]~P29(x16391)+E(f13(x16391,f3(x16391),f18(x16391,x16392)),f18(x16391,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),x16392)))
% 7.29/7.43 [1640]~P29(x16401)+E(f13(x16401,f18(x16401,x16402),f3(x16401)),f18(x16401,f13(a1,x16402,f13(a1,f13(a1,f3(a1),a14),a14))))
% 7.29/7.43 [1685]~P29(x16851)+E(f30(f30(f12(x16851),f18(x16851,f13(a1,f13(a1,f3(a1),a14),a14))),x16852),x16852)
% 7.29/7.43 [1709]~P28(x17091)+E(f30(f30(f12(x17091),x17092),x17092),f30(f30(f22(x17091),x17092),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [1710]~P1(x17101)+E(f30(f30(f22(x17101),x17102),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f12(x17101),x17102),x17102))
% 7.29/7.43 [1711]~P29(x17111)+E(f30(f30(f12(x17111),x17112),f18(x17111,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f13(x17111,x17112,x17112))
% 7.29/7.43 [1720]~P1(x17201)+E(f30(f30(f22(x17201),x17202),f18(a39,f13(a1,f13(a1,f3(a1),f13(a1,f13(a1,f3(a1),a14),a14)),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f12(x17201),f30(f30(f12(x17201),x17202),x17202)),x17202))
% 7.29/7.43 [1722]~P27(x17221)+E(f30(f30(f22(x17221),f9(x17221,x17222)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17221),x17222),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [1723]~P27(x17231)+P6(x17231,f2(x17231),f30(f30(f22(x17231),x17232),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [1730]~P7(a38,x17301,x17302)+P7(a38,x17301,f25(a38,f13(a38,x17301,x17302),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [1731]~P7(a38,x17311,x17312)+P7(a38,f25(a38,f13(a38,x17311,x17312),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17312)
% 7.29/7.43 [1733]~P27(x17331)+~P7(x17331,f30(f30(f22(x17331),x17332),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f2(x17331))
% 7.29/7.43 [1721]~P29(x17211)+E(f30(f30(f12(x17211),f18(x17211,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17212),f13(x17211,x17212,x17212))
% 7.29/7.43 [1732]~P27(x17321)+E(f9(x17321,f30(f30(f22(x17321),x17322),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f30(f30(f22(x17321),x17322),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [1743]E(x17431,f2(a38))+~E(f13(a38,f30(f30(f22(a38),x17432),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x17431),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(a38))
% 7.29/7.43 [1744]E(x17441,f2(a38))+~E(f13(a38,f30(f30(f22(a38),x17441),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x17442),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(a38))
% 7.29/7.43 [1737]~P29(x17371)+E(f30(f30(f22(x17371),f18(x17371,a15)),f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17372)),f3(x17371))
% 7.29/7.43 [1760]E(x17601,f2(a38))+~E(f17(f13(a38,f30(f30(f22(a38),x17602),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x17601),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),x17602)
% 7.29/7.43 [1761]E(x17611,f2(a38))+~E(f17(f13(a38,f30(f30(f22(a38),x17611),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x17612),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),x17612)
% 7.29/7.43 [590]~E(f4(x5902,x5901),f18(a16,x5903))+E(x5901,f2(a38))
% 7.29/7.43 [599]E(x5991,f18(a38,x5992))+~E(f4(x5991,x5993),f18(a16,x5992))
% 7.29/7.43 [750]~P28(x7501)+E(f13(x7501,x7502,x7503),f13(x7501,x7503,x7502))
% 7.29/7.43 [787]P6(a39,x7871,x7872)+~E(x7872,f13(a39,x7871,x7873))
% 7.29/7.43 [871]E(x8711,x8712)+~E(f13(a39,x8713,x8711),f13(a39,x8713,x8712))
% 7.29/7.43 [872]E(x8721,x8722)+~E(f13(a39,x8721,x8723),f13(a39,x8722,x8723))
% 7.29/7.43 [995]~P6(a39,x9951,x9953)+P6(a39,x9951,f13(a39,x9952,x9953))
% 7.29/7.43 [996]~P6(a39,x9961,x9962)+P6(a39,x9961,f13(a39,x9962,x9963))
% 7.29/7.43 [997]~P7(a39,x9971,x9973)+P7(a39,x9971,f13(a39,x9972,x9973))
% 7.29/7.43 [998]~P7(a39,x9981,x9982)+P7(a39,x9981,f13(a39,x9982,x9983))
% 7.29/7.43 [999]~P7(a39,x9991,x9993)+P7(a39,f11(a39,x9991,x9992),x9993)
% 7.29/7.43 [1073]P6(a39,x10731,x10732)+~P6(a39,f13(a39,x10733,x10731),x10732)
% 7.29/7.43 [1074]P6(a39,x10741,x10742)+~P6(a39,f13(a39,x10741,x10743),x10742)
% 7.29/7.43 [1075]P7(a39,x10751,x10752)+~P7(a39,f13(a39,x10751,x10753),x10752)
% 7.29/7.43 [1137]~P6(a38,x11372,x11373)+P6(a38,f13(a38,x11371,x11372),f13(a38,x11371,x11373))
% 7.29/7.43 [1138]~P6(a39,x11382,x11383)+P6(a39,f13(a39,x11381,x11382),f13(a39,x11381,x11383))
% 7.29/7.43 [1139]~P6(a39,x11391,x11393)+P6(a39,f13(a39,x11391,x11392),f13(a39,x11393,x11392))
% 7.29/7.43 [1140]~P6(a39,x11403,x11402)+P6(a39,f11(a39,x11401,x11402),f11(a39,x11401,x11403))
% 7.29/7.43 [1141]~P6(a39,x11411,x11413)+P6(a39,f11(a39,x11411,x11412),f11(a39,x11413,x11412))
% 7.29/7.43 [1142]~P6(a1,x11422,x11423)+P6(a1,f13(a1,x11421,x11422),f13(a1,x11421,x11423))
% 7.29/7.43 [1145]~P7(a39,x11452,x11453)+P7(a39,f13(a39,x11451,x11452),f13(a39,x11451,x11453))
% 7.29/7.43 [1146]~P7(a39,x11461,x11463)+P7(a39,f13(a39,x11461,x11462),f13(a39,x11463,x11462))
% 7.29/7.43 [1147]~P7(a1,x11471,x11473)+P7(a1,f13(a1,x11471,x11472),f13(a1,x11473,x11472))
% 7.29/7.43 [1254]~P6(a39,f11(a39,x12541,x12543),x12542)+P6(a39,x12541,f13(a39,x12542,x12543))
% 7.29/7.43 [1255]~P6(a39,x12551,f13(a39,x12553,x12552))+P6(a39,f11(a39,x12551,x12552),x12553)
% 7.29/7.43 [1352]P6(a39,x13521,x13522)+~P6(a39,f13(a39,x13523,x13521),f13(a39,x13523,x13522))
% 7.29/7.43 [1355]P7(a39,x13551,x13552)+~P7(a39,f13(a39,x13553,x13551),f13(a39,x13553,x13552))
% 7.29/7.43 [875]~P15(x8751)+E(f13(x8751,f11(x8751,x8752,x8753),x8753),x8752)
% 7.29/7.43 [876]~P15(x8761)+E(f11(x8761,f13(x8761,x8762,x8763),x8763),x8762)
% 7.29/7.43 [962]~P29(x9621)+E(f11(x9621,f18(x9621,x9622),f18(x9621,x9623)),f18(x9621,f11(a1,x9622,x9623)))
% 7.29/7.43 [963]~P29(x9631)+E(f13(x9631,f18(x9631,x9632),f18(x9631,x9633)),f18(x9631,f13(a1,x9632,x9633)))
% 7.29/7.43 [966]~P8(x9661)+E(f25(x9661,f9(x9661,x9662),f9(x9661,x9663)),f9(x9661,f25(x9661,x9662,x9663)))
% 7.29/7.43 [1023]~P19(x10231)+E(f9(x10231,f11(x10231,x10232,x10233)),f9(x10231,f11(x10231,x10233,x10232)))
% 7.29/7.43 [1024]~P37(x10241)+E(f21(x10241,f11(x10241,x10242,x10243)),f21(x10241,f11(x10241,x10243,x10242)))
% 7.29/7.43 [1080]P7(a39,x10801,x10802)+~E(x10802,f13(a39,f13(a39,x10801,x10803),f3(a39)))
% 7.29/7.43 [1249]~P6(a39,x12492,x12493)+E(f11(a39,f13(a39,x12491,x12492),x12493),f11(a39,x12491,f11(a39,x12493,x12492)))
% 7.29/7.43 [1250]~P6(a39,x12503,x12502)+E(f11(a39,f13(a39,x12501,x12502),x12503),f13(a39,x12501,f11(a39,x12502,x12503)))
% 7.29/7.43 [1252]~P6(a39,x12523,x12521)+E(f11(a39,f13(a39,x12521,x12522),x12523),f13(a39,f11(a39,x12521,x12523),x12522))
% 7.29/7.43 [1314]~P6(a39,x13143,x13142)+P6(a39,x13141,f11(a39,f13(a39,x13142,x13141),x13143))
% 7.29/7.43 [1381]~P37(x13811)+P6(a38,f21(x13811,f13(x13811,x13812,x13813)),f13(a38,f21(x13811,x13812),f21(x13811,x13813)))
% 7.29/7.43 [1382]~P37(x13821)+P6(a38,f21(x13821,f11(x13821,x13822,x13823)),f13(a38,f21(x13821,x13822),f21(x13821,x13823)))
% 7.29/7.43 [1383]~P37(x13831)+P6(a38,f11(a38,f21(x13831,x13832),f21(x13831,x13833)),f21(x13831,f13(x13831,x13832,x13833)))
% 7.29/7.43 [1384]~P37(x13841)+P6(a38,f11(a38,f21(x13841,x13842),f21(x13841,x13843)),f21(x13841,f11(x13841,x13842,x13843)))
% 7.29/7.43 [1406]~P19(x14061)+P6(x14061,f9(x14061,f13(x14061,x14062,x14063)),f13(x14061,f9(x14061,x14062),f9(x14061,x14063)))
% 7.29/7.43 [1407]~P19(x14071)+P6(x14071,f9(x14071,f11(x14071,x14072,x14073)),f13(x14071,f9(x14071,x14072),f9(x14071,x14073)))
% 7.29/7.43 [1408]~P19(x14081)+P6(x14081,f11(x14081,f9(x14081,x14082),f9(x14081,x14083)),f9(x14081,f11(x14081,x14083,x14082)))
% 7.29/7.43 [1409]~P19(x14091)+P6(x14091,f11(x14091,f9(x14091,x14092),f9(x14091,x14093)),f9(x14091,f11(x14091,x14092,x14093)))
% 7.29/7.43 [721]~E(x7212,f2(a39))+E(f30(f30(f12(a39),x7211),x7212),f30(f30(f12(a39),x7213),x7212))
% 7.29/7.43 [723]~E(x7231,f2(a39))+E(f30(f30(f12(a39),x7231),x7232),f30(f30(f12(a39),x7231),x7233))
% 7.29/7.43 [747]~P28(x7471)+E(f30(f30(f12(x7471),x7472),x7473),f30(f30(f12(x7471),x7473),x7472))
% 7.29/7.43 [1049]~P27(x10491)+P6(x10491,f2(x10491),f30(f30(f22(x10491),f9(x10491,x10492)),x10493))
% 7.29/7.43 [1093]~P6(a39,x10932,x10933)+P6(a39,f30(f30(f12(a39),x10931),x10932),f30(f30(f12(a39),x10931),x10933))
% 7.29/7.43 [1094]~P6(a39,x10941,x10943)+P6(a39,f30(f30(f12(a39),x10941),x10942),f30(f30(f12(a39),x10943),x10942))
% 7.29/7.43 [1129]~P19(x11291)+E(f9(x11291,f13(x11291,f9(x11291,x11292),f9(x11291,x11293))),f13(x11291,f9(x11291,x11292),f9(x11291,x11293)))
% 7.29/7.43 [1273]P7(a39,x12731,x12732)+~P7(a39,f30(f30(f12(a39),x12733),x12731),f30(f30(f12(a39),x12733),x12732))
% 7.29/7.43 [1274]P7(a39,x12741,x12742)+~P7(a39,f30(f30(f12(a39),x12741),x12743),f30(f30(f12(a39),x12742),x12743))
% 7.29/7.43 [1277]P7(a39,f2(a39),x12771)+~P7(a39,f30(f30(f12(a39),x12772),x12771),f30(f30(f12(a39),x12773),x12771))
% 7.29/7.43 [1278]P7(a39,f2(a39),x12781)+~P7(a39,f30(f30(f12(a39),x12781),x12782),f30(f30(f12(a39),x12781),x12783))
% 7.29/7.43 [1575]~P6(a39,x15752,x15753)+E(f11(a39,f13(a39,x15751,x15752),f13(a39,x15753,f3(a39))),f11(a39,x15751,f13(a39,f11(a39,x15753,x15752),f3(a39))))
% 7.29/7.43 [1576]~P6(a39,x15762,x15761)+E(f11(a39,f13(a39,f11(a39,x15761,x15762),f3(a39)),x15763),f11(a39,f13(a39,x15761,f3(a39)),f13(a39,x15762,x15763)))
% 7.29/7.43 [1587]~P37(x15871)+P6(a38,f9(a38,f11(a38,f21(x15871,x15872),f21(x15871,x15873))),f21(x15871,f11(x15871,x15872,x15873)))
% 7.29/7.43 [1596]~P19(x15961)+P6(x15961,f9(x15961,f11(x15961,f9(x15961,x15962),f9(x15961,x15963))),f9(x15961,f11(x15961,x15962,x15963)))
% 7.29/7.43 [950]~P41(x9501)+E(f21(x9501,f30(f30(f22(x9501),x9502),x9503)),f30(f30(f22(a38),f21(x9501,x9502)),x9503))
% 7.29/7.43 [956]~P27(x9561)+E(f30(f30(f22(x9561),f9(x9561,x9562)),x9563),f9(x9561,f30(f30(f22(x9561),x9562),x9563)))
% 7.29/7.43 [1004]~P29(x10041)+E(f30(f30(f12(x10041),f18(x10041,x10042)),f18(x10041,x10043)),f18(x10041,f30(f30(f12(a1),x10042),x10043)))
% 7.29/7.43 [1018]~P41(x10181)+E(f30(f30(f12(a38),f21(x10181,x10182)),f21(x10181,x10183)),f21(x10181,f30(f30(f12(x10181),x10182),x10183)))
% 7.29/7.43 [1027]~P27(x10271)+E(f30(f30(f12(x10271),f9(x10271,x10272)),f9(x10271,x10273)),f9(x10271,f30(f30(f12(x10271),x10272),x10273)))
% 7.29/7.43 [1102]~P28(x11021)+E(f30(f30(f12(x11021),x11022),f30(f30(f22(x11021),x11022),x11023)),f30(f30(f22(x11021),x11022),f13(a39,x11023,f3(a39))))
% 7.29/7.43 [1103]~P35(x11031)+E(f30(f30(f12(x11031),x11032),f30(f30(f22(x11031),x11032),x11033)),f30(f30(f22(x11031),x11032),f13(a39,x11033,f3(a39))))
% 7.29/7.43 [1337]~P28(x13371)+E(f13(x13371,x13372,f30(f30(f12(x13371),x13373),x13372)),f30(f30(f12(x13371),f13(x13371,x13373,f3(x13371))),x13372))
% 7.29/7.43 [1338]~P28(x13381)+E(f13(x13381,f30(f30(f12(x13381),x13382),x13383),x13383),f30(f30(f12(x13381),f13(x13381,x13382,f3(x13381))),x13383))
% 7.29/7.43 [1347]~P4(x13471)+E(f25(x13471,f3(x13471),f30(f30(f22(x13471),x13472),x13473)),f30(f30(f22(x13471),f25(x13471,f3(x13471),x13472)),x13473))
% 7.29/7.43 [1373]~P38(x13731)+P6(a38,f21(x13731,f30(f30(f22(x13731),x13732),x13733)),f30(f30(f22(a38),f21(x13731,x13732)),x13733))
% 7.29/7.43 [1454]~P39(x14541)+P6(a38,f21(x14541,f30(f30(f12(x14541),x14542),x14543)),f30(f30(f12(a38),f21(x14541,x14542)),f21(x14541,x14543)))
% 7.29/7.43 [1510]~P50(x15101)+P6(x15101,f2(x15101),f13(x15101,f30(f30(f12(x15101),x15102),x15102),f30(f30(f12(x15101),x15103),x15103)))
% 7.29/7.43 [1638]E(x16381,x16382)+~E(f30(f30(f12(a39),f13(a39,x16383,f3(a39))),x16381),f30(f30(f12(a39),f13(a39,x16383,f3(a39))),x16382))
% 7.29/7.43 [1642]~P50(x16421)+~P7(x16421,f13(x16421,f30(f30(f12(x16421),x16422),x16422),f30(f30(f12(x16421),x16423),x16423)),f2(x16421))
% 7.29/7.43 [1687]P6(a39,x16871,x16872)+~P6(a39,f30(f30(f12(a39),f13(a39,x16873,f3(a39))),x16871),f30(f30(f12(a39),f13(a39,x16873,f3(a39))),x16872))
% 7.29/7.43 [1690]~P36(x16901)+E(f11(x16901,f30(f30(f22(x16901),x16902),f13(a39,f13(a39,f2(a39),f3(a39)),f3(a39))),f30(f30(f22(x16901),x16903),f13(a39,f13(a39,f2(a39),f3(a39)),f3(a39)))),f30(f30(f12(x16901),f11(x16901,x16902,x16903)),f13(x16901,x16902,x16903)))
% 7.29/7.43 [1272]~P1(x12721)+E(f30(f30(f12(x12721),f30(f30(f22(x12721),x12722),x12723)),x12722),f30(f30(f12(x12721),x12722),f30(f30(f22(x12721),x12722),x12723)))
% 7.29/7.43 [1285]~P1(x12851)+E(f30(f30(f12(x12851),f30(f30(f22(x12851),x12852),x12853)),x12852),f30(f30(f22(x12851),x12852),f13(a39,x12853,f3(a39))))
% 7.29/7.43 [1286]~P28(x12861)+E(f30(f30(f12(x12861),f30(f30(f22(x12861),x12862),x12863)),x12862),f30(f30(f22(x12861),x12862),f13(a39,x12863,f3(a39))))
% 7.29/7.43 [1757]~P28(x17571)+E(f30(f30(f22(x17571),x17572),f13(a39,f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17573),f3(a39))),f30(f30(f12(x17571),x17572),f30(f30(f12(x17571),f30(f30(f22(x17571),x17572),x17573)),f30(f30(f22(x17571),x17572),x17573))))
% 7.29/7.43 [1752]~P27(x17521)+P6(x17521,f2(x17521),f13(x17521,f30(f30(f22(x17521),x17522),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17521),x17523),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))
% 7.29/7.43 [1758]~P1(x17581)+E(f30(f30(f12(x17581),x17582),f30(f30(f22(x17581),f30(f30(f22(x17581),x17582),x17583)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f30(f30(f22(x17581),x17582),f13(a39,f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17583),f3(a39))))
% 7.29/7.43 [1762]~P27(x17621)+~P7(x17621,f13(x17621,f30(f30(f22(x17621),x17622),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17621),x17623),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(x17621))
% 7.29/7.43 [1741]~P28(x17411)+E(f30(f30(f22(x17411),x17412),f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17413)),f30(f30(f12(x17411),f30(f30(f22(x17411),x17412),x17413)),f30(f30(f22(x17411),x17412),x17413)))
% 7.29/7.43 [1742]~P1(x17421)+E(f30(f30(f22(x17421),f30(f30(f22(x17421),x17422),x17423)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17421),x17422),f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17423)))
% 7.29/7.43 [1749]~E(f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17491),f25(a38,x17492,x17493))+E(x17491,f25(a38,x17492,f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17493)))
% 7.29/7.43 [1750]~P27(x17501)+P6(x17501,f2(x17501),f30(f30(f22(x17501),x17502),f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17503)))
% 7.29/7.43 [1756]E(f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17561),f25(a38,x17562,x17563))+~E(x17561,f25(a38,x17562,f30(f30(f12(a38),f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17563)))
% 7.29/7.43 [1768]~P29(x17681)+E(f13(x17681,f13(x17681,f30(f30(f22(x17681),x17682),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17681),x17683),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f30(f30(f12(x17681),f30(f30(f12(x17681),f18(x17681,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17682)),x17683)),f30(f30(f22(x17681),f13(x17681,x17682,x17683)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [1769]~P29(x17691)+E(f11(x17691,f13(x17691,f30(f30(f22(x17691),x17692),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17691),x17693),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f30(f30(f12(x17691),f30(f30(f12(x17691),f18(x17691,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17692)),x17693)),f30(f30(f22(x17691),f11(x17691,x17692,x17693)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [591]E(x5911,x5912)+~E(f4(x5913,x5911),f4(x5914,x5912))
% 7.29/7.43 [592]E(x5921,x5922)+~E(f4(x5921,x5923),f4(x5922,x5924))
% 7.29/7.43 [1111]~P28(x11111)+E(f13(x11111,x11112,f13(x11111,x11113,x11114)),f13(x11111,x11113,f13(x11111,x11112,x11114)))
% 7.29/7.43 [1113]~P28(x11131)+E(f13(x11131,f13(x11131,x11132,x11133),x11134),f13(x11131,x11132,f13(x11131,x11133,x11134)))
% 7.29/7.43 [1114]~P12(x11141)+E(f13(x11141,f13(x11141,x11142,x11143),x11144),f13(x11141,x11142,f13(x11141,x11143,x11144)))
% 7.29/7.43 [1115]~P28(x11151)+E(f13(x11151,f13(x11151,x11152,x11153),x11154),f13(x11151,f13(x11151,x11152,x11154),x11153))
% 7.29/7.43 [1293]~P44(x12931)+E(f13(x12931,f25(x12931,x12932,x12933),f25(x12931,x12934,x12933)),f25(x12931,f13(x12931,x12932,x12934),x12933))
% 7.29/7.43 [1294]~P42(x12941)+E(f13(x12941,f25(x12941,x12942,x12943),f25(x12941,x12944,x12943)),f25(x12941,f13(x12941,x12942,x12944),x12943))
% 7.29/7.43 [1295]~P44(x12951)+E(f11(x12951,f25(x12951,x12952,x12953),f25(x12951,x12954,x12953)),f25(x12951,f11(x12951,x12952,x12954),x12953))
% 7.29/7.43 [1296]~P42(x12961)+E(f11(x12961,f25(x12961,x12962,x12963),f25(x12961,x12964,x12963)),f25(x12961,f11(x12961,x12962,x12964),x12963))
% 7.29/7.43 [1452]~P29(x14521)+E(f13(x14521,f18(x14521,x14522),f13(x14521,f18(x14521,x14523),x14524)),f13(x14521,f18(x14521,f13(a1,x14522,x14523)),x14524))
% 7.29/7.43 [1453]~P29(x14531)+E(f13(x14531,f18(x14531,x14532),f11(x14531,f18(x14531,x14533),x14534)),f11(x14531,f18(x14531,f13(a1,x14532,x14533)),x14534))
% 7.29/7.43 [1092]~P28(x10921)+E(f30(f30(f12(x10921),x10922),f30(f30(f12(x10921),x10923),x10924)),f30(f30(f12(x10921),x10923),f30(f30(f12(x10921),x10922),x10924)))
% 7.29/7.43 [1099]~P44(x10991)+E(f25(x10991,f30(f30(f12(x10991),x10992),x10993),x10994),f30(f30(f12(x10991),x10992),f25(x10991,x10993,x10994)))
% 7.29/7.43 [1279]~P28(x12791)+E(f13(x12791,f30(f30(f12(x12791),x12792),x12793),f30(f30(f12(x12791),x12792),x12794)),f30(f30(f12(x12791),x12792),f13(x12791,x12793,x12794)))
% 7.29/7.43 [1281]~P39(x12811)+E(f13(x12811,f30(f30(f12(x12811),x12812),x12813),f30(f30(f12(x12811),x12812),x12814)),f30(f30(f12(x12811),x12812),f13(x12811,x12813,x12814)))
% 7.29/7.43 [1283]~P39(x12831)+E(f11(x12831,f30(f30(f12(x12831),x12832),x12833),f30(f30(f12(x12831),x12832),x12834)),f30(f30(f12(x12831),x12832),f11(x12831,x12833,x12834)))
% 7.29/7.43 [1433]~P1(x14331)+E(f30(f30(f12(x14331),f30(f30(f22(x14331),x14332),x14333)),f30(f30(f22(x14331),x14332),x14334)),f30(f30(f22(x14331),x14332),f13(a39,x14333,x14334)))
% 7.29/7.43 [1434]~P28(x14341)+E(f30(f30(f12(x14341),f30(f30(f22(x14341),x14342),x14343)),f30(f30(f22(x14341),x14342),x14344)),f30(f30(f22(x14341),x14342),f13(a39,x14343,x14344)))
% 7.29/7.43 [1446]~P39(x14461)+E(f13(x14461,f30(f30(f12(x14461),x14462),x14463),f30(f30(f12(x14461),x14464),x14463)),f30(f30(f12(x14461),f13(x14461,x14462,x14464)),x14463))
% 7.29/7.43 [1447]~P43(x14471)+E(f13(x14471,f30(f30(f12(x14471),x14472),x14473),f30(f30(f12(x14471),x14474),x14473)),f30(f30(f12(x14471),f13(x14471,x14472,x14474)),x14473))
% 7.29/7.43 [1449]~P39(x14491)+E(f11(x14491,f30(f30(f12(x14491),x14492),x14493),f30(f30(f12(x14491),x14494),x14493)),f30(f30(f12(x14491),f11(x14491,x14492,x14494)),x14493))
% 7.29/7.43 [1450]~P4(x14501)+E(f25(x14501,f30(f30(f22(x14501),x14502),x14503),f30(f30(f22(x14501),x14504),x14503)),f30(f30(f22(x14501),f25(x14501,x14502,x14504)),x14503))
% 7.29/7.43 [1451]~P28(x14511)+E(f13(x14511,f30(f30(f12(x14511),x14512),x14513),f30(f30(f12(x14511),x14514),x14513)),f30(f30(f12(x14511),f13(x14511,x14512,x14514)),x14513))
% 7.29/7.43 [1265]~P28(x12651)+E(f30(f30(f22(x12651),f30(f30(f22(x12651),x12652),x12653)),x12654),f30(f30(f22(x12651),x12652),f30(f30(f12(a39),x12653),x12654)))
% 7.29/7.43 [1266]~P1(x12661)+E(f30(f30(f22(x12661),f30(f30(f22(x12661),x12662),x12663)),x12664),f30(f30(f22(x12661),x12662),f30(f30(f12(a39),x12663),x12664)))
% 7.29/7.43 [1270]~P28(x12701)+E(f30(f30(f12(x12701),f30(f30(f12(x12701),x12702),x12703)),x12704),f30(f30(f12(x12701),x12702),f30(f30(f12(x12701),x12703),x12704)))
% 7.29/7.43 [1271]~P11(x12711)+E(f30(f30(f12(x12711),f30(f30(f12(x12711),x12712),x12713)),x12714),f30(f30(f12(x12711),x12712),f30(f30(f12(x12711),x12713),x12714)))
% 7.29/7.43 [1432]~P28(x14321)+E(f30(f30(f12(x14321),f30(f30(f12(x14321),x14322),x14323)),x14324),f30(f30(f12(x14321),f30(f30(f12(x14321),x14322),x14324)),x14323))
% 7.29/7.43 [1519]~P28(x15191)+E(f30(f30(f12(x15191),f30(f30(f22(x15191),x15192),x15193)),f30(f30(f22(x15191),x15194),x15193)),f30(f30(f22(x15191),f30(f30(f12(x15191),x15192),x15194)),x15193))
% 7.29/7.43 [1520]~P2(x15201)+E(f30(f30(f12(x15201),f30(f30(f22(x15201),x15202),x15203)),f30(f30(f22(x15201),x15204),x15203)),f30(f30(f22(x15201),f30(f30(f12(x15201),x15202),x15204)),x15203))
% 7.29/7.43 [1613]~P29(x16131)+E(f30(f30(f12(x16131),f18(x16131,x16132)),f30(f30(f12(x16131),f18(x16131,x16133)),x16134)),f30(f30(f12(x16131),f18(x16131,f30(f30(f12(a1),x16132),x16133))),x16134))
% 7.29/7.43 [1467]~P28(x14671)+E(f13(x14671,f13(x14671,x14672,x14673),f13(x14671,x14674,x14675)),f13(x14671,f13(x14671,x14672,x14674),f13(x14671,x14673,x14675)))
% 7.29/7.43 [1468]~P3(x14681)+E(f11(x14681,f13(x14681,x14682,x14683),f13(x14681,x14684,x14685)),f13(x14681,f11(x14681,x14682,x14684),f11(x14681,x14683,x14685)))
% 7.29/7.43 [1691]~P37(x16911)+P6(a38,f21(x16911,f11(x16911,f13(x16911,x16912,x16913),f13(x16911,x16914,x16915))),f13(a38,f21(x16911,f11(x16911,x16912,x16914)),f21(x16911,f11(x16911,x16913,x16915))))
% 7.29/7.43 [1692]~P19(x16921)+P6(x16921,f9(x16921,f11(x16921,f13(x16921,x16922,x16923),f13(x16921,x16924,x16925))),f13(x16921,f9(x16921,f11(x16921,x16922,x16924)),f9(x16921,f11(x16921,x16923,x16925))))
% 7.29/7.43 [1532]~P4(x15321)+E(f25(x15321,f30(f30(f12(x15321),x15322),x15323),f30(f30(f12(x15321),x15324),x15325)),f30(f30(f12(x15321),f25(x15321,x15322,x15324)),f25(x15321,x15323,x15325)))
% 7.29/7.43 [1580]~P28(x15801)+E(f30(f30(f12(x15801),f30(f30(f12(x15801),x15802),x15803)),f30(f30(f12(x15801),x15804),x15805)),f30(f30(f12(x15801),f30(f30(f12(x15801),x15802),x15804)),f30(f30(f12(x15801),x15803),x15805)))
% 7.29/7.43 [1677]~P59(x16771)+E(f13(x16771,f30(f30(f12(x16771),x16772),f11(x16771,x16773,x16774)),f30(f30(f12(x16771),f11(x16771,x16772,x16775)),x16774)),f11(x16771,f30(f30(f12(x16771),x16772),x16773),f30(f30(f12(x16771),x16775),x16774)))
% 7.29/7.43 [1715]~P39(x17151)+E(f13(x17151,f13(x17151,f30(f30(f12(x17151),f11(x17151,x17152,x17153)),f11(x17151,x17154,x17155)),f30(f30(f12(x17151),f11(x17151,x17152,x17153)),x17155)),f30(f30(f12(x17151),x17153),f11(x17151,x17154,x17155))),f11(x17151,f30(f30(f12(x17151),x17152),x17154),f30(f30(f12(x17151),x17153),x17155)))
% 7.29/7.43 [1659]~P51(x16591)+E(f13(x16591,f30(f30(f12(x16591),x16592),x16593),f13(x16591,f30(f30(f12(x16591),x16594),x16593),x16595)),f13(x16591,f30(f30(f12(x16591),f13(x16591,x16592,x16594)),x16593),x16595))
% 7.29/7.43 [1688]~P6(a39,x16881,x16884)+E(f11(a39,f13(a39,f30(f30(f12(a39),x16881),x16882),x16883),f13(a39,f30(f30(f12(a39),x16884),x16882),x16885)),f11(a39,x16883,f13(a39,f30(f30(f12(a39),f11(a39,x16884,x16881)),x16882),x16885)))
% 7.29/7.43 [1689]~P6(a39,x16894,x16891)+E(f11(a39,f13(a39,f30(f30(f12(a39),x16891),x16892),x16893),f13(a39,f30(f30(f12(a39),x16894),x16892),x16895)),f11(a39,f13(a39,f30(f30(f12(a39),f11(a39,x16891,x16894)),x16892),x16893),x16895))
% 7.29/7.43 [1705]~P40(x17051)+E(f13(x17051,f30(f30(f12(x17051),x17052),f25(x17051,f11(x17051,x17053,x17054),x17055)),f30(f30(f12(x17051),f25(x17051,f11(x17051,x17052,x17056),x17055)),x17054)),f25(x17051,f11(x17051,f30(f30(f12(x17051),x17052),x17053),f30(f30(f12(x17051),x17056),x17054)),x17055))
% 7.29/7.43 [598]~P27(x5981)+~P29(x5981)+E(f9(x5981,f18(x5981,a15)),f3(x5981))
% 7.29/7.43 [1554]E(x15541,f2(a39))+E(x15541,f13(a39,f2(a39),f3(a39)))+~P7(a39,x15541,f13(a39,f13(a39,f2(a39),f3(a39)),f3(a39)))
% 7.29/7.43 [1725]~P29(x17251)+~P8(x17251)+P7(x17251,f2(x17251),f25(x17251,f3(x17251),f18(x17251,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.29/7.43 [744]E(x7441,x7442)+P7(a39,x7442,x7441)+P7(a39,x7441,x7442)
% 7.29/7.43 [745]E(x7451,x7452)+P7(a1,x7452,x7451)+P7(a1,x7451,x7452)
% 7.29/7.43 [791]E(x7911,x7912)+P7(a38,x7911,x7912)+~P6(a38,x7911,x7912)
% 7.29/7.43 [794]E(x7941,x7942)+P7(a39,x7941,x7942)+~P6(a39,x7941,x7942)
% 7.29/7.43 [795]E(x7951,x7952)+P7(a1,x7951,x7952)+~P6(a1,x7951,x7952)
% 7.29/7.43 [877]E(x8771,x8772)+~P6(a38,x8772,x8771)+~P6(a38,x8771,x8772)
% 7.29/7.43 [878]E(x8781,x8782)+~P6(a39,x8782,x8781)+~P6(a39,x8781,x8782)
% 7.29/7.43 [879]E(x8791,x8792)+~P6(a1,x8792,x8791)+~P6(a1,x8791,x8792)
% 7.29/7.43 [570]~E(x5702,f3(a38))+~E(x5701,f2(a38))+E(f4(x5701,x5702),a5)
% 7.29/7.43 [573]~E(x5732,f2(a38))+~E(x5731,f3(a38))+E(f4(x5731,x5732),f3(a16))
% 7.29/7.43 [574]~E(x5742,f2(a38))+~E(x5741,f2(a38))+E(f4(x5741,x5742),f2(a16))
% 7.29/7.43 [583]~P37(x5831)+~E(x5832,f2(x5831))+E(f21(x5831,x5832),f2(a38))
% 7.29/7.43 [584]~P19(x5841)+~E(x5842,f2(x5841))+E(f9(x5841,x5842),f2(x5841))
% 7.29/7.43 [588]~P37(x5882)+E(x5881,f2(x5882))+~E(f21(x5882,x5881),f2(a38))
% 7.29/7.43 [589]~P19(x5892)+~E(f9(x5892,x5891),f2(x5892))+E(x5891,f2(x5892))
% 7.29/7.43 [629]~E(x6292,f2(a39))+~E(x6291,f2(a39))+E(f13(a39,x6291,x6292),f2(a39))
% 7.29/7.43 [645]~P44(x6452)+E(f25(x6452,x6451,x6451),f3(x6452))+E(x6451,f2(x6452))
% 7.29/7.43 [646]~P45(x6462)+E(f25(x6462,x6461,x6461),f3(x6462))+E(x6461,f2(x6462))
% 7.29/7.43 [659]~P17(x6591)+~E(x6592,f2(x6591))+E(f13(x6591,x6592,x6592),f2(x6591))
% 7.29/7.43 [660]~P45(x6601)+~E(x6602,f2(x6601))+E(f25(x6601,x6602,x6602),f2(x6601))
% 7.29/7.43 [708]~P37(x7082)+E(x7081,f2(x7082))+P7(a38,f2(a38),f21(x7082,x7081))
% 7.29/7.43 [720]~P37(x7201)+~E(x7202,f2(x7201))+P6(a38,f21(x7201,x7202),f2(a38))
% 7.29/7.43 [724]~P19(x7242)+P7(x7242,f2(x7242),f9(x7242,x7241))+E(x7241,f2(x7242))
% 7.29/7.43 [730]~P19(x7301)+P6(x7301,f9(x7301,x7302),f2(x7301))+~E(x7302,f2(x7301))
% 7.29/7.43 [733]~P17(x7332)+~E(f13(x7332,x7331,x7331),f2(x7332))+E(x7331,f2(x7332))
% 7.29/7.43 [758]~P19(x7581)+~P6(x7581,f2(x7581),x7582)+E(f9(x7581,x7582),x7582)
% 7.29/7.43 [759]~P19(x7591)+~P7(x7591,f2(x7591),x7592)+E(f9(x7591,x7592),x7592)
% 7.29/7.43 [797]~P37(x7972)+E(x7971,f2(x7972))+~P6(a38,f21(x7972,x7971),f2(a38))
% 7.29/7.43 [799]~P37(x7992)+~E(x7991,f2(x7992))+~P7(a38,f2(a38),f21(x7992,x7991))
% 7.29/7.43 [807]~P19(x8072)+~P6(x8072,f9(x8072,x8071),f2(x8072))+E(x8071,f2(x8072))
% 7.29/7.43 [847]~P19(x8472)+~P7(x8472,f2(x8472),f9(x8472,x8471))+~E(x8471,f2(x8472))
% 7.29/7.43 [885]E(x8851,x8852)+~E(f11(a39,x8852,x8851),f2(a39))+~E(f11(a39,x8851,x8852),f2(a39))
% 7.29/7.43 [1032]P6(a1,x10321,x10322)+P6(a1,x10321,a14)+~P6(a39,f18(a39,x10321),f18(a39,x10322))
% 7.29/7.43 [1037]~P7(a1,x10371,x10372)+~P7(a1,a14,x10372)+P7(a39,f18(a39,x10371),f18(a39,x10372))
% 7.29/7.43 [1044]~P17(x10441)+~P6(x10441,f2(x10441),x10442)+P6(x10441,f2(x10441),f13(x10441,x10442,x10442))
% 7.29/7.43 [1045]~P17(x10451)+~P7(x10451,f2(x10451),x10452)+P7(x10451,f2(x10451),f13(x10451,x10452,x10452))
% 7.29/7.43 [1046]~P17(x10461)+~P6(x10461,x10462,f2(x10461))+P6(x10461,f13(x10461,x10462,x10462),f2(x10461))
% 7.29/7.43 [1047]~P27(x10471)+~P7(x10471,x10472,f2(x10471))+P7(x10471,f13(x10471,x10472,x10472),f2(x10471))
% 7.29/7.43 [1048]~P17(x10481)+~P7(x10481,x10482,f2(x10481))+P7(x10481,f13(x10481,x10482,x10482),f2(x10481))
% 7.29/7.43 [1057]~P7(a1,x10572,x10571)+P7(a1,a14,x10571)+~P7(a39,f18(a39,x10572),f18(a39,x10571))
% 7.29/7.43 [1117]~P17(x11171)+~P6(x11171,f13(x11171,x11172,x11172),f2(x11171))+P6(x11171,x11172,f2(x11171))
% 7.29/7.43 [1118]~P27(x11181)+~P7(x11181,f13(x11181,x11182,x11182),f2(x11181))+P7(x11181,x11182,f2(x11181))
% 7.29/7.43 [1119]~P17(x11191)+~P7(x11191,f13(x11191,x11192,x11192),f2(x11191))+P7(x11191,x11192,f2(x11191))
% 7.29/7.43 [1120]~P17(x11201)+~P6(x11201,f2(x11201),f13(x11201,x11202,x11202))+P6(x11201,f2(x11201),x11202)
% 7.29/7.43 [1121]~P17(x11211)+~P7(x11211,f2(x11211),f13(x11211,x11212,x11212))+P7(x11211,f2(x11211),x11212)
% 7.29/7.43 [1124]~P6(a38,x11241,f2(a38))+~P6(a38,x11242,f2(a38))+P6(a38,f2(a38),f25(a38,x11241,x11242))
% 7.29/7.43 [1125]~P6(a38,x11252,f2(a38))+~P6(a38,f2(a38),x11252)+P6(a38,f2(a38),f25(a38,x11251,x11252))
% 7.29/7.43 [1126]~P6(a38,x11261,f2(a38))+~P6(a38,f2(a38),x11261)+P6(a38,f2(a38),f25(a38,x11261,x11262))
% 7.29/7.43 [1127]~P6(a38,f2(a38),x11272)+~P6(a38,f2(a38),x11271)+P6(a38,f2(a38),f25(a38,x11271,x11272))
% 7.29/7.43 [1128]~P6(a1,f2(a1),x11282)+~P6(a1,f2(a1),x11281)+P6(a1,f2(a1),f13(a1,x11281,x11282))
% 7.29/7.43 [1187]P6(a38,x11871,f2(a38))+P6(a38,f2(a38),x11872)+~P6(a38,f2(a38),f25(a38,x11872,x11871))
% 7.29/7.43 [1188]P6(a38,x11881,f2(a38))+P6(a38,f2(a38),x11882)+~P6(a38,f2(a38),f25(a38,x11881,x11882))
% 7.29/7.43 [1189]P7(a39,f2(a39),x11891)+P7(a39,f2(a39),x11892)+~P7(a39,f2(a39),f13(a39,x11892,x11891))
% 7.29/7.43 [695]~P29(x6951)+~P38(x6951)+E(f21(x6951,f18(x6951,x6952)),f9(a38,f18(a38,x6952)))
% 7.29/7.43 [709]~P29(x7091)+~P4(x7091)+E(f25(x7091,x7092,f18(x7091,a14)),f2(x7091))
% 7.29/7.43 [919]E(x9191,f2(a39))+E(x9192,f2(a39))+~E(f13(a39,x9192,x9191),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [920]E(x9201,f2(a39))+E(x9202,f2(a39))+~E(f13(a39,f2(a39),f3(a39)),f13(a39,x9202,x9201))
% 7.29/7.43 [939]~E(x9392,f2(a39))+~E(x9391,f13(a39,f2(a39),f3(a39)))+E(f13(a39,x9391,x9392),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [940]~E(x9401,f2(a39))+~E(x9402,f13(a39,f2(a39),f3(a39)))+E(f13(a39,x9401,x9402),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [941]~E(x9412,f2(a39))+~E(x9411,f13(a39,f2(a39),f3(a39)))+E(f13(a39,f2(a39),f3(a39)),f13(a39,x9411,x9412))
% 7.29/7.43 [942]~E(x9421,f2(a39))+~E(x9422,f13(a39,f2(a39),f3(a39)))+E(f13(a39,f2(a39),f3(a39)),f13(a39,x9421,x9422))
% 7.29/7.43 [989]E(x9891,f2(a39))+E(x9891,f13(a39,f2(a39),f3(a39)))+~E(f13(a39,x9892,x9891),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [990]E(x9901,f2(a39))+E(x9901,f13(a39,f2(a39),f3(a39)))+~E(f13(a39,x9901,x9902),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [991]E(x9911,f2(a39))+E(x9911,f13(a39,f2(a39),f3(a39)))+~E(f13(a39,f2(a39),f3(a39)),f13(a39,x9912,x9911))
% 7.29/7.43 [992]E(x9921,f2(a39))+E(x9921,f13(a39,f2(a39),f3(a39)))+~E(f13(a39,f2(a39),f3(a39)),f13(a39,x9921,x9922))
% 7.29/7.43 [1069]E(x10691,f13(a39,f2(a39),f3(a39)))+E(x10692,f13(a39,f2(a39),f3(a39)))+~E(f13(a39,x10691,x10692),f13(a39,f2(a39),f3(a39)))
% 7.29/7.43 [1070]E(x10701,f13(a39,f2(a39),f3(a39)))+E(x10702,f13(a39,f2(a39),f3(a39)))+~E(f13(a39,f2(a39),f3(a39)),f13(a39,x10701,x10702))
% 7.29/7.43 [1077]~P7(a39,x10771,x10772)+P7(a39,f13(a39,x10771,f3(a39)),x10772)+E(f13(a39,x10771,f3(a39)),x10772)
% 7.29/7.43 [1091]E(x10911,x10912)+P7(a39,x10911,x10912)+~P7(a39,x10911,f13(a39,x10912,f3(a39)))
% 7.29/7.43 [1130]P7(a39,f35(x11302,x11301),x11302)+E(x11301,f2(a39))+~P7(a39,x11301,f13(a39,x11302,f3(a39)))
% 7.29/7.43 [1135]E(x11351,x11352)+~P6(a39,x11352,x11351)+~P7(a39,x11351,f13(a39,x11352,f3(a39)))
% 7.29/7.43 [1136]E(x11361,f2(a39))+~P7(a39,x11361,f13(a39,x11362,f3(a39)))+E(f13(a39,f35(x11362,x11361),f3(a39)),x11361)
% 7.29/7.43 [1215]P6(a39,x12151,x12152)+~P6(a39,x12151,f13(a39,x12152,f3(a39)))+E(x12151,f13(a39,x12152,f3(a39)))
% 7.29/7.43 [611]~E(x6112,f3(a39))+~E(x6111,f3(a39))+E(f30(f30(f12(a39),x6111),x6112),f3(a39))
% 7.29/7.43 [612]~E(x6122,f3(a1))+~E(x6121,f3(a1))+E(f30(f30(f12(a1),x6121),x6122),f3(a1))
% 7.29/7.43 [676]E(x6761,f3(a39))+E(x6762,f2(a39))+~E(f30(f30(f12(a39),x6762),x6761),x6762)
% 7.29/7.43 [677]E(x6771,f2(a39))+E(x6772,f2(a39))+~E(f30(f30(f12(a39),x6772),x6771),f2(a39))
% 7.29/7.43 [683]~E(x6831,f18(a1,a15))+~E(x6832,f18(a1,a15))+E(f30(f30(f12(a1),x6831),x6832),f3(a1))
% 7.29/7.43 [700]E(x7002,f18(a1,a15))+E(x7001,f3(a1))+~E(f30(f30(f12(a1),x7001),x7002),f3(a1))
% 7.29/7.43 [701]E(x7012,f18(a1,a15))+E(x7011,f3(a1))+~E(f30(f30(f12(a1),x7012),x7011),f3(a1))
% 7.56/7.43 [702]E(x7021,f18(a1,a15))+E(x7021,f3(a1))+~E(f30(f30(f12(a1),x7022),x7021),f3(a1))
% 7.56/7.43 [704]E(x7041,f18(a1,a15))+E(x7041,f3(a1))+~E(f30(f30(f12(a1),x7041),x7042),f3(a1))
% 7.56/7.43 [926]~P35(x9261)+~P67(x9261)+E(f30(f30(f22(x9261),f2(x9261)),f13(a39,x9262,f3(a39))),f2(x9261))
% 7.56/7.43 [960]E(x9601,f2(a39))+E(x9602,f13(a39,f2(a39),f3(a39)))+~E(f30(f30(f22(a39),x9602),x9601),f13(a39,f2(a39),f3(a39)))
% 7.56/7.43 [1059]~E(x10592,f13(a39,f2(a39),f3(a39)))+~E(x10591,f13(a39,f2(a39),f3(a39)))+E(f30(f30(f12(a39),x10591),x10592),f13(a39,f2(a39),f3(a39)))
% 7.56/7.43 [1104]~P6(a1,f2(a1),x11042)+~P6(a1,f2(a1),x11041)+P6(a1,f2(a1),f30(f30(f12(a1),x11041),x11042))
% 7.56/7.43 [1105]~P7(a38,f2(a38),x11052)+~P7(a38,f2(a38),x11051)+P7(a38,f2(a38),f30(f30(f12(a38),x11051),x11052))
% 7.56/7.43 [1106]~P7(a39,f2(a39),x11062)+~P7(a39,f2(a39),x11061)+P7(a39,f2(a39),f30(f30(f12(a39),x11061),x11062))
% 7.56/7.43 [1622]~P6(a39,f13(a39,f2(a39),f3(a39)),x16222)+~P6(a39,f13(a39,f2(a39),f3(a39)),x16221)+P6(a39,f13(a39,f2(a39),f3(a39)),f30(f30(f12(a39),x16221),x16222))
% 7.56/7.43 [955]~P27(x9551)+~P29(x9551)+E(f9(x9551,f30(f30(f22(x9551),f18(x9551,a15)),x9552)),f3(x9551))
% 7.56/7.43 [1019]~E(x10192,f2(a38))+~E(x10191,f2(a38))+E(f13(a38,f30(f30(f12(a38),x10191),x10191),f30(f30(f12(a38),x10192),x10192)),f2(a38))
% 7.56/7.43 [1578]~P29(x15781)+~P5(x15781)+E(f25(x15781,x15782,f18(x15781,f13(a1,f13(a1,f3(a1),a14),a14))),x15782)
% 7.56/7.43 [1679]~P6(a38,f9(a38,x16791),f3(a38))+~P7(a38,f9(a38,x16792),f3(a38))+E(f20(f25(a38,f13(a38,x16791,x16792),f11(a38,f3(a38),f30(f30(f12(a38),x16791),x16792)))),f13(a38,f20(x16791),f20(x16792)))
% 7.56/7.43 [1706]~P58(x17061)+~E(x17062,f2(x17061))+E(f30(f30(f22(x17061),x17062),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f2(x17061))
% 7.56/7.43 [1719]E(f17(x17191),x17192)+~P6(a38,f2(a38),x17192)+~E(f30(f30(f22(a38),x17192),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17191)
% 7.56/7.43 [1724]~P27(x17242)+E(x17241,f2(x17242))+P7(x17242,f2(x17242),f30(f30(f22(x17242),x17241),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.56/7.43 [1734]~P27(x17342)+~E(x17341,f2(x17342))+~P7(x17342,f2(x17342),f30(f30(f22(x17342),x17341),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.56/7.43 [1738]~E(x17382,f2(a38))+~E(x17381,f2(a38))+E(f13(a38,f30(f30(f22(a38),x17381),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x17382),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(a38))
% 7.56/7.43 [620]~E(x6202,x6203)+~P31(x6201)+P6(x6201,x6202,x6203)
% 7.56/7.43 [622]~E(x6222,x6223)+~P34(x6221)+P6(x6221,x6222,x6223)
% 7.56/7.43 [717]~P7(x7173,x7171,x7172)+~E(x7171,x7172)+~P32(x7173)
% 7.56/7.43 [718]~P7(x7183,x7181,x7182)+~E(x7181,x7182)+~P34(x7183)
% 7.56/7.43 [752]P6(x7521,x7523,x7522)+~P32(x7521)+P6(x7521,x7522,x7523)
% 7.56/7.43 [757]P7(x7571,x7573,x7572)+~P32(x7571)+P6(x7571,x7572,x7573)
% 7.56/7.43 [802]~P31(x8021)+~P7(x8021,x8022,x8023)+P6(x8021,x8022,x8023)
% 7.56/7.43 [804]~P34(x8041)+~P7(x8041,x8042,x8043)+P6(x8041,x8042,x8043)
% 7.56/7.43 [889]~P7(x8891,x8893,x8892)+~P31(x8891)+~P6(x8891,x8892,x8893)
% 7.56/7.43 [893]~P7(x8931,x8933,x8932)+~P31(x8931)+~P7(x8931,x8932,x8933)
% 7.56/7.43 [896]~P7(x8961,x8963,x8962)+~P32(x8961)+~P6(x8961,x8962,x8963)
% 7.56/7.43 [897]~P7(x8971,x8973,x8972)+~P32(x8971)+~P7(x8971,x8972,x8973)
% 7.56/7.43 [898]~P7(x8981,x8983,x8982)+~P34(x8981)+~P7(x8981,x8982,x8983)
% 7.56/7.43 [947]~P6(a38,x9471,x9473)+P6(a38,x9471,x9472)+~P6(a38,x9473,x9472)
% 7.56/7.43 [948]~P6(a39,x9481,x9483)+P6(a39,x9481,x9482)+~P6(a39,x9483,x9482)
% 7.56/7.43 [949]~P6(a1,x9491,x9493)+P6(a1,x9491,x9492)+~P6(a1,x9493,x9492)
% 7.56/7.43 [593]~E(x5931,f18(a38,x5933))+E(f4(x5931,x5932),f18(a16,x5933))+~E(x5932,f2(a38))
% 7.56/7.43 [638]~E(x6382,x6383)+~P15(x6381)+E(f11(x6381,x6382,x6383),f2(x6381))
% 7.56/7.43 [639]~E(x6392,x6393)+~P3(x6391)+E(f11(x6391,x6392,x6393),f2(x6391))
% 7.56/7.43 [647]~P68(x6471)+~E(x6473,f2(x6471))+E(f13(x6471,x6472,x6473),x6472)
% 7.56/7.43 [726]~P68(x7262)+~E(f13(x7262,x7263,x7261),x7263)+E(x7261,f2(x7262))
% 7.56/7.43 [728]~P15(x7283)+E(x7281,x7282)+~E(f11(x7283,x7281,x7282),f2(x7283))
% 7.56/7.43 [729]~P3(x7293)+E(x7291,x7292)+~E(f11(x7293,x7291,x7292),f2(x7293))
% 7.56/7.43 [923]~P19(x9231)+P6(x9231,x9232,x9233)+~P6(x9231,f9(x9231,x9232),x9233)
% 7.56/7.43 [951]~P6(a39,x9513,x9511)+~E(f11(a39,x9511,x9513),x9512)+E(x9511,f13(a39,x9512,x9513))
% 7.56/7.43 [952]~P6(a39,x9522,x9521)+~E(x9521,f13(a39,x9523,x9522))+E(f11(a39,x9521,x9522),x9523)
% 7.56/7.43 [1033]~P20(x10331)+~P6(x10331,x10332,x10333)+P6(x10331,f11(x10331,x10332,x10333),f2(x10331))
% 7.56/7.43 [1034]~P20(x10341)+~P7(x10341,x10342,x10343)+P7(x10341,f11(x10341,x10342,x10343),f2(x10341))
% 7.56/7.43 [1107]~P20(x11071)+P6(x11071,x11072,x11073)+~P6(x11071,f11(x11071,x11072,x11073),f2(x11071))
% 7.56/7.43 [1108]~P20(x11081)+P7(x11081,x11082,x11083)+~P7(x11081,f11(x11081,x11082,x11083),f2(x11081))
% 7.56/7.43 [1291]~P7(a39,x12913,x12911)+~P7(a39,x12913,x12912)+P7(a39,f11(a39,x12911,x12912),f11(a39,x12911,x12913))
% 7.56/7.43 [1375]~P6(a39,x13753,x13752)+~P6(a39,f13(a39,x13751,x13753),x13752)+P6(a39,x13751,f11(a39,x13752,x13753))
% 7.56/7.43 [1376]~P6(a39,x13762,x13763)+~P6(a39,x13761,f11(a39,x13763,x13762))+P6(a39,f13(a39,x13761,x13762),x13763)
% 7.56/7.43 [984]~P42(x9842)+E(x9841,f2(x9842))+E(f25(a38,f21(x9842,x9843),f21(x9842,x9841)),f21(x9842,f25(x9842,x9843,x9841)))
% 7.56/7.43 [987]~P9(x9872)+E(x9871,f2(x9872))+E(f25(x9872,f9(x9872,x9873),f9(x9872,x9871)),f9(x9872,f25(x9872,x9873,x9871)))
% 7.56/7.43 [988]~P42(x9881)+~P4(x9881)+E(f25(a38,f21(x9881,x9882),f21(x9881,x9883)),f21(x9881,f25(x9881,x9882,x9883)))
% 7.56/7.43 [1078]~P8(x10781)+~P7(x10781,f2(x10781),x10783)+E(f25(x10781,f9(x10781,x10782),x10783),f9(x10781,f25(x10781,x10782,x10783)))
% 7.56/7.43 [1116]~P7(a39,x11161,x11163)+~P7(a39,x11163,x11162)+P7(a39,f13(a39,x11161,f3(a39)),x11162)
% 7.56/7.43 [1123]~P7(a39,x11233,x11232)+P7(a39,x11231,f13(a39,x11232,f3(a39)))+~E(x11231,f13(a39,x11233,f3(a39)))
% 7.56/7.43 [1284]E(x12841,f2(a38))+~P6(a38,x12842,f2(a38))+~P6(a38,f9(a38,x12841),f30(f30(f12(a38),x12842),f9(a38,x12843)))
% 7.56/7.43 [1361]~P6(a39,x13612,x13613)+~P6(a39,x13612,x13611)+E(f11(a39,f11(a39,x13611,x13612),f11(a39,x13613,x13612)),f11(a39,x13611,x13613))
% 7.56/7.43 [640]~P35(x6401)+~E(x6403,f2(a39))+E(f30(f30(f22(x6401),x6402),x6403),f3(x6401))
% 7.56/7.43 [651]~P66(x6511)+~E(x6513,f2(x6511))+E(f30(f30(f12(x6511),x6512),x6513),f2(x6511))
% 7.56/7.43 [652]~P66(x6521)+~E(x6522,f2(x6521))+E(f30(f30(f12(x6521),x6522),x6523),f2(x6521))
% 7.56/7.43 [727]~P58(x7272)+E(x7271,f2(x7272))+~E(f30(f30(f22(x7272),x7271),x7273),f2(x7272))
% 7.56/7.43 [824]E(x8241,x8242)+E(x8243,f2(a38))+~E(f30(f30(f12(a38),x8243),x8241),f30(f30(f12(a38),x8243),x8242))
% 7.56/7.43 [826]E(x8261,x8262)+E(x8263,f2(a39))+~E(f30(f30(f12(a39),x8263),x8261),f30(f30(f12(a39),x8263),x8262))
% 7.56/7.43 [827]E(x8271,x8272)+E(x8273,f2(a38))+~E(f30(f30(f12(a38),x8271),x8273),f30(f30(f12(a38),x8272),x8273))
% 7.56/7.43 [828]E(x8281,x8282)+E(x8283,f2(a39))+~E(f30(f30(f12(a39),x8281),x8283),f30(f30(f12(a39),x8282),x8283))
% 7.56/7.43 [1039]~P48(x10391)+~P6(x10391,f3(x10391),x10392)+P6(x10391,f3(x10391),f30(f30(f22(x10391),x10392),x10393))
% 7.56/7.43 [1040]~P48(x10401)+~P6(x10401,f2(x10401),x10402)+P6(x10401,f2(x10401),f30(f30(f22(x10401),x10402),x10403))
% 7.56/7.43 [1041]~P48(x10411)+~P7(x10411,f2(x10411),x10412)+P7(x10411,f2(x10411),f30(f30(f22(x10411),x10412),x10413))
% 7.56/7.43 [1257]~P6(a38,x12572,x12573)+~P7(a38,f2(a38),x12571)+P6(a38,f30(f30(f12(a38),x12571),x12572),f30(f30(f12(a38),x12571),x12573))
% 7.56/7.43 [1258]~P6(a38,x12581,x12583)+~P7(a38,f2(a38),x12582)+P6(a38,f30(f30(f12(a38),x12581),x12582),f30(f30(f12(a38),x12583),x12582))
% 7.56/7.43 [1259]~P7(a38,x12591,x12593)+~P7(a38,f2(a38),x12592)+P7(a38,f30(f30(f12(a38),x12591),x12592),f30(f30(f12(a38),x12593),x12592))
% 7.56/7.43 [1260]~P7(a38,x12602,x12603)+~P7(a38,f2(a38),x12601)+P7(a38,f30(f30(f12(a38),x12601),x12602),f30(f30(f12(a38),x12601),x12603))
% 7.56/7.43 [1263]~P7(a39,x12631,x12633)+~P7(a39,f2(a39),x12632)+P7(a39,f30(f30(f12(a39),x12631),x12632),f30(f30(f12(a39),x12633),x12632))
% 7.56/7.43 [1264]~P7(a39,x12642,x12643)+~P7(a39,f2(a39),x12641)+P7(a39,f30(f30(f12(a39),x12641),x12642),f30(f30(f12(a39),x12641),x12643))
% 7.56/7.43 [1374]~P48(x13741)+~P7(x13741,f3(x13741),x13742)+P7(x13741,f3(x13741),f30(f30(f22(x13741),x13742),f13(a39,x13743,f3(a39))))
% 7.56/7.43 [1385]P6(a38,x13851,x13852)+~P7(a38,f2(a38),x13853)+~P6(a38,f30(f30(f12(a38),x13853),x13851),f30(f30(f12(a38),x13853),x13852))
% 7.56/7.43 [1386]P6(a38,x13861,x13862)+~P7(a38,f2(a38),x13863)+~P6(a38,f30(f30(f12(a38),x13861),x13863),f30(f30(f12(a38),x13862),x13863))
% 7.56/7.43 [1387]P7(a38,x13871,x13872)+~P7(a38,f2(a38),x13873)+~P7(a38,f30(f30(f12(a38),x13871),x13873),f30(f30(f12(a38),x13872),x13873))
% 7.56/7.43 [1585]~P9(x15851)+~P7(x15851,x15852,x15853)+P7(x15851,x15852,f25(x15851,f13(x15851,x15852,x15853),f13(x15851,f3(x15851),f3(x15851))))
% 7.56/7.43 [1586]~P9(x15861)+~P7(x15861,x15862,x15863)+P7(x15861,f25(x15861,f13(x15861,x15862,x15863),f13(x15861,f3(x15861),f3(x15861))),x15863)
% 7.56/7.43 [1766]~P27(x17661)+~P7(x17661,x17662,f2(x17661))+P7(x17661,f30(f30(f22(x17661),x17662),f13(a39,f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17663),f3(a39))),f2(x17661))
% 7.56/7.43 [1770]~P27(x17701)+P6(x17701,f2(x17701),x17702)+~P6(x17701,f2(x17701),f30(f30(f22(x17701),x17702),f13(a39,f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17703),f3(a39))))
% 7.56/7.43 [1100]~P27(x11001)+~P6(x11001,f2(x11001),x11003)+E(f30(f30(f12(x11001),f9(x11001,x11002)),x11003),f9(x11001,f30(f30(f12(x11001),x11002),x11003)))
% 7.56/7.43 [1287]~P49(x12872)+E(x12871,f2(x12872))+~E(f13(x12872,f30(f30(f12(x12872),x12873),x12873),f30(f30(f12(x12872),x12871),x12871)),f2(x12872))
% 7.56/7.43 [1288]~P49(x12882)+E(x12881,f2(x12882))+~E(f13(x12882,f30(f30(f12(x12882),x12881),x12881),f30(f30(f12(x12882),x12883),x12883)),f2(x12882))
% 7.56/7.43 [1297]~P35(x12972)+E(x12971,f2(a39))+E(f30(f30(f12(x12972),x12973),f30(f30(f22(x12972),x12973),f11(a39,x12971,f3(a39)))),f30(f30(f22(x12972),x12973),x12971))
% 7.56/7.43 [1360]~P48(x13601)+~P7(x13601,f3(x13601),x13602)+P7(x13601,f3(x13601),f30(f30(f12(x13601),x13602),f30(f30(f22(x13601),x13602),x13603)))
% 7.56/7.43 [1488]~P48(x14881)+~P7(x14881,f3(x14881),x14882)+P7(x14881,f30(f30(f22(x14881),x14882),x14883),f30(f30(f12(x14881),x14882),f30(f30(f22(x14881),x14882),x14883)))
% 7.56/7.43 [1515]~P49(x15152)+E(x15151,f2(x15152))+P7(x15152,f2(x15152),f13(x15152,f30(f30(f12(x15152),x15153),x15153),f30(f30(f12(x15152),x15151),x15151)))
% 7.56/7.43 [1516]~P49(x15162)+E(x15161,f2(x15162))+P7(x15162,f2(x15162),f13(x15162,f30(f30(f12(x15162),x15161),x15161),f30(f30(f12(x15162),x15163),x15163)))
% 7.56/7.43 [1643]~P49(x16432)+E(x16431,f2(x16432))+~P6(x16432,f13(x16432,f30(f30(f12(x16432),x16433),x16433),f30(f30(f12(x16432),x16431),x16431)),f2(x16432))
% 7.56/7.43 [1644]~P49(x16442)+E(x16441,f2(x16442))+~P6(x16442,f13(x16442,f30(f30(f12(x16442),x16441),x16441),f30(f30(f12(x16442),x16443),x16443)),f2(x16442))
% 7.56/7.43 [1745]~P27(x17452)+E(x17451,f2(x17452))+~E(f13(x17452,f30(f30(f22(x17452),x17453),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17452),x17451),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(x17452))
% 7.56/7.43 [1746]~P27(x17462)+E(x17461,f2(x17462))+~E(f13(x17462,f30(f30(f22(x17462),x17461),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17462),x17463),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(x17462))
% 7.56/7.43 [1753]~P27(x17532)+E(x17531,f2(x17532))+P7(x17532,f2(x17532),f13(x17532,f30(f30(f22(x17532),x17533),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17532),x17531),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))
% 7.56/7.43 [1754]~P27(x17542)+E(x17541,f2(x17542))+P7(x17542,f2(x17542),f13(x17542,f30(f30(f22(x17542),x17541),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17542),x17543),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))
% 7.56/7.43 [1763]~P27(x17632)+E(x17631,f2(x17632))+~P6(x17632,f13(x17632,f30(f30(f22(x17632),x17633),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17632),x17631),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(x17632))
% 7.56/7.43 [1764]~P27(x17642)+E(x17641,f2(x17642))+~P6(x17642,f13(x17642,f30(f30(f22(x17642),x17641),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17642),x17643),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(x17642))
% 7.56/7.43 [1759]~P27(x17592)+E(x17591,f2(x17592))+~P6(x17592,f30(f30(f22(x17592),x17591),f30(f30(f12(a39),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x17593)),f2(x17592))
% 7.56/7.43 [1771]~P7(a38,f9(a38,x17711),f25(a38,x17713,f17(f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))+~P7(a38,f9(a38,x17712),f25(a38,x17713,f17(f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))+P7(a38,f17(f13(a38,f30(f30(f22(a38),x17711),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x17712),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),x17713)
% 7.56/7.43 [902]~P13(x9023)+E(x9021,x9022)+~E(f13(x9023,x9024,x9021),f13(x9023,x9024,x9022))
% 7.56/7.43 [903]~P14(x9033)+E(x9031,x9032)+~E(f13(x9033,x9034,x9031),f13(x9033,x9034,x9032))
% 7.56/7.43 [905]~P13(x9053)+E(x9051,x9052)+~E(f13(x9053,x9051,x9054),f13(x9053,x9052,x9054))
% 7.56/7.43 [943]~P33(x9432)+~P7(f41(x9431,x9432),x9433,x9434)+P6(f41(x9431,x9432),x9433,x9434)
% 7.56/7.43 [1035]~P33(x10351)+~P7(f41(x10352,x10351),x10354,x10353)+~P6(f41(x10352,x10351),x10353,x10354)
% 7.56/7.43 [1076]~P7(a39,x10763,x10764)+P7(a39,x10761,x10762)+~E(f13(a39,x10763,x10762),f13(a39,x10761,x10764))
% 7.56/7.43 [1160]~P24(x11601)+~P6(x11601,x11603,x11604)+P6(x11601,f13(x11601,x11602,x11603),f13(x11601,x11602,x11604))
% 7.56/7.43 [1161]~P25(x11611)+~P6(x11611,x11613,x11614)+P6(x11611,f13(x11611,x11612,x11613),f13(x11611,x11612,x11614))
% 7.56/7.43 [1162]~P24(x11621)+~P6(x11621,x11622,x11624)+P6(x11621,f13(x11621,x11622,x11623),f13(x11621,x11624,x11623))
% 7.56/7.43 [1163]~P25(x11631)+~P6(x11631,x11632,x11634)+P6(x11631,f13(x11631,x11632,x11633),f13(x11631,x11634,x11633))
% 7.56/7.43 [1164]~P24(x11641)+~P7(x11641,x11643,x11644)+P7(x11641,f13(x11641,x11642,x11643),f13(x11641,x11642,x11644))
% 7.56/7.43 [1165]~P26(x11651)+~P7(x11651,x11653,x11654)+P7(x11651,f13(x11651,x11652,x11653),f13(x11651,x11652,x11654))
% 7.56/7.43 [1166]~P24(x11661)+~P7(x11661,x11662,x11664)+P7(x11661,f13(x11661,x11662,x11663),f13(x11661,x11664,x11663))
% 7.56/7.43 [1167]~P26(x11671)+~P7(x11671,x11672,x11674)+P7(x11671,f13(x11671,x11672,x11673),f13(x11671,x11674,x11673))
% 7.56/7.43 [1289]~P6(a39,x12892,x12894)+~P6(a39,x12891,x12893)+P6(a39,f13(a39,x12891,x12892),f13(a39,x12893,x12894))
% 7.56/7.43 [1290]~P7(a39,x12902,x12904)+~P7(a39,x12901,x12903)+P7(a39,f13(a39,x12901,x12902),f13(a39,x12903,x12904))
% 7.56/7.43 [1366]~P24(x13661)+P6(x13661,x13662,x13663)+~P6(x13661,f13(x13661,x13664,x13662),f13(x13661,x13664,x13663))
% 7.56/7.43 [1368]~P24(x13681)+P6(x13681,x13682,x13683)+~P6(x13681,f13(x13681,x13682,x13684),f13(x13681,x13683,x13684))
% 7.56/7.43 [1370]~P24(x13701)+P7(x13701,x13702,x13703)+~P7(x13701,f13(x13701,x13704,x13702),f13(x13701,x13704,x13703))
% 7.56/7.43 [1372]~P24(x13721)+P7(x13721,x13722,x13723)+~P7(x13721,f13(x13721,x13722,x13724),f13(x13721,x13723,x13724))
% 7.56/7.43 [1529]~P27(x15291)+P7(x15291,x15292,f13(x15291,x15293,x15294))+~P7(x15291,f9(x15291,f11(x15291,x15292,x15293)),x15294)
% 7.56/7.43 [1530]~P27(x15301)+P7(x15301,f11(x15301,x15302,x15303),x15304)+~P7(x15301,f9(x15301,f11(x15301,x15304,x15302)),x15303)
% 7.56/7.43 [1716]~P33(x17162)+P6(f41(x17161,x17162),x17163,x17164)+~P6(x17162,f30(x17163,f33(x17164,x17163,x17161,x17162)),f30(x17164,f33(x17164,x17163,x17161,x17162)))
% 7.56/7.43 [1253]~P6(a39,x12532,x12534)+~P6(a39,x12531,x12533)+P6(a39,f30(f30(f12(a39),x12531),x12532),f30(f30(f12(a39),x12533),x12534))
% 7.56/7.43 [1547]~P18(x15471)+~P51(x15471)+E(f13(x15471,f30(f30(f12(x15471),x15472),f18(x15471,x15473)),f30(f30(f12(x15471),x15474),f18(x15471,x15473))),f30(f30(f12(x15471),f13(x15471,x15472,x15474)),f18(x15471,x15473)))
% 7.56/7.43 [1548]~P18(x15481)+~P59(x15481)+E(f11(x15481,f30(f30(f12(x15481),x15482),f18(x15481,x15483)),f30(f30(f12(x15481),x15484),f18(x15481,x15483))),f30(f30(f12(x15481),f11(x15481,x15482,x15484)),f18(x15481,x15483)))
% 7.56/7.43 [1109]~P4(x11092)+E(x11091,f2(x11092))+E(f25(x11092,f30(f30(f12(x11092),x11093),x11091),f30(f30(f12(x11092),x11094),x11091)),f25(x11092,x11093,x11094))
% 7.56/7.43 [1110]~P4(x11102)+E(x11101,f2(x11102))+E(f25(x11102,f30(f30(f12(x11102),x11101),x11103),f30(f30(f12(x11102),x11101),x11104)),f25(x11102,x11103,x11104))
% 7.56/7.43 [1457]~P5(x14572)+E(x14571,f2(x14572))+E(f25(x14572,f30(f30(f22(x14572),x14573),x14574),f30(f30(f22(x14572),x14571),x14574)),f30(f30(f22(x14572),f25(x14572,x14573,x14571)),x14574))
% 7.56/7.43 [1555]~P18(x15551)+~P51(x15551)+E(f13(x15551,f30(f30(f12(x15551),f18(x15551,x15552)),x15553),f30(f30(f12(x15551),f18(x15551,x15552)),x15554)),f30(f30(f12(x15551),f18(x15551,x15552)),f13(x15551,x15553,x15554)))
% 7.56/7.43 [1556]~P18(x15561)+~P59(x15561)+E(f11(x15561,f30(f30(f12(x15561),f18(x15561,x15562)),x15563),f30(f30(f12(x15561),f18(x15561,x15562)),x15564)),f30(f30(f12(x15561),f18(x15561,x15562)),f11(x15561,x15563,x15564)))
% 7.56/7.43 [1668]~P1(x16681)+~P6(a39,x16684,x16683)+E(f30(f30(f12(x16681),f30(f30(f22(x16681),x16682),f11(a39,x16683,x16684))),x16682),f30(f30(f22(x16681),x16682),f11(a39,f13(a39,x16683,f3(a39)),x16684)))
% 7.56/7.43 [1459]~P4(x14592)+E(x14591,f2(x14592))+E(f25(x14592,f13(x14592,x14593,f30(f30(f12(x14592),x14594),x14591)),x14591),f13(x14592,x14594,f25(x14592,x14593,x14591)))
% 7.56/7.43 [1460]~P5(x14602)+E(x14601,f2(x14602))+E(f25(x14602,f13(x14602,f30(f30(f12(x14602),x14601),x14603),x14604),x14601),f13(x14602,x14603,f25(x14602,x14604,x14601)))
% 7.56/7.43 [1461]~P5(x14612)+E(x14611,f2(x14612))+E(f25(x14612,f11(x14612,f30(f30(f12(x14612),x14611),x14613),x14614),x14611),f11(x14612,x14613,f25(x14612,x14614,x14611)))
% 7.56/7.43 [1462]~P4(x14622)+E(x14621,f2(x14622))+E(f25(x14622,f13(x14622,x14623,f30(f30(f12(x14622),x14624),x14621)),x14621),f13(x14622,f25(x14622,x14623,x14621),x14624))
% 7.56/7.43 [1463]~P5(x14632)+E(x14631,f2(x14632))+E(f25(x14632,f13(x14632,x14633,f30(f30(f12(x14632),x14631),x14634)),x14631),f13(x14632,f25(x14632,x14633,x14631),x14634))
% 7.56/7.43 [1464]~P5(x14642)+E(x14641,f2(x14642))+E(f25(x14642,f11(x14642,x14643,f30(f30(f12(x14642),x14641),x14644)),x14641),f11(x14642,f25(x14642,x14643,x14641),x14644))
% 7.56/7.43 [1002]~P33(x10021)+P6(x10021,f30(x10022,x10023),f30(x10024,x10023))+~P6(f41(x10025,x10021),x10022,x10024)
% 7.56/7.43 [1439]~E(x14392,x14394)+~P68(x14391)+E(f13(x14391,f30(f30(f12(x14391),x14392),x14393),f30(f30(f12(x14391),x14394),x14395)),f13(x14391,f30(f30(f12(x14391),x14392),x14395),f30(f30(f12(x14391),x14394),x14393)))
% 7.56/7.43 [1662]~P6(a39,x16623,x16622)+E(x16621,f13(a39,f30(f30(f12(a39),f11(a39,x16622,x16623)),x16624),x16625))+~E(f13(a39,f30(f30(f12(a39),x16623),x16624),x16621),f13(a39,f30(f30(f12(a39),x16622),x16624),x16625))
% 7.56/7.43 [1663]~P6(a39,x16632,x16631)+E(f13(a39,f30(f30(f12(a39),f11(a39,x16631,x16632)),x16633),x16634),x16635)+~E(f13(a39,f30(f30(f12(a39),x16631),x16633),x16634),f13(a39,f30(f30(f12(a39),x16632),x16633),x16635))
% 7.56/7.43 [1682]~P6(a39,x16824,x16821)+~E(x16825,f13(a39,f30(f30(f12(a39),f11(a39,x16821,x16824)),x16822),x16823))+E(f13(a39,f30(f30(f12(a39),x16821),x16822),x16823),f13(a39,f30(f30(f12(a39),x16824),x16822),x16825))
% 7.56/7.43 [1683]~P6(a39,x16834,x16831)+~E(f13(a39,f30(f30(f12(a39),f11(a39,x16831,x16834)),x16832),x16833),x16835)+E(f13(a39,f30(f30(f12(a39),x16831),x16832),x16833),f13(a39,f30(f30(f12(a39),x16834),x16832),x16835))
% 7.56/7.43 [1693]~P6(a39,x16933,x16932)+P6(a39,x16931,f13(a39,f30(f30(f12(a39),f11(a39,x16932,x16933)),x16934),x16935))+~P6(a39,f13(a39,f30(f30(f12(a39),x16933),x16934),x16931),f13(a39,f30(f30(f12(a39),x16932),x16934),x16935))
% 7.56/7.43 [1694]~P6(a39,x16942,x16941)+P6(a39,f13(a39,f30(f30(f12(a39),f11(a39,x16941,x16942)),x16943),x16944),x16945)+~P6(a39,f13(a39,f30(f30(f12(a39),x16941),x16943),x16944),f13(a39,f30(f30(f12(a39),x16942),x16943),x16945))
% 7.56/7.43 [1699]~P6(a39,x16991,x16994)+~P6(a39,x16993,f13(a39,f30(f30(f12(a39),f11(a39,x16994,x16991)),x16992),x16995))+P6(a39,f13(a39,f30(f30(f12(a39),x16991),x16992),x16993),f13(a39,f30(f30(f12(a39),x16994),x16992),x16995))
% 7.56/7.43 [1700]~P6(a39,x17004,x17001)+~P6(a39,f13(a39,f30(f30(f12(a39),f11(a39,x17001,x17004)),x17002),x17003),x17005)+P6(a39,f13(a39,f30(f30(f12(a39),x17001),x17002),x17003),f13(a39,f30(f30(f12(a39),x17004),x17002),x17005))
% 7.56/7.43 [1660]~P59(x16602)+~E(f13(x16602,f30(f30(f12(x16602),x16604),x16605),x16601),f13(x16602,f30(f30(f12(x16602),x16603),x16605),x16606))+E(x16601,f13(x16602,f30(f30(f12(x16602),f11(x16602,x16603,x16604)),x16605),x16606))
% 7.56/7.43 [1661]~P59(x16611)+~E(f13(x16611,f30(f30(f12(x16611),x16612),x16614),x16615),f13(x16611,f30(f30(f12(x16611),x16613),x16614),x16616))+E(f13(x16611,f30(f30(f12(x16611),f11(x16611,x16612,x16613)),x16614),x16615),x16616)
% 7.56/7.43 [1680]~P59(x16801)+~E(x16806,f13(x16801,f30(f30(f12(x16801),f11(x16801,x16802,x16805)),x16803),x16804))+E(f13(x16801,f30(f30(f12(x16801),x16802),x16803),x16804),f13(x16801,f30(f30(f12(x16801),x16805),x16803),x16806))
% 7.56/7.43 [1681]~P59(x16811)+~E(f13(x16811,f30(f30(f12(x16811),f11(x16811,x16812,x16815)),x16813),x16814),x16816)+E(f13(x16811,f30(f30(f12(x16811),x16812),x16813),x16814),f13(x16811,f30(f30(f12(x16811),x16815),x16813),x16816))
% 7.56/7.43 [1695]~P61(x16951)+~P6(x16951,f13(x16951,f30(f30(f12(x16951),x16954),x16955),x16952),f13(x16951,f30(f30(f12(x16951),x16953),x16955),x16956))+P6(x16951,x16952,f13(x16951,f30(f30(f12(x16951),f11(x16951,x16953,x16954)),x16955),x16956))
% 7.56/7.43 [1696]~P61(x16961)+~P7(x16961,f13(x16961,f30(f30(f12(x16961),x16964),x16965),x16962),f13(x16961,f30(f30(f12(x16961),x16963),x16965),x16966))+P7(x16961,x16962,f13(x16961,f30(f30(f12(x16961),f11(x16961,x16963,x16964)),x16965),x16966))
% 7.56/7.43 [1697]~P61(x16971)+~P6(x16971,f13(x16971,f30(f30(f12(x16971),x16972),x16974),x16975),f13(x16971,f30(f30(f12(x16971),x16973),x16974),x16976))+P6(x16971,f13(x16971,f30(f30(f12(x16971),f11(x16971,x16972,x16973)),x16974),x16975),x16976)
% 7.56/7.43 [1698]~P61(x16981)+~P7(x16981,f13(x16981,f30(f30(f12(x16981),x16982),x16984),x16985),f13(x16981,f30(f30(f12(x16981),x16983),x16984),x16986))+P7(x16981,f13(x16981,f30(f30(f12(x16981),f11(x16981,x16982,x16983)),x16984),x16985),x16986)
% 7.56/7.43 [1701]~P61(x17011)+~P6(x17011,x17014,f13(x17011,f30(f30(f12(x17011),f11(x17011,x17015,x17012)),x17013),x17016))+P6(x17011,f13(x17011,f30(f30(f12(x17011),x17012),x17013),x17014),f13(x17011,f30(f30(f12(x17011),x17015),x17013),x17016))
% 7.56/7.43 [1702]~P61(x17021)+~P7(x17021,x17024,f13(x17021,f30(f30(f12(x17021),f11(x17021,x17025,x17022)),x17023),x17026))+P7(x17021,f13(x17021,f30(f30(f12(x17021),x17022),x17023),x17024),f13(x17021,f30(f30(f12(x17021),x17025),x17023),x17026))
% 7.56/7.43 [1703]~P61(x17031)+~P6(x17031,f13(x17031,f30(f30(f12(x17031),f11(x17031,x17032,x17035)),x17033),x17034),x17036)+P6(x17031,f13(x17031,f30(f30(f12(x17031),x17032),x17033),x17034),f13(x17031,f30(f30(f12(x17031),x17035),x17033),x17036))
% 7.56/7.43 [1704]~P61(x17041)+~P7(x17041,f13(x17041,f30(f30(f12(x17041),f11(x17041,x17042,x17045)),x17043),x17044),x17046)+P7(x17041,f13(x17041,f30(f30(f12(x17041),x17042),x17043),x17044),f13(x17041,f30(f30(f12(x17041),x17045),x17043),x17046))
% 7.56/7.43 [911]~P27(x9111)+~P29(x9111)+P6(x9111,f2(x9111),f18(x9111,x9112))+~P6(a1,a14,x9112)
% 7.56/7.43 [912]~P27(x9121)+~P29(x9121)+P7(x9121,f2(x9121),f18(x9121,x9122))+~P7(a1,a14,x9122)
% 7.56/7.43 [913]~P27(x9131)+~P29(x9131)+P6(x9131,f18(x9131,x9132),f2(x9131))+~P6(a1,x9132,a14)
% 7.56/7.43 [914]~P27(x9141)+~P29(x9141)+P7(x9141,f18(x9141,x9142),f2(x9141))+~P7(a1,x9142,a14)
% 7.56/7.43 [929]~P29(x9292)+~P27(x9292)+~P6(x9292,f18(x9292,x9291),f2(x9292))+P6(a1,x9291,a14)
% 7.56/7.43 [930]~P29(x9302)+~P27(x9302)+~P7(x9302,f18(x9302,x9301),f2(x9302))+P7(a1,x9301,a14)
% 7.56/7.43 [931]~P29(x9312)+~P27(x9312)+~P6(x9312,f2(x9312),f18(x9312,x9311))+P6(a1,a14,x9311)
% 7.56/7.43 [932]~P29(x9322)+~P27(x9322)+~P7(x9322,f2(x9322),f18(x9322,x9321))+P7(a1,a14,x9321)
% 7.56/7.43 [682]~P35(x6822)+~P67(x6822)+E(x6821,f2(a39))+E(f30(f30(f22(x6822),f2(x6822)),x6821),f2(x6822))
% 7.56/7.43 [1428]~P29(x14282)+~P27(x14282)+~P6(x14282,f18(x14282,x14281),f3(x14282))+P6(a1,x14281,f13(a1,f13(a1,f3(a1),a14),a14))
% 7.56/7.43 [1429]~P29(x14292)+~P27(x14292)+~P7(x14292,f18(x14292,x14291),f3(x14292))+P7(a1,x14291,f13(a1,f13(a1,f3(a1),a14),a14))
% 7.56/7.43 [1430]~P29(x14302)+~P27(x14302)+~P6(x14302,f3(x14302),f18(x14302,x14301))+P6(a1,f13(a1,f13(a1,f3(a1),a14),a14),x14301)
% 7.56/7.43 [1431]~P29(x14312)+~P27(x14312)+~P7(x14312,f3(x14312),f18(x14312,x14311))+P7(a1,f13(a1,f13(a1,f3(a1),a14),a14),x14311)
% 7.56/7.43 [1550]~P27(x15501)+~P29(x15501)+P6(x15501,f3(x15501),f18(x15501,x15502))+~P6(a1,f13(a1,f13(a1,f3(a1),a14),a14),x15502)
% 7.56/7.43 [1551]~P27(x15511)+~P29(x15511)+P7(x15511,f3(x15511),f18(x15511,x15512))+~P7(a1,f13(a1,f13(a1,f3(a1),a14),a14),x15512)
% 7.56/7.43 [1552]~P27(x15521)+~P29(x15521)+P6(x15521,f18(x15521,x15522),f3(x15521))+~P6(a1,x15522,f13(a1,f13(a1,f3(a1),a14),a14))
% 7.56/7.43 [1553]~P27(x15531)+~P29(x15531)+P7(x15531,f18(x15531,x15532),f3(x15531))+~P7(a1,x15532,f13(a1,f13(a1,f3(a1),a14),a14))
% 7.56/7.43 [1729]~P29(x17291)+~P8(x17291)+~P7(x17291,f2(x17291),x17292)+P7(x17291,f2(x17291),f25(x17291,x17292,f18(x17291,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.56/7.43 [1735]~P29(x17351)+~P8(x17351)+P7(x17351,f2(x17351),x17352)+~P7(x17351,f2(x17351),f25(x17351,x17352,f18(x17351,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.56/7.43 [760]P7(x7603,x7601,x7602)+~P27(x7603)+E(x7601,x7602)+P7(x7603,x7602,x7601)
% 7.56/7.43 [766]P7(x7663,x7661,x7662)+~P32(x7663)+E(x7661,x7662)+P7(x7663,x7662,x7661)
% 7.56/7.43 [769]P7(x7691,x7692,x7693)+~E(x7692,x7693)+~P32(x7691)+P6(x7691,x7692,x7693)
% 7.56/7.43 [815]~P34(x8153)+~P6(x8153,x8152,x8151)+E(x8151,x8152)+P7(x8153,x8152,x8151)
% 7.56/7.43 [817]~P32(x8173)+~P6(x8173,x8171,x8172)+E(x8171,x8172)+P7(x8173,x8171,x8172)
% 7.56/7.43 [823]~P34(x8233)+~P6(x8233,x8231,x8232)+E(x8231,x8232)+P7(x8233,x8231,x8232)
% 7.56/7.43 [910]~P6(x9103,x9102,x9101)+~P6(x9103,x9101,x9102)+E(x9101,x9102)+~P34(x9103)
% 7.56/7.43 [933]P7(x9331,x9333,x9332)+~P31(x9331)+~P6(x9331,x9333,x9332)+P6(x9331,x9332,x9333)
% 7.56/7.43 [613]~P29(x6133)+~P30(x6133)+E(x6131,x6132)+~E(f18(x6133,x6131),f18(x6133,x6132))
% 7.56/7.43 [661]~E(x6613,x6611)+~P44(x6612)+E(f25(x6612,x6613,x6611),f3(x6612))+E(x6611,f2(x6612))
% 7.56/7.43 [740]~P44(x7403)+E(x7401,x7402)+~E(f25(x7403,x7401,x7402),f3(x7403))+E(x7402,f2(x7403))
% 7.56/7.43 [934]~P27(x9341)+~P29(x9341)+~P6(a1,x9342,x9343)+P6(x9341,f18(x9341,x9342),f18(x9341,x9343))
% 7.56/7.43 [935]~P27(x9351)+~P29(x9351)+~P7(a1,x9352,x9353)+P7(x9351,f18(x9351,x9352),f18(x9351,x9353))
% 7.56/7.43 [976]~P29(x9763)+~P27(x9763)+~P6(x9763,f18(x9763,x9761),f18(x9763,x9762))+P6(a1,x9761,x9762)
% 7.56/7.43 [977]~P29(x9773)+~P27(x9773)+~P7(x9773,f18(x9773,x9771),f18(x9773,x9772))+P7(a1,x9771,x9772)
% 7.56/7.43 [1122]E(x11221,x11222)+~P6(a39,x11223,x11222)+~P6(a39,x11223,x11221)+~E(f11(a39,x11221,x11223),f11(a39,x11222,x11223))
% 7.56/7.43 [1190]~P8(x11901)+~P6(x11901,x11903,f2(x11901))+~P6(x11901,x11902,f2(x11901))+P6(x11901,f2(x11901),f25(x11901,x11902,x11903))
% 7.56/7.43 [1191]~P9(x11911)+~P6(x11911,x11912,f2(x11911))+~P7(x11911,x11913,f2(x11911))+P6(x11911,f2(x11911),f25(x11911,x11912,x11913))
% 7.56/7.43 [1192]~P8(x11921)+~P7(x11921,x11923,f2(x11921))+~P7(x11921,x11922,f2(x11921))+P7(x11921,f2(x11921),f25(x11921,x11922,x11923))
% 7.56/7.43 [1193]~P9(x11931)+~P7(x11931,x11933,f2(x11931))+~P7(x11931,x11932,f2(x11931))+P7(x11931,f2(x11931),f25(x11931,x11932,x11933))
% 7.56/7.43 [1195]~P8(x11951)+~P6(x11951,f2(x11951),x11953)+~P6(x11951,f2(x11951),x11952)+P6(x11951,f2(x11951),f25(x11951,x11952,x11953))
% 7.56/7.43 [1196]~P9(x11961)+~P6(x11961,f2(x11961),x11962)+~P7(x11961,f2(x11961),x11963)+P6(x11961,f2(x11961),f25(x11961,x11962,x11963))
% 7.56/7.43 [1199]~P23(x11991)+~P7(x11991,f2(x11991),x11993)+~P7(x11991,f2(x11991),x11992)+P7(x11991,f2(x11991),f13(x11991,x11992,x11993))
% 7.56/7.43 [1200]~P8(x12001)+~P7(x12001,f2(x12001),x12003)+~P7(x12001,f2(x12001),x12002)+P7(x12001,f2(x12001),f25(x12001,x12002,x12003))
% 7.56/7.43 [1201]~P9(x12011)+~P7(x12011,f2(x12011),x12013)+~P7(x12011,f2(x12011),x12012)+P7(x12011,f2(x12011),f25(x12011,x12012,x12013))
% 7.56/7.43 [1202]~P23(x12021)+~P6(x12021,x12023,f2(x12021))+~P6(x12021,x12022,f2(x12021))+P6(x12021,f13(x12021,x12022,x12023),f2(x12021))
% 7.56/7.43 [1203]~P23(x12031)+~P6(x12031,x12033,f2(x12031))+~P7(x12031,x12032,f2(x12031))+P7(x12031,f13(x12031,x12032,x12033),f2(x12031))
% 7.56/7.43 [1204]~P23(x12041)+~P6(x12041,x12042,f2(x12041))+~P7(x12041,x12043,f2(x12041))+P7(x12041,f13(x12041,x12042,x12043),f2(x12041))
% 7.56/7.43 [1205]~P23(x12051)+~P7(x12051,x12053,f2(x12051))+~P7(x12051,x12052,f2(x12051))+P7(x12051,f13(x12051,x12052,x12053),f2(x12051))
% 7.56/7.43 [1206]~P8(x12061)+~P6(x12061,x12063,f2(x12061))+~P6(x12061,f2(x12061),x12062)+P6(x12061,f25(x12061,x12062,x12063),f2(x12061))
% 7.56/7.43 [1207]~P8(x12071)+~P6(x12071,x12072,f2(x12071))+~P6(x12071,f2(x12071),x12073)+P6(x12071,f25(x12071,x12072,x12073),f2(x12071))
% 7.56/7.43 [1208]~P9(x12081)+~P6(x12081,x12082,f2(x12081))+~P7(x12081,f2(x12081),x12083)+P6(x12081,f25(x12081,x12082,x12083),f2(x12081))
% 7.56/7.43 [1209]~P9(x12091)+~P7(x12091,x12093,f2(x12091))+~P6(x12091,f2(x12091),x12092)+P6(x12091,f25(x12091,x12092,x12093),f2(x12091))
% 7.56/7.43 [1210]~P8(x12101)+~P7(x12101,x12103,f2(x12101))+~P7(x12101,f2(x12101),x12102)+P7(x12101,f25(x12101,x12102,x12103),f2(x12101))
% 7.56/7.43 [1211]~P8(x12111)+~P7(x12111,x12112,f2(x12111))+~P7(x12111,f2(x12111),x12113)+P7(x12111,f25(x12111,x12112,x12113),f2(x12111))
% 7.56/7.43 [1212]~P9(x12121)+~P7(x12121,x12123,f2(x12121))+~P7(x12121,f2(x12121),x12122)+P7(x12121,f25(x12121,x12122,x12123),f2(x12121))
% 7.56/7.43 [1213]~P9(x12131)+~P7(x12131,x12132,f2(x12131))+~P7(x12131,f2(x12131),x12133)+P7(x12131,f25(x12131,x12132,x12133),f2(x12131))
% 7.56/7.43 [1232]~P8(x12321)+~P6(x12321,f25(x12321,x12323,x12322),f2(x12321))+P6(x12321,x12322,f2(x12321))+P6(x12321,x12323,f2(x12321))
% 7.56/7.43 [1233]~P8(x12331)+~P7(x12331,f25(x12331,x12333,x12332),f2(x12331))+P7(x12331,x12332,f2(x12331))+P7(x12331,x12333,f2(x12331))
% 7.56/7.43 [1234]~P8(x12341)+~P6(x12341,f2(x12341),f25(x12341,x12343,x12342))+P6(x12341,x12342,f2(x12341))+P6(x12341,f2(x12341),x12343)
% 7.56/7.43 [1235]~P8(x12351)+~P6(x12351,f2(x12351),f25(x12351,x12352,x12353))+P6(x12351,x12352,f2(x12351))+P6(x12351,f2(x12351),x12353)
% 7.56/7.43 [1236]~P8(x12361)+P6(x12361,f2(x12361),x12362)+~P6(x12361,f2(x12361),f25(x12361,x12363,x12362))+P6(x12361,x12362,f2(x12361))
% 7.56/7.43 [1237]~P8(x12371)+P6(x12371,f2(x12371),x12372)+~P6(x12371,f2(x12371),f25(x12371,x12372,x12373))+P6(x12371,x12372,f2(x12371))
% 7.56/7.43 [1238]~P8(x12381)+~P7(x12381,f2(x12381),f25(x12381,x12383,x12382))+P7(x12381,x12382,f2(x12381))+P7(x12381,f2(x12381),x12383)
% 7.56/7.43 [1239]~P8(x12391)+~P7(x12391,f2(x12391),f25(x12391,x12392,x12393))+P7(x12391,x12392,f2(x12391))+P7(x12391,f2(x12391),x12393)
% 7.56/7.43 [1240]~P8(x12401)+P7(x12401,f2(x12401),x12402)+~P7(x12401,f2(x12401),f25(x12401,x12403,x12402))+P7(x12401,x12402,f2(x12401))
% 7.56/7.43 [1241]~P8(x12411)+P7(x12411,f2(x12411),x12412)+~P7(x12411,f2(x12411),f25(x12411,x12412,x12413))+P7(x12411,x12412,f2(x12411))
% 7.56/7.43 [1242]~P8(x12421)+P6(x12421,f2(x12421),x12422)+~P6(x12421,f25(x12421,x12423,x12422),f2(x12421))+P6(x12421,x12422,f2(x12421))
% 7.56/7.43 [1243]~P8(x12431)+P6(x12431,f2(x12431),x12432)+~P6(x12431,f25(x12431,x12432,x12433),f2(x12431))+P6(x12431,x12432,f2(x12431))
% 7.56/7.43 [1244]~P8(x12441)+P7(x12441,f2(x12441),x12442)+~P7(x12441,f25(x12441,x12443,x12442),f2(x12441))+P7(x12441,x12442,f2(x12441))
% 7.56/7.43 [1245]~P8(x12451)+P7(x12451,f2(x12451),x12452)+~P7(x12451,f25(x12451,x12452,x12453),f2(x12451))+P7(x12451,x12452,f2(x12451))
% 7.56/7.43 [1246]~P8(x12461)+~P6(x12461,f25(x12461,x12462,x12463),f2(x12461))+P6(x12461,f2(x12461),x12462)+P6(x12461,f2(x12461),x12463)
% 7.56/7.43 [1247]~P8(x12471)+~P7(x12471,f25(x12471,x12472,x12473),f2(x12471))+P7(x12471,f2(x12471),x12472)+P7(x12471,f2(x12471),x12473)
% 7.56/7.43 [1528]~P6(a39,x15283,x15281)+P6(a39,x15281,x15282)+~P6(a39,x15283,x15282)+~P6(a39,f11(a39,x15281,x15283),f11(a39,x15282,x15283))
% 7.56/7.43 [735]~P57(x7352)+E(x7351,f2(x7352))+E(x7353,f2(x7352))+~E(f30(f30(f12(x7352),x7353),x7351),f2(x7352))
% 7.56/7.43 [736]~P66(x7362)+E(x7361,f2(x7362))+E(x7363,f2(x7362))+~E(f30(f30(f12(x7362),x7363),x7361),f2(x7362))
% 7.56/7.43 [1156]~P48(x11561)+~P7(x11561,f3(x11561),x11562)+~P7(a39,f2(a39),x11563)+P7(x11561,f3(x11561),f30(f30(f22(x11561),x11562),x11563))
% 7.56/7.43 [1168]~P49(x11681)+~P6(x11681,x11683,f2(x11681))+~P6(x11681,x11682,f2(x11681))+P6(x11681,f2(x11681),f30(f30(f12(x11681),x11682),x11683))
% 7.56/7.43 [1170]~P61(x11701)+~P6(x11701,x11703,f2(x11701))+~P6(x11701,x11702,f2(x11701))+P6(x11701,f2(x11701),f30(f30(f12(x11701),x11702),x11703))
% 7.56/7.43 [1171]~P49(x11711)+~P7(x11711,x11713,f2(x11711))+~P7(x11711,x11712,f2(x11711))+P7(x11711,f2(x11711),f30(f30(f12(x11711),x11712),x11713))
% 7.56/7.43 [1172]~P49(x11721)+~P6(x11721,f2(x11721),x11723)+~P6(x11721,f2(x11721),x11722)+P6(x11721,f2(x11721),f30(f30(f12(x11721),x11722),x11723))
% 7.56/7.43 [1173]~P60(x11731)+~P6(x11731,f2(x11731),x11733)+~P6(x11731,f2(x11731),x11732)+P6(x11731,f2(x11731),f30(f30(f12(x11731),x11732),x11733))
% 7.56/7.43 [1174]~P61(x11741)+~P6(x11741,f2(x11741),x11743)+~P6(x11741,f2(x11741),x11742)+P6(x11741,f2(x11741),f30(f30(f12(x11741),x11742),x11743))
% 7.56/7.43 [1175]~P48(x11751)+~P7(x11751,f3(x11751),x11753)+~P7(x11751,f3(x11751),x11752)+P7(x11751,f3(x11751),f30(f30(f12(x11751),x11752),x11753))
% 7.56/7.43 [1176]~P55(x11761)+~P7(x11761,f2(x11761),x11763)+~P7(x11761,f2(x11761),x11762)+P7(x11761,f2(x11761),f30(f30(f12(x11761),x11762),x11763))
% 7.56/7.43 [1178]~P49(x11781)+~P6(x11781,x11783,f2(x11781))+~P6(x11781,f2(x11781),x11782)+P6(x11781,f30(f30(f12(x11781),x11782),x11783),f2(x11781))
% 7.56/7.43 [1179]~P49(x11791)+~P6(x11791,x11792,f2(x11791))+~P6(x11791,f2(x11791),x11793)+P6(x11791,f30(f30(f12(x11791),x11792),x11793),f2(x11791))
% 7.56/7.43 [1181]~P60(x11811)+~P6(x11811,x11813,f2(x11811))+~P6(x11811,f2(x11811),x11812)+P6(x11811,f30(f30(f12(x11811),x11812),x11813),f2(x11811))
% 7.56/7.43 [1183]~P60(x11831)+~P6(x11831,x11832,f2(x11831))+~P6(x11831,f2(x11831),x11833)+P6(x11831,f30(f30(f12(x11831),x11832),x11833),f2(x11831))
% 7.56/7.43 [1185]~P55(x11851)+~P7(x11851,x11853,f2(x11851))+~P7(x11851,f2(x11851),x11852)+P7(x11851,f30(f30(f12(x11851),x11852),x11853),f2(x11851))
% 7.56/7.43 [1186]~P55(x11861)+~P7(x11861,x11862,f2(x11861))+~P7(x11861,f2(x11861),x11863)+P7(x11861,f30(f30(f12(x11861),x11862),x11863),f2(x11861))
% 7.56/7.43 [1220]~P49(x12201)+P6(x12201,x12202,f2(x12201))+P6(x12201,x12203,f2(x12201))+~P6(x12201,f30(f30(f12(x12201),x12203),x12202),f2(x12201))
% 7.56/7.43 [1221]~P49(x12211)+P6(x12211,x12212,f2(x12211))+P6(x12211,f2(x12211),x12213)+~P6(x12211,f2(x12211),f30(f30(f12(x12211),x12213),x12212))
% 7.56/7.43 [1222]~P49(x12221)+P6(x12221,x12222,f2(x12221))+P6(x12221,f2(x12221),x12223)+~P6(x12221,f2(x12221),f30(f30(f12(x12221),x12222),x12223))
% 7.56/7.43 [1223]~P49(x12231)+P6(x12231,f2(x12231),x12232)+P6(x12231,x12232,f2(x12231))+~P6(x12231,f2(x12231),f30(f30(f12(x12231),x12233),x12232))
% 7.56/7.43 [1224]~P49(x12241)+P6(x12241,f2(x12241),x12242)+P6(x12241,x12242,f2(x12241))+~P6(x12241,f2(x12241),f30(f30(f12(x12241),x12242),x12243))
% 7.56/7.43 [1225]~P49(x12251)+P6(x12251,f2(x12251),x12252)+P6(x12251,x12252,f2(x12251))+~P6(x12251,f30(f30(f12(x12251),x12253),x12252),f2(x12251))
% 7.56/7.43 [1226]~P49(x12261)+P6(x12261,f2(x12261),x12262)+P6(x12261,x12262,f2(x12261))+~P6(x12261,f30(f30(f12(x12261),x12262),x12263),f2(x12261))
% 7.56/7.43 [1227]~P49(x12271)+P6(x12271,f2(x12271),x12272)+P6(x12271,f2(x12271),x12273)+~P6(x12271,f30(f30(f12(x12271),x12272),x12273),f2(x12271))
% 7.56/7.43 [1275]~P55(x12751)+P7(x12751,f2(x12751),x12752)+~P7(x12751,f2(x12751),x12753)+~P7(x12751,f2(x12751),f30(f30(f12(x12751),x12753),x12752))
% 7.56/7.43 [1276]~P55(x12761)+P7(x12761,f2(x12761),x12762)+~P7(x12761,f2(x12761),x12763)+~P7(x12761,f2(x12761),f30(f30(f12(x12761),x12762),x12763))
% 7.56/7.43 [1505]~P48(x15051)+~P6(x15051,x15052,f3(x15051))+~P6(x15051,f2(x15051),x15052)+P6(x15051,f30(f30(f22(x15051),x15052),f13(a39,x15053,f3(a39))),x15052)
% 7.56/7.43 [1509]~P48(x15091)+~P7(x15091,x15092,f3(x15091))+~P7(x15091,f2(x15091),x15092)+P7(x15091,f30(f30(f22(x15091),x15092),f13(a39,x15093,f3(a39))),f3(x15091))
% 7.56/7.43 [1055]~P49(x10551)+~E(x10553,f2(x10551))+~E(x10552,f2(x10551))+E(f13(x10551,f30(f30(f12(x10551),x10552),x10552),f30(f30(f12(x10551),x10553),x10553)),f2(x10551))
% 7.56/7.43 [1302]~P64(x13021)+~P6(x13021,x13022,f2(x13021))+~P6(x13021,x13023,f2(x13021))+E(f30(f30(f12(x13021),f9(x13021,x13022)),f9(x13021,x13023)),f9(x13021,f30(f30(f12(x13021),x13022),x13023)))
% 7.56/7.43 [1303]~P64(x13031)+~P6(x13031,x13032,f2(x13031))+~P6(x13031,f2(x13031),x13033)+E(f30(f30(f12(x13031),f9(x13031,x13032)),f9(x13031,x13033)),f9(x13031,f30(f30(f12(x13031),x13032),x13033)))
% 7.56/7.43 [1304]~P64(x13041)+~P6(x13041,x13043,f2(x13041))+~P6(x13041,f2(x13041),x13042)+E(f30(f30(f12(x13041),f9(x13041,x13042)),f9(x13041,x13043)),f9(x13041,f30(f30(f12(x13041),x13042),x13043)))
% 7.56/7.43 [1305]~P64(x13051)+~P6(x13051,f2(x13051),x13052)+~P6(x13051,f2(x13051),x13053)+E(f30(f30(f12(x13051),f9(x13051,x13052)),f9(x13051,x13053)),f9(x13051,f30(f30(f12(x13051),x13052),x13053)))
% 7.56/7.43 [1518]~P49(x15181)+~E(x15183,f2(x15181))+~E(x15182,f2(x15181))+P6(x15181,f13(x15181,f30(f30(f12(x15181),x15182),x15182),f30(f30(f12(x15181),x15183),x15183)),f2(x15181))
% 7.56/7.43 [1542]~P48(x15421)+~P7(x15421,x15422,f3(x15421))+~P7(x15421,f2(x15421),x15422)+P7(x15421,f30(f30(f12(x15421),x15422),f30(f30(f22(x15421),x15422),x15423)),f30(f30(f22(x15421),x15422),x15423))
% 7.56/7.43 [1646]~P49(x16462)+~E(x16461,f2(x16462))+~E(x16463,f2(x16462))+~P7(x16462,f2(x16462),f13(x16462,f30(f30(f12(x16462),x16463),x16463),f30(f30(f12(x16462),x16461),x16461)))
% 7.56/7.43 [1747]~P48(x17471)+P6(x17471,x17472,x17473)+~P6(x17471,f2(x17471),x17473)+~P6(x17471,f30(f30(f22(x17471),x17472),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17471),x17473),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.56/7.43 [1740]~P27(x17401)+~E(x17403,f2(x17401))+~E(x17402,f2(x17401))+E(f13(x17401,f30(f30(f22(x17401),x17402),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17401),x17403),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(x17401))
% 7.56/7.43 [1755]~P27(x17551)+~E(x17553,f2(x17551))+~E(x17552,f2(x17551))+P6(x17551,f13(x17551,f30(f30(f22(x17551),x17552),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17551),x17553),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))),f2(x17551))
% 7.56/7.43 [1765]~P27(x17652)+~E(x17651,f2(x17652))+~E(x17653,f2(x17652))+~P7(x17652,f2(x17652),f13(x17652,f30(f30(f22(x17652),x17653),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17652),x17651),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14))))))
% 7.56/7.43 [967]~P34(x9671)+~P6(x9671,x9674,x9673)+P6(x9671,x9672,x9673)+~P6(x9671,x9672,x9674)
% 7.56/7.43 [968]~P31(x9681)+~P6(x9681,x9682,x9684)+P6(x9681,x9682,x9683)+~P6(x9681,x9684,x9683)
% 7.56/7.43 [969]~P34(x9691)+~P7(x9691,x9694,x9693)+P7(x9691,x9692,x9693)+~P6(x9691,x9692,x9694)
% 7.56/7.43 [970]~P34(x9701)+~P7(x9701,x9702,x9704)+P7(x9701,x9702,x9703)+~P6(x9701,x9704,x9703)
% 7.56/7.43 [971]~P34(x9711)+~P7(x9711,x9714,x9713)+P7(x9711,x9712,x9713)+~P7(x9711,x9712,x9714)
% 7.56/7.43 [972]~P31(x9721)+~P7(x9721,x9722,x9724)+P7(x9721,x9722,x9723)+~P6(x9721,x9724,x9723)
% 7.56/7.43 [973]~P31(x9731)+~P7(x9731,x9734,x9733)+P7(x9731,x9732,x9733)+~P6(x9731,x9732,x9734)
% 7.56/7.43 [974]~P31(x9741)+~P7(x9741,x9742,x9744)+P7(x9741,x9742,x9743)+~P7(x9741,x9744,x9743)
% 7.56/7.43 [670]~P4(x6702)+~E(x6704,f2(x6702))+~E(x6701,f2(x6702))+E(x6701,f25(x6702,x6703,x6704))
% 7.56/7.43 [671]~P4(x6711)+~E(x6713,f2(x6711))+~E(x6714,f2(x6711))+E(f25(x6711,x6712,x6713),x6714)
% 7.56/7.43 [741]~P4(x7412)+E(x7411,f2(x7412))+~E(x7411,f25(x7412,x7414,x7413))+~E(x7413,f2(x7412))
% 7.56/7.43 [742]~P4(x7422)+E(x7421,f2(x7422))+~E(f25(x7422,x7424,x7423),x7421)+~E(x7423,f2(x7422))
% 7.56/7.43 [1060]~P33(x10602)+P7(f41(x10601,x10602),x10604,x10603)+~P6(f41(x10601,x10602),x10604,x10603)+P6(f41(x10601,x10602),x10603,x10604)
% 7.56/7.43 [1151]~P23(x11511)+~P6(x11511,x11512,x11513)+~P6(x11511,f2(x11511),x11514)+P6(x11511,x11512,f13(x11511,x11513,x11514))
% 7.56/7.43 [1152]~P23(x11521)+~P6(x11521,x11522,x11524)+~P6(x11521,f2(x11521),x11523)+P6(x11521,x11522,f13(x11521,x11523,x11524))
% 7.56/7.43 [1153]~P48(x11531)+~P7(x11531,x11532,x11534)+~P7(x11531,f2(x11531),x11533)+P7(x11531,x11532,f13(x11531,x11533,x11534))
% 7.56/7.43 [1154]~P23(x11541)+~P6(x11541,x11542,x11544)+~P7(x11541,f2(x11541),x11543)+P7(x11541,x11542,f13(x11541,x11543,x11544))
% 7.56/7.43 [1155]~P23(x11551)+~P7(x11551,x11552,x11554)+~P6(x11551,f2(x11551),x11553)+P7(x11551,x11552,f13(x11551,x11553,x11554))
% 7.56/7.43 [1343]~P8(x13431)+~P6(x13431,x13434,x13432)+~P6(x13431,x13433,f2(x13431))+P6(x13431,f25(x13431,x13432,x13433),f25(x13431,x13434,x13433))
% 7.56/7.43 [1344]~P9(x13441)+~P7(x13441,x13444,x13442)+~P7(x13441,x13443,f2(x13441))+P7(x13441,f25(x13441,x13442,x13443),f25(x13441,x13444,x13443))
% 7.56/7.43 [1345]~P8(x13451)+~P6(x13451,x13452,x13454)+~P6(x13451,f2(x13451),x13453)+P6(x13451,f25(x13451,x13452,x13453),f25(x13451,x13454,x13453))
% 7.56/7.43 [1346]~P9(x13461)+~P7(x13461,x13462,x13464)+~P7(x13461,f2(x13461),x13463)+P7(x13461,f25(x13461,x13462,x13463),f25(x13461,x13464,x13463))
% 7.56/7.43 [1334]~P37(x13342)+E(x13341,f2(x13342))+~P6(a38,x13343,f2(a38))+~P6(a38,f21(x13342,x13341),f30(f30(f12(a38),x13343),f21(x13342,x13344)))
% 7.56/7.43 [1635]~P27(x16351)+~P7(x16351,x16352,f13(x16351,x16353,x16354))+~P7(x16351,f11(x16351,x16353,x16354),x16352)+P7(x16351,f9(x16351,f11(x16351,x16352,x16353)),x16354)
% 7.56/7.43 [842]~P44(x8422)+E(x8421,f2(x8422))+E(x8423,f25(x8422,x8424,x8421))+~E(f30(f30(f12(x8422),x8423),x8421),x8424)
% 7.56/7.43 [843]~P4(x8432)+E(x8431,f2(x8432))+E(x8433,f25(x8432,x8434,x8431))+~E(f30(f30(f12(x8432),x8433),x8431),x8434)
% 7.56/7.43 [845]~P44(x8452)+E(x8451,f2(x8452))+E(f25(x8452,x8453,x8451),x8454)+~E(x8453,f30(f30(f12(x8452),x8454),x8451))
% 7.56/7.43 [846]~P4(x8462)+E(x8461,f2(x8462))+E(f25(x8462,x8463,x8461),x8464)+~E(x8463,f30(f30(f12(x8462),x8464),x8461))
% 7.56/7.43 [848]~P44(x8482)+~E(f25(x8482,x8483,x8481),x8484)+E(x8481,f2(x8482))+E(x8483,f30(f30(f12(x8482),x8484),x8481))
% 7.56/7.43 [849]~P4(x8492)+~E(f25(x8492,x8493,x8491),x8494)+E(x8491,f2(x8492))+E(x8493,f30(f30(f12(x8492),x8494),x8491))
% 7.56/7.43 [850]~P44(x8502)+~E(x8503,f25(x8502,x8504,x8501))+E(x8501,f2(x8502))+E(f30(f30(f12(x8502),x8503),x8501),x8504)
% 7.56/7.43 [851]~P4(x8512)+~E(x8513,f25(x8512,x8514,x8511))+E(x8511,f2(x8512))+E(f30(f30(f12(x8512),x8513),x8511),x8514)
% 7.56/7.43 [860]~P4(x8602)+~E(x8601,f2(x8602))+E(x8601,f25(x8602,x8603,x8604))+~E(f30(f30(f12(x8602),x8601),x8604),x8603)
% 7.56/7.43 [861]~P4(x8611)+~E(x8614,f2(x8611))+E(f25(x8611,x8612,x8613),x8614)+~E(x8612,f30(f30(f12(x8611),x8614),x8613))
% 7.56/7.43 [1042]~P48(x10423)+E(x10421,x10422)+~P7(x10423,f3(x10423),x10424)+~E(f30(f30(f22(x10423),x10424),x10421),f30(f30(f22(x10423),x10424),x10422))
% 7.56/7.43 [1306]~P48(x13061)+~P6(a39,x13063,x13064)+~P7(x13061,f3(x13061),x13062)+P6(x13061,f30(f30(f22(x13061),x13062),x13063),f30(f30(f22(x13061),x13062),x13064))
% 7.56/7.43 [1307]~P48(x13071)+~P6(a39,x13073,x13074)+~P6(x13071,f3(x13071),x13072)+P6(x13071,f30(f30(f22(x13071),x13072),x13073),f30(f30(f22(x13071),x13072),x13074))
% 7.56/7.43 [1309]~P48(x13091)+~P7(a39,x13093,x13094)+~P7(x13091,f3(x13091),x13092)+P7(x13091,f30(f30(f22(x13091),x13092),x13093),f30(f30(f22(x13091),x13092),x13094))
% 7.56/7.43 [1315]~P49(x13151)+~P6(x13151,x13154,x13153)+~P7(x13151,x13152,f2(x13151))+P6(x13151,f30(f30(f12(x13151),x13152),x13153),f30(f30(f12(x13151),x13152),x13154))
% 7.56/7.43 [1316]~P61(x13161)+~P6(x13161,x13164,x13163)+~P6(x13161,x13162,f2(x13161))+P6(x13161,f30(f30(f12(x13161),x13162),x13163),f30(f30(f12(x13161),x13162),x13164))
% 7.56/7.43 [1317]~P61(x13171)+~P6(x13171,x13174,x13172)+~P6(x13171,x13173,f2(x13171))+P6(x13171,f30(f30(f12(x13171),x13172),x13173),f30(f30(f12(x13171),x13174),x13173))
% 7.56/7.43 [1321]~P49(x13211)+~P7(x13211,x13214,x13212)+~P7(x13211,x13213,f2(x13211))+P7(x13211,f30(f30(f12(x13211),x13212),x13213),f30(f30(f12(x13211),x13214),x13213))
% 7.56/7.43 [1322]~P49(x13221)+~P7(x13221,x13224,x13223)+~P7(x13221,x13222,f2(x13221))+P7(x13221,f30(f30(f12(x13221),x13222),x13223),f30(f30(f12(x13221),x13222),x13224))
% 7.56/7.43 [1323]~P49(x13231)+~P6(x13231,x13233,x13234)+~P7(x13231,f2(x13231),x13232)+P6(x13231,f30(f30(f12(x13231),x13232),x13233),f30(f30(f12(x13231),x13232),x13234))
% 7.56/7.43 [1324]~P63(x13241)+~P6(x13241,x13243,x13244)+~P6(x13241,f2(x13241),x13242)+P6(x13241,f30(f30(f12(x13241),x13242),x13243),f30(f30(f12(x13241),x13242),x13244))
% 7.56/7.43 [1325]~P62(x13251)+~P6(x13251,x13253,x13254)+~P6(x13251,f2(x13251),x13252)+P6(x13251,f30(f30(f12(x13251),x13252),x13253),f30(f30(f12(x13251),x13252),x13254))
% 7.56/7.43 [1326]~P63(x13261)+~P6(x13261,x13262,x13264)+~P6(x13261,f2(x13261),x13263)+P6(x13261,f30(f30(f12(x13261),x13262),x13263),f30(f30(f12(x13261),x13264),x13263))
% 7.56/7.43 [1327]~P48(x13271)+~P6(x13271,x13272,x13274)+~P6(x13271,f2(x13271),x13272)+P6(x13271,f30(f30(f22(x13271),x13272),x13273),f30(f30(f22(x13271),x13274),x13273))
% 7.56/7.43 [1329]~P46(x13291)+~P7(x13291,x13293,x13294)+~P7(x13291,f2(x13291),x13292)+P7(x13291,f30(f30(f12(x13291),x13292),x13293),f30(f30(f12(x13291),x13292),x13294))
% 7.56/7.43 [1330]~P55(x13301)+~P7(x13301,x13303,x13304)+~P7(x13301,f2(x13301),x13302)+P7(x13301,f30(f30(f12(x13301),x13302),x13303),f30(f30(f12(x13301),x13302),x13304))
% 7.56/7.43 [1331]~P49(x13311)+~P7(x13311,x13312,x13314)+~P7(x13311,f2(x13311),x13313)+P7(x13311,f30(f30(f12(x13311),x13312),x13313),f30(f30(f12(x13311),x13314),x13313))
% 7.56/7.43 [1332]~P55(x13321)+~P7(x13321,x13322,x13324)+~P7(x13321,f2(x13321),x13323)+P7(x13321,f30(f30(f12(x13321),x13322),x13323),f30(f30(f12(x13321),x13324),x13323))
% 7.56/7.43 [1333]~P49(x13331)+~P7(x13331,x13333,x13334)+~P7(x13331,f2(x13331),x13332)+P7(x13331,f30(f30(f12(x13331),x13332),x13333),f30(f30(f12(x13331),x13332),x13334))
% 7.56/7.43 [1390]~P9(x13901)+~P7(x13901,x13904,f2(x13901))+P6(x13901,x13902,f25(x13901,x13903,x13904))+~P6(x13901,x13903,f30(f30(f12(x13901),x13902),x13904))
% 7.56/7.43 [1391]~P9(x13911)+~P7(x13911,x13914,f2(x13911))+P7(x13911,x13912,f25(x13911,x13913,x13914))+~P7(x13911,x13913,f30(f30(f12(x13911),x13912),x13914))
% 7.56/7.43 [1392]~P8(x13921)+~P7(x13921,f2(x13921),x13924)+P6(x13921,x13922,f25(x13921,x13923,x13924))+~P6(x13921,f30(f30(f12(x13921),x13922),x13924),x13923)
% 7.56/7.43 [1394]~P9(x13941)+~P7(x13941,f2(x13941),x13944)+P6(x13941,x13942,f25(x13941,x13943,x13944))+~P6(x13941,f30(f30(f12(x13941),x13942),x13944),x13943)
% 7.56/7.43 [1395]~P8(x13951)+~P7(x13951,f2(x13951),x13954)+P7(x13951,x13952,f25(x13951,x13953,x13954))+~P7(x13951,f30(f30(f12(x13951),x13952),x13954),x13953)
% 7.56/7.43 [1397]~P9(x13971)+~P7(x13971,f2(x13971),x13974)+P7(x13971,x13972,f25(x13971,x13973,x13974))+~P7(x13971,f30(f30(f12(x13971),x13972),x13974),x13973)
% 7.56/7.43 [1398]~P9(x13981)+~P7(x13981,x13983,f2(x13981))+P6(x13981,f25(x13981,x13982,x13983),x13984)+~P6(x13981,f30(f30(f12(x13981),x13984),x13983),x13982)
% 7.56/7.43 [1399]~P9(x13991)+~P7(x13991,x13993,f2(x13991))+P7(x13991,f25(x13991,x13992,x13993),x13994)+~P7(x13991,f30(f30(f12(x13991),x13994),x13993),x13992)
% 7.56/7.43 [1400]~P8(x14001)+~P7(x14001,f2(x14001),x14003)+P6(x14001,f25(x14001,x14002,x14003),x14004)+~P6(x14001,x14002,f30(f30(f12(x14001),x14004),x14003))
% 7.56/7.43 [1402]~P9(x14021)+~P7(x14021,f2(x14021),x14023)+P6(x14021,f25(x14021,x14022,x14023),x14024)+~P6(x14021,x14022,f30(f30(f12(x14021),x14024),x14023))
% 7.56/7.43 [1403]~P8(x14031)+~P7(x14031,f2(x14031),x14033)+P7(x14031,f25(x14031,x14032,x14033),x14034)+~P7(x14031,x14032,f30(f30(f12(x14031),x14034),x14033))
% 7.56/7.43 [1405]~P9(x14051)+~P7(x14051,f2(x14051),x14053)+P7(x14051,f25(x14051,x14052,x14053),x14054)+~P7(x14051,x14052,f30(f30(f12(x14051),x14054),x14053))
% 7.56/7.43 [1412]~P9(x14121)+~P7(x14121,x14124,f2(x14121))+~P6(x14121,x14123,f25(x14121,x14122,x14124))+P6(x14121,x14122,f30(f30(f12(x14121),x14123),x14124))
% 7.56/7.43 [1413]~P9(x14131)+~P7(x14131,x14134,f2(x14131))+~P7(x14131,x14133,f25(x14131,x14132,x14134))+P7(x14131,x14132,f30(f30(f12(x14131),x14133),x14134))
% 7.56/7.43 [1414]~P8(x14141)+~P7(x14141,f2(x14141),x14144)+~P6(x14141,f25(x14141,x14142,x14144),x14143)+P6(x14141,x14142,f30(f30(f12(x14141),x14143),x14144))
% 7.56/7.43 [1415]~P9(x14151)+~P7(x14151,f2(x14151),x14154)+~P6(x14151,f25(x14151,x14152,x14154),x14153)+P6(x14151,x14152,f30(f30(f12(x14151),x14153),x14154))
% 7.56/7.43 [1416]~P8(x14161)+~P7(x14161,f2(x14161),x14164)+~P7(x14161,f25(x14161,x14162,x14164),x14163)+P7(x14161,x14162,f30(f30(f12(x14161),x14163),x14164))
% 7.56/7.43 [1417]~P9(x14171)+~P7(x14171,f2(x14171),x14174)+~P7(x14171,f25(x14171,x14172,x14174),x14173)+P7(x14171,x14172,f30(f30(f12(x14171),x14173),x14174))
% 7.56/7.43 [1418]~P9(x14181)+~P7(x14181,x14183,f2(x14181))+~P6(x14181,f25(x14181,x14184,x14183),x14182)+P6(x14181,f30(f30(f12(x14181),x14182),x14183),x14184)
% 7.56/7.43 [1419]~P9(x14191)+~P7(x14191,x14193,f2(x14191))+~P7(x14191,f25(x14191,x14194,x14193),x14192)+P7(x14191,f30(f30(f12(x14191),x14192),x14193),x14194)
% 7.56/7.43 [1420]~P8(x14201)+~P7(x14201,f2(x14201),x14203)+~P6(x14201,x14202,f25(x14201,x14204,x14203))+P6(x14201,f30(f30(f12(x14201),x14202),x14203),x14204)
% 7.56/7.43 [1421]~P9(x14211)+~P7(x14211,f2(x14211),x14213)+~P6(x14211,x14212,f25(x14211,x14214,x14213))+P6(x14211,f30(f30(f12(x14211),x14212),x14213),x14214)
% 7.56/7.43 [1422]~P8(x14221)+~P7(x14221,f2(x14221),x14223)+~P7(x14221,x14222,f25(x14221,x14224,x14223))+P7(x14221,f30(f30(f12(x14221),x14222),x14223),x14224)
% 7.56/7.43 [1423]~P9(x14231)+~P7(x14231,f2(x14231),x14233)+~P7(x14231,x14232,f25(x14231,x14234,x14233))+P7(x14231,f30(f30(f12(x14231),x14232),x14233),x14234)
% 7.56/7.43 [1435]P7(x14351,x14353,x14352)+~P49(x14351)+P7(x14351,x14352,x14353)+~P7(x14351,f30(f30(f12(x14351),x14354),x14352),f30(f30(f12(x14351),x14354),x14353))
% 7.56/7.43 [1436]P7(x14361,x14363,x14362)+~P49(x14361)+P7(x14361,x14362,x14363)+~P7(x14361,f30(f30(f12(x14361),x14362),x14364),f30(f30(f12(x14361),x14363),x14364))
% 7.56/7.43 [1440]~P49(x14401)+P7(x14401,x14402,x14403)+P7(x14401,x14404,f2(x14401))+~P7(x14401,f30(f30(f12(x14401),x14402),x14404),f30(f30(f12(x14401),x14403),x14404))
% 7.56/7.43 [1441]~P49(x14411)+P7(x14411,x14412,x14413)+P7(x14411,x14414,f2(x14411))+~P7(x14411,f30(f30(f12(x14411),x14414),x14412),f30(f30(f12(x14411),x14414),x14413))
% 7.56/7.43 [1442]~P49(x14421)+P7(x14421,x14422,x14423)+P7(x14421,f2(x14421),x14424)+~P7(x14421,f30(f30(f12(x14421),x14424),x14423),f30(f30(f12(x14421),x14424),x14422))
% 7.56/7.43 [1443]~P49(x14431)+P7(x14431,x14432,x14433)+P7(x14431,f2(x14431),x14434)+~P7(x14431,f30(f30(f12(x14431),x14433),x14434),f30(f30(f12(x14431),x14432),x14434))
% 7.56/7.43 [1455]~P49(x14551)+P7(x14551,f2(x14551),x14552)+P7(x14551,x14552,f2(x14551))+~P7(x14551,f30(f30(f12(x14551),x14553),x14552),f30(f30(f12(x14551),x14554),x14552))
% 7.56/7.43 [1456]~P49(x14561)+P7(x14561,f2(x14561),x14562)+P7(x14561,x14562,f2(x14561))+~P7(x14561,f30(f30(f12(x14561),x14562),x14563),f30(f30(f12(x14561),x14562),x14564))
% 7.56/7.43 [1470]~P48(x14703)+P6(a39,x14701,x14702)+~P7(x14703,f3(x14703),x14704)+~P6(x14703,f30(f30(f22(x14703),x14704),x14701),f30(f30(f22(x14703),x14704),x14702))
% 7.56/7.43 [1472]~P48(x14723)+P7(a39,x14721,x14722)+~P7(x14723,f3(x14723),x14724)+~P7(x14723,f30(f30(f22(x14723),x14724),x14721),f30(f30(f22(x14723),x14724),x14722))
% 7.56/7.43 [1477]~P49(x14771)+P6(x14771,x14772,x14773)+~P7(x14771,x14774,f2(x14771))+~P6(x14771,f30(f30(f12(x14771),x14774),x14773),f30(f30(f12(x14771),x14774),x14772))
% 7.56/7.43 [1478]~P49(x14781)+P7(x14781,x14782,x14783)+~P7(x14781,x14784,f2(x14781))+~P7(x14781,f30(f30(f12(x14781),x14784),x14783),f30(f30(f12(x14781),x14784),x14782))
% 7.56/7.43 [1479]~P49(x14791)+P6(x14791,x14792,x14793)+~P7(x14791,f2(x14791),x14794)+~P6(x14791,f30(f30(f12(x14791),x14794),x14792),f30(f30(f12(x14791),x14794),x14793))
% 7.56/7.43 [1480]~P55(x14801)+P6(x14801,x14802,x14803)+~P7(x14801,f2(x14801),x14804)+~P6(x14801,f30(f30(f12(x14801),x14804),x14802),f30(f30(f12(x14801),x14804),x14803))
% 7.56/7.43 [1481]~P55(x14811)+P6(x14811,x14812,x14813)+~P7(x14811,f2(x14811),x14814)+~P6(x14811,f30(f30(f12(x14811),x14812),x14814),f30(f30(f12(x14811),x14813),x14814))
% 7.56/7.43 [1482]~P49(x14821)+P7(x14821,x14822,x14823)+~P7(x14821,f2(x14821),x14824)+~P7(x14821,f30(f30(f12(x14821),x14824),x14822),f30(f30(f12(x14821),x14824),x14823))
% 7.56/7.43 [1483]~P55(x14831)+P7(x14831,x14832,x14833)+~P6(x14831,f2(x14831),x14834)+~P7(x14831,f30(f30(f12(x14831),x14834),x14832),f30(f30(f12(x14831),x14834),x14833))
% 7.56/7.43 [1484]~P54(x14841)+P7(x14841,x14842,x14843)+~P6(x14841,f2(x14841),x14844)+~P7(x14841,f30(f30(f12(x14841),x14844),x14842),f30(f30(f12(x14841),x14844),x14843))
% 7.56/7.43 [1485]~P48(x14851)+P7(x14851,x14852,x14853)+~P6(x14851,f2(x14851),x14853)+~P7(x14851,f30(f30(f22(x14851),x14852),x14854),f30(f30(f22(x14851),x14853),x14854))
% 7.56/7.43 [1486]~P55(x14861)+P7(x14861,x14862,x14863)+~P6(x14861,f2(x14861),x14864)+~P7(x14861,f30(f30(f12(x14861),x14862),x14864),f30(f30(f12(x14861),x14863),x14864))
% 7.56/7.43 [1487]~P54(x14871)+P7(x14871,x14872,x14873)+~P6(x14871,f2(x14871),x14874)+~P7(x14871,f30(f30(f12(x14871),x14872),x14874),f30(f30(f12(x14871),x14873),x14874))
% 7.56/7.43 [1684]~P48(x16841)+P6(x16841,x16842,x16843)+~P6(x16841,f2(x16841),x16843)+~P6(x16841,f30(f30(f22(x16841),x16842),f13(a39,x16844,f3(a39))),f30(f30(f22(x16841),x16843),f13(a39,x16844,f3(a39))))
% 7.56/7.43 [1389]~P5(x13892)+~P6(a39,x13894,x13893)+E(x13891,f2(x13892))+E(f25(x13892,f30(f30(f22(x13892),x13891),x13893),f30(f30(f22(x13892),x13891),x13894)),f30(f30(f22(x13892),x13891),f11(a39,x13893,x13894)))
% 7.56/7.43 [922]~P3(x9225)+E(x9221,x9222)+~E(x9223,x9224)+~E(f11(x9225,x9223,x9224),f11(x9225,x9221,x9222))
% 7.56/7.43 [1096]~P20(x10961)+~P6(x10961,x10964,x10965)+P6(x10961,x10962,x10963)+~E(f11(x10961,x10964,x10965),f11(x10961,x10962,x10963))
% 7.56/7.43 [1098]~P20(x10981)+~P7(x10981,x10984,x10985)+P7(x10981,x10982,x10983)+~E(f11(x10981,x10984,x10985),f11(x10981,x10982,x10983))
% 7.56/7.43 [1310]~P25(x13101)+~P6(x13101,x13103,x13105)+~P6(x13101,x13102,x13104)+P6(x13101,f13(x13101,x13102,x13103),f13(x13101,x13104,x13105))
% 7.56/7.43 [1311]~P26(x13111)+~P6(x13111,x13113,x13115)+~P7(x13111,x13112,x13114)+P7(x13111,f13(x13111,x13112,x13113),f13(x13111,x13114,x13115))
% 7.56/7.43 [1312]~P26(x13121)+~P6(x13121,x13122,x13124)+~P7(x13121,x13123,x13125)+P7(x13121,f13(x13121,x13122,x13123),f13(x13121,x13124,x13125))
% 7.56/7.43 [1313]~P26(x13131)+~P7(x13131,x13133,x13135)+~P7(x13131,x13132,x13134)+P7(x13131,f13(x13131,x13132,x13133),f13(x13131,x13134,x13135))
% 7.56/7.43 [1540]~P37(x15401)+~P7(a38,f21(x15401,x15403),x15405)+~P7(a38,f21(x15401,x15402),x15404)+P7(a38,f21(x15401,f13(x15401,x15402,x15403)),f13(a38,x15404,x15405))
% 7.56/7.43 [1549]~P27(x15491)+~P7(x15491,f9(x15491,x15492),x15494)+~P7(x15491,f9(x15491,x15493),x15495)+P7(x15491,f30(f30(f12(x15491),f9(x15491,x15492)),f9(x15491,x15493)),f30(f30(f12(x15491),x15494),x15495))
% 7.56/7.43 [1521]~P39(x15211)+~P7(a38,f21(x15211,x15213),x15215)+~P7(a38,f21(x15211,x15212),x15214)+P7(a38,f21(x15211,f30(f30(f12(x15211),x15212),x15213)),f30(f30(f12(a38),x15214),x15215))
% 7.56/7.43 [1637]~P68(x16375)+E(x16371,x16372)+E(x16373,x16374)+~E(f13(x16375,f30(f30(f12(x16375),x16373),x16371),f30(f30(f12(x16375),x16374),x16372)),f13(x16375,f30(f30(f12(x16375),x16373),x16372),f30(f30(f12(x16375),x16374),x16371)))
% 7.56/7.43 [1647]~P5(x16472)+E(x16471,f2(x16472))+E(x16473,f2(x16472))+E(f25(x16472,f13(x16472,f30(f30(f12(x16472),x16474),x16471),f30(f30(f12(x16472),x16475),x16473)),f30(f30(f12(x16472),x16473),x16471)),f13(x16472,f25(x16472,x16474,x16473),f25(x16472,x16475,x16471)))
% 7.56/7.43 [1648]~P5(x16482)+E(x16481,f2(x16482))+E(x16483,f2(x16482))+E(f25(x16482,f11(x16482,f30(f30(f12(x16482),x16484),x16481),f30(f30(f12(x16482),x16485),x16483)),f30(f30(f12(x16482),x16483),x16481)),f11(x16482,f25(x16482,x16484,x16483),f25(x16482,x16485,x16481)))
% 7.56/7.43 [1066]~P23(x10662)+~P6(x10662,f2(x10662),x10663)+~P6(x10662,f2(x10662),x10661)+~E(f13(x10662,x10663,x10661),f2(x10662))+E(x10661,f2(x10662))
% 7.56/7.43 [1067]~P23(x10672)+~P6(x10672,f2(x10672),x10673)+~P6(x10672,f2(x10672),x10671)+~E(f13(x10672,x10671,x10673),f2(x10672))+E(x10671,f2(x10672))
% 7.56/7.43 [1335]~P27(x13351)+~P6(x13351,x13352,f3(x13351))+~P6(x13351,f2(x13351),x13352)+~P6(x13351,f2(x13351),x13353)+P6(x13351,f30(f30(f12(x13351),x13352),x13353),x13353)
% 7.56/7.43 [1336]~P27(x13361)+~P6(x13361,x13363,f3(x13361))+~P6(x13361,f2(x13361),x13363)+~P6(x13361,f2(x13361),x13362)+P6(x13361,f30(f30(f12(x13361),x13362),x13363),x13362)
% 7.56/7.43 [1736]~P48(x17363)+E(x17361,x17362)+~P6(x17363,f2(x17363),x17362)+~P6(x17363,f2(x17363),x17361)+~E(f30(f30(f22(x17363),x17361),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(x17363),x17362),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))
% 7.56/7.43 [1228]~P8(x12281)+P7(x12281,f2(x12281),x12282)+~P6(x12281,x12283,f2(x12281))+P7(x12281,x12282,f2(x12281))+P6(x12281,x12283,f25(x12281,x12284,x12282))
% 7.56/7.43 [1229]~P8(x12291)+P7(x12291,f2(x12291),x12292)+~P7(x12291,x12293,f2(x12291))+P7(x12291,x12292,f2(x12291))+P7(x12291,x12293,f25(x12291,x12294,x12292))
% 7.56/7.43 [1230]~P8(x12301)+P7(x12301,f2(x12301),x12302)+~P6(x12301,f2(x12301),x12304)+P7(x12301,x12302,f2(x12301))+P6(x12301,f25(x12301,x12303,x12302),x12304)
% 7.56/7.43 [1231]~P8(x12311)+P7(x12311,f2(x12311),x12312)+~P7(x12311,f2(x12311),x12314)+P7(x12311,x12312,f2(x12311))+P7(x12311,f25(x12311,x12313,x12312),x12314)
% 7.56/7.43 [1298]~P8(x12981)+P7(x12981,f2(x12981),x12983)+P6(x12981,x12982,f2(x12981))+~P6(x12981,x12982,f25(x12981,x12984,x12983))+P7(x12981,x12983,f2(x12981))
% 7.56/7.43 [1299]~P8(x12991)+P7(x12991,f2(x12991),x12993)+P7(x12991,x12992,f2(x12991))+~P7(x12991,x12992,f25(x12991,x12994,x12993))+P7(x12991,x12993,f2(x12991))
% 7.56/7.43 [1300]~P8(x13001)+P7(x13001,f2(x13001),x13002)+P7(x13001,x13002,f2(x13001))+~P6(x13001,f25(x13001,x13004,x13002),x13003)+P6(x13001,f2(x13001),x13003)
% 7.56/7.43 [1301]~P8(x13011)+P7(x13011,f2(x13011),x13012)+P7(x13011,x13012,f2(x13011))+~P7(x13011,f25(x13011,x13014,x13012),x13013)+P7(x13011,f2(x13011),x13013)
% 7.56/7.43 [1458]~P48(x14581)+~P7(x14581,x14582,x14584)+~P6(x14581,f2(x14581),x14582)+~P7(a39,f2(a39),x14583)+P7(x14581,f30(f30(f22(x14581),x14582),x14583),f30(f30(f22(x14581),x14584),x14583))
% 7.56/7.43 [1465]~P48(x14651)+~P6(a39,x14654,x14653)+~P6(x14651,x14652,f3(x14651))+~P6(x14651,f2(x14651),x14652)+P6(x14651,f30(f30(f22(x14651),x14652),x14653),f30(f30(f22(x14651),x14652),x14654))
% 7.56/7.43 [1466]~P48(x14661)+~P7(a39,x14664,x14663)+~P7(x14661,x14662,f3(x14661))+~P7(x14661,f2(x14661),x14662)+P7(x14661,f30(f30(f22(x14661),x14662),x14663),f30(f30(f22(x14661),x14662),x14664))
% 7.56/7.43 [1489]~P8(x14891)+~P6(x14891,x14893,f2(x14891))+P7(x14891,x14892,f2(x14891))+P6(x14891,x14893,f25(x14891,x14894,x14892))+~P6(x14891,f30(f30(f12(x14891),x14893),x14892),x14894)
% 7.56/7.43 [1490]~P8(x14901)+~P7(x14901,x14903,f2(x14901))+P7(x14901,x14902,f2(x14901))+P7(x14901,x14903,f25(x14901,x14904,x14902))+~P7(x14901,f30(f30(f12(x14901),x14903),x14902),x14904)
% 7.56/7.43 [1491]~P8(x14911)+~P6(x14911,f2(x14911),x14914)+P7(x14911,x14912,f2(x14911))+P6(x14911,f25(x14911,x14913,x14912),x14914)+~P6(x14911,x14913,f30(f30(f12(x14911),x14914),x14912))
% 7.56/7.43 [1492]~P8(x14921)+~P7(x14921,f2(x14921),x14924)+P7(x14921,x14922,f2(x14921))+P7(x14921,f25(x14921,x14923,x14922),x14924)+~P7(x14921,x14923,f30(f30(f12(x14921),x14924),x14922))
% 7.56/7.43 [1493]~P8(x14931)+~P6(x14931,x14933,f2(x14931))+P7(x14931,f2(x14931),x14932)+P6(x14931,x14933,f25(x14931,x14934,x14932))+~P6(x14931,x14934,f30(f30(f12(x14931),x14933),x14932))
% 7.56/7.43 [1494]~P8(x14941)+~P7(x14941,x14943,f2(x14941))+P7(x14941,f2(x14941),x14942)+P7(x14941,x14943,f25(x14941,x14944,x14942))+~P7(x14941,x14944,f30(f30(f12(x14941),x14943),x14942))
% 7.56/7.43 [1495]~P8(x14951)+~P7(x14951,x14952,f2(x14951))+P7(x14951,f2(x14951),x14952)+P6(x14951,x14953,f25(x14951,x14954,x14952))+~P6(x14951,x14954,f30(f30(f12(x14951),x14953),x14952))
% 7.56/7.43 [1496]~P8(x14961)+~P7(x14961,x14962,f2(x14961))+P7(x14961,f2(x14961),x14962)+P7(x14961,x14963,f25(x14961,x14964,x14962))+~P7(x14961,x14964,f30(f30(f12(x14961),x14963),x14962))
% 7.56/7.43 [1497]~P8(x14971)+~P7(x14971,x14972,f2(x14971))+P7(x14971,f2(x14971),x14972)+P6(x14971,f25(x14971,x14973,x14972),x14974)+~P6(x14971,f30(f30(f12(x14971),x14974),x14972),x14973)
% 7.56/7.43 [1498]~P8(x14981)+~P7(x14981,x14982,f2(x14981))+P7(x14981,f2(x14981),x14982)+P7(x14981,f25(x14981,x14983,x14982),x14984)+~P7(x14981,f30(f30(f12(x14981),x14984),x14982),x14983)
% 7.56/7.43 [1499]~P8(x14991)+~P6(x14991,f2(x14991),x14994)+P7(x14991,f2(x14991),x14992)+P6(x14991,f25(x14991,x14993,x14992),x14994)+~P6(x14991,f30(f30(f12(x14991),x14994),x14992),x14993)
% 7.56/7.43 [1500]~P8(x15001)+~P7(x15001,f2(x15001),x15004)+P7(x15001,f2(x15001),x15002)+P7(x15001,f25(x15001,x15003,x15002),x15004)+~P7(x15001,f30(f30(f12(x15001),x15004),x15002),x15003)
% 7.56/7.43 [1501]~P8(x15011)+~P7(x15011,x15012,f2(x15011))+~P6(x15011,x15014,f25(x15011,x15013,x15012))+P7(x15011,f2(x15011),x15012)+P6(x15011,x15013,f30(f30(f12(x15011),x15014),x15012))
% 7.56/7.43 [1502]~P8(x15021)+~P7(x15021,x15022,f2(x15021))+~P7(x15021,x15024,f25(x15021,x15023,x15022))+P7(x15021,f2(x15021),x15022)+P7(x15021,x15023,f30(f30(f12(x15021),x15024),x15022))
% 7.56/7.43 [1503]~P8(x15031)+~P7(x15031,x15032,f2(x15031))+~P6(x15031,f25(x15031,x15034,x15032),x15033)+P7(x15031,f2(x15031),x15032)+P6(x15031,f30(f30(f12(x15031),x15033),x15032),x15034)
% 7.56/7.43 [1504]~P8(x15041)+~P7(x15041,x15042,f2(x15041))+~P7(x15041,f25(x15041,x15044,x15042),x15043)+P7(x15041,f2(x15041),x15042)+P7(x15041,f30(f30(f12(x15041),x15043),x15042),x15044)
% 7.56/7.43 [1569]~P48(x15693)+E(x15691,x15692)+~P6(x15693,f2(x15693),x15692)+~P6(x15693,f2(x15693),x15691)+~E(f30(f30(f22(x15693),x15691),f13(a39,x15694,f3(a39))),f30(f30(f22(x15693),x15692),f13(a39,x15694,f3(a39))))
% 7.56/7.43 [1570]~P8(x15701)+~P6(x15701,x15703,x15704)+~P6(x15701,x15702,f2(x15701))+P6(x15701,f25(x15701,x15702,x15703),f25(x15701,x15702,x15704))+~P7(x15701,f2(x15701),f30(f30(f12(x15701),x15703),x15704))
% 7.56/7.43 [1571]~P9(x15711)+~P7(x15711,x15713,x15714)+~P7(x15711,x15712,f2(x15711))+P7(x15711,f25(x15711,x15712,x15713),f25(x15711,x15712,x15714))+~P7(x15711,f2(x15711),f30(f30(f12(x15711),x15713),x15714))
% 7.56/7.43 [1572]~P9(x15721)+~P6(x15721,x15724,x15723)+~P6(x15721,f2(x15721),x15722)+P6(x15721,f25(x15721,x15722,x15723),f25(x15721,x15722,x15724))+~P7(x15721,f2(x15721),f30(f30(f12(x15721),x15723),x15724))
% 7.56/7.43 [1573]~P9(x15731)+~P7(x15731,x15734,x15733)+~P7(x15731,f2(x15731),x15732)+P7(x15731,f25(x15731,x15732,x15733),f25(x15731,x15732,x15734))+~P7(x15731,f2(x15731),f30(f30(f12(x15731),x15733),x15734))
% 7.56/7.43 [1597]~P8(x15971)+~P7(x15971,x15974,f2(x15971))+P6(x15971,x15972,f25(x15971,x15973,x15974))+~P6(x15971,x15973,f30(f30(f12(x15971),x15972),x15974))+~P6(x15971,f30(f30(f12(x15971),x15972),x15974),x15973)
% 7.56/7.43 [1598]~P8(x15981)+~P6(x15981,x15982,f2(x15981))+P6(x15981,x15982,f25(x15981,x15983,x15984))+~P6(x15981,x15983,f30(f30(f12(x15981),x15982),x15984))+~P6(x15981,f30(f30(f12(x15981),x15982),x15984),x15983)
% 7.56/7.43 [1599]~P8(x15991)+~P7(x15991,x15994,f2(x15991))+P7(x15991,x15992,f25(x15991,x15993,x15994))+~P7(x15991,x15993,f30(f30(f12(x15991),x15992),x15994))+~P7(x15991,f30(f30(f12(x15991),x15992),x15994),x15993)
% 7.56/7.43 [1600]~P8(x16001)+~P7(x16001,x16002,f2(x16001))+P7(x16001,x16002,f25(x16001,x16003,x16004))+~P7(x16001,x16003,f30(f30(f12(x16001),x16002),x16004))+~P7(x16001,f30(f30(f12(x16001),x16002),x16004),x16003)
% 7.56/7.43 [1601]~P8(x16011)+~P7(x16011,x16013,f2(x16011))+P6(x16011,f25(x16011,x16012,x16013),x16014)+~P6(x16011,x16012,f30(f30(f12(x16011),x16014),x16013))+~P6(x16011,f30(f30(f12(x16011),x16014),x16013),x16012)
% 7.56/7.43 [1602]~P8(x16021)+~P7(x16021,x16023,f2(x16021))+P7(x16021,f25(x16021,x16022,x16023),x16024)+~P7(x16021,x16022,f30(f30(f12(x16021),x16024),x16023))+~P7(x16021,f30(f30(f12(x16021),x16024),x16023),x16022)
% 7.56/7.43 [1603]~P8(x16031)+~P6(x16031,f2(x16031),x16034)+P6(x16031,f25(x16031,x16032,x16033),x16034)+~P6(x16031,x16032,f30(f30(f12(x16031),x16034),x16033))+~P6(x16031,f30(f30(f12(x16031),x16034),x16033),x16032)
% 7.56/7.43 [1604]~P8(x16041)+~P7(x16041,f2(x16041),x16044)+P7(x16041,f25(x16041,x16042,x16043),x16044)+~P7(x16041,x16042,f30(f30(f12(x16041),x16044),x16043))+~P7(x16041,f30(f30(f12(x16041),x16044),x16043),x16042)
% 7.56/7.43 [1056]~P5(x10562)+E(f25(x10562,x10564,x10561),f25(x10562,x10565,x10563))+E(x10561,f2(x10562))+E(x10563,f2(x10562))+~E(f30(f30(f12(x10562),x10564),x10563),f30(f30(f12(x10562),x10565),x10561))
% 7.56/7.43 [1058]~P5(x10582)+~E(f25(x10582,x10584,x10583),f25(x10582,x10585,x10581))+E(x10581,f2(x10582))+E(x10583,f2(x10582))+E(f30(f30(f12(x10582),x10584),x10581),f30(f30(f12(x10582),x10585),x10583))
% 7.56/7.43 [1388]~P68(x13884)+E(x13881,x13882)+~E(x13885,x13886)+E(x13883,f2(x13884))+~E(f13(x13884,x13885,f30(f30(f12(x13884),x13883),x13881)),f13(x13884,x13886,f30(f30(f12(x13884),x13883),x13882)))
% 7.56/7.43 [1050]~P23(x10501)+~P6(x10501,f2(x10501),x10503)+~P6(x10501,f2(x10501),x10502)+~E(x10503,f2(x10501))+~E(x10502,f2(x10501))+E(f13(x10501,x10502,x10503),f2(x10501))
% 7.56/7.43 [771]~P35(x7712)+~P52(x7712)+~P57(x7712)+~P69(x7712)+E(x7711,f2(x7712))+~E(f30(f30(f22(x7712),x7711),x7713),f2(x7712))
% 7.56/7.43 [772]~P35(x7722)+~P52(x7722)+~P57(x7722)+~P69(x7722)+~E(x7721,f2(a39))+~E(f30(f30(f22(x7722),x7723),x7721),f2(x7722))
% 7.56/7.43 [1767]~P6(a38,f2(a38),x17672)+~P6(a38,f2(a38),x17671)+~P7(a38,f2(a38),x17673)+~P7(a38,x17671,f25(a38,x17673,f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))+~P7(a38,x17672,f25(a38,x17673,f18(a38,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))+P7(a38,f17(f13(a38,f30(f30(f22(a38),x17671),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),f30(f30(f22(a38),x17672),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))))),x17673)
% 7.56/7.43 [1533]~P9(x15331)+~P6(x15331,x15335,x15333)+~P6(x15331,x15332,x15334)+~P6(x15331,f2(x15331),x15332)+~P7(x15331,f2(x15331),x15335)+P6(x15331,f25(x15331,x15332,x15333),f25(x15331,x15334,x15335))
% 7.56/7.43 [1534]~P9(x15341)+~P6(x15341,x15345,x15343)+~P7(x15341,x15342,x15344)+~P6(x15341,f2(x15341),x15342)+~P7(x15341,f2(x15341),x15345)+P7(x15341,f25(x15341,x15342,x15343),f25(x15341,x15344,x15345))
% 7.56/7.43 [1535]~P9(x15351)+~P6(x15351,x15352,x15354)+~P7(x15351,x15355,x15353)+~P7(x15351,f2(x15351),x15355)+~P7(x15351,f2(x15351),x15352)+P7(x15351,f25(x15351,x15352,x15353),f25(x15351,x15354,x15355))
% 7.56/7.43 [1522]~P63(x15221)+~P6(x15221,x15223,x15225)+~P6(x15221,x15222,x15224)+~P6(x15221,f2(x15221),x15223)+~P6(x15221,f2(x15221),x15224)+P6(x15221,f30(f30(f12(x15221),x15222),x15223),f30(f30(f12(x15221),x15224),x15225))
% 7.56/7.43 [1523]~P63(x15231)+~P6(x15231,x15233,x15235)+~P6(x15231,x15232,x15234)+~P6(x15231,f2(x15231),x15233)+~P6(x15231,f2(x15231),x15232)+P6(x15231,f30(f30(f12(x15231),x15232),x15233),f30(f30(f12(x15231),x15234),x15235))
% 7.56/7.44 [1524]~P55(x15241)+~P6(x15241,x15243,x15245)+~P7(x15241,x15242,x15244)+~P6(x15241,f2(x15241),x15242)+~P7(x15241,f2(x15241),x15243)+P7(x15241,f30(f30(f12(x15241),x15242),x15243),f30(f30(f12(x15241),x15244),x15245))
% 7.56/7.44 [1525]~P55(x15251)+~P6(x15251,x15252,x15254)+~P7(x15251,x15253,x15255)+~P6(x15251,f2(x15251),x15253)+~P7(x15251,f2(x15251),x15252)+P7(x15251,f30(f30(f12(x15251),x15252),x15253),f30(f30(f12(x15251),x15254),x15255))
% 7.56/7.44 [1526]~P55(x15261)+~P7(x15261,x15263,x15265)+~P7(x15261,x15262,x15264)+~P6(x15261,f2(x15261),x15263)+~P6(x15261,f2(x15261),x15262)+P7(x15261,f30(f30(f12(x15261),x15262),x15263),f30(f30(f12(x15261),x15264),x15265))
% 7.56/7.44 [1527]~P55(x15271)+~P7(x15271,x15273,x15275)+~P7(x15271,x15272,x15274)+~P6(x15271,f2(x15271),x15273)+~P7(x15271,f2(x15271),x15274)+P7(x15271,f30(f30(f12(x15271),x15272),x15273),f30(f30(f12(x15271),x15274),x15275))
% 7.56/7.44 [719]~P35(x7192)+~P52(x7192)+~P57(x7192)+~P69(x7192)+~E(x7193,f2(x7192))+E(x7191,f2(a39))+E(f30(f30(f22(x7192),x7193),x7191),f2(x7192))
% 7.56/7.44 [1657]~P53(x16571)+~P6(x16571,x16575,x16576)+~P6(x16571,x16573,x16576)+~P6(x16571,f2(x16571),x16574)+~P6(x16571,f2(x16571),x16572)+~E(f13(x16571,x16572,x16574),f3(x16571))+P6(x16571,f13(x16571,f30(f30(f12(x16571),x16572),x16573),f30(f30(f12(x16571),x16574),x16575)),x16576)
% 7.56/7.44 [1658]~P56(x16581)+~P7(x16581,x16585,x16586)+~P7(x16581,x16583,x16586)+~P6(x16581,f2(x16581),x16584)+~P6(x16581,f2(x16581),x16582)+~E(f13(x16581,x16582,x16584),f3(x16581))+P7(x16581,f13(x16581,f30(f30(f12(x16581),x16582),x16583),f30(f30(f12(x16581),x16584),x16585)),x16586)
% 7.56/7.44 %EqnAxiom
% 7.56/7.44 [1]E(x11,x11)
% 7.56/7.44 [2]E(x22,x21)+~E(x21,x22)
% 7.56/7.44 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 7.56/7.44 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 7.56/7.44 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 7.56/7.44 [6]~E(x61,x62)+E(f17(x61),f17(x62))
% 7.56/7.44 [7]~E(x71,x72)+E(f30(x71,x73),f30(x72,x73))
% 7.56/7.44 [8]~E(x81,x82)+E(f30(x83,x81),f30(x83,x82))
% 7.56/7.44 [9]~E(x91,x92)+E(f25(x91,x93,x94),f25(x92,x93,x94))
% 7.56/7.44 [10]~E(x101,x102)+E(f25(x103,x101,x104),f25(x103,x102,x104))
% 7.56/7.44 [11]~E(x111,x112)+E(f25(x113,x114,x111),f25(x113,x114,x112))
% 7.56/7.44 [12]~E(x121,x122)+E(f13(x121,x123,x124),f13(x122,x123,x124))
% 7.56/7.44 [13]~E(x131,x132)+E(f13(x133,x131,x134),f13(x133,x132,x134))
% 7.56/7.44 [14]~E(x141,x142)+E(f13(x143,x144,x141),f13(x143,x144,x142))
% 7.56/7.44 [15]~E(x151,x152)+E(f18(x151,x153),f18(x152,x153))
% 7.56/7.44 [16]~E(x161,x162)+E(f18(x163,x161),f18(x163,x162))
% 7.56/7.44 [17]~E(x171,x172)+E(f12(x171),f12(x172))
% 7.56/7.44 [18]~E(x181,x182)+E(f20(x181),f20(x182))
% 7.56/7.44 [19]~E(x191,x192)+E(f22(x191),f22(x192))
% 7.56/7.44 [20]~E(x201,x202)+E(f4(x201,x203),f4(x202,x203))
% 7.56/7.44 [21]~E(x211,x212)+E(f4(x213,x211),f4(x213,x212))
% 7.56/7.44 [22]~E(x221,x222)+E(f9(x221,x223),f9(x222,x223))
% 7.56/7.44 [23]~E(x231,x232)+E(f9(x233,x231),f9(x233,x232))
% 7.56/7.44 [24]~E(x241,x242)+E(f11(x241,x243,x244),f11(x242,x243,x244))
% 7.56/7.44 [25]~E(x251,x252)+E(f11(x253,x251,x254),f11(x253,x252,x254))
% 7.56/7.44 [26]~E(x261,x262)+E(f11(x263,x264,x261),f11(x263,x264,x262))
% 7.56/7.44 [27]~E(x271,x272)+E(f21(x271,x273),f21(x272,x273))
% 7.56/7.44 [28]~E(x281,x282)+E(f21(x283,x281),f21(x283,x282))
% 7.56/7.44 [29]~E(x291,x292)+E(f23(x291,x293,x294),f23(x292,x293,x294))
% 7.56/7.44 [30]~E(x301,x302)+E(f23(x303,x301,x304),f23(x303,x302,x304))
% 7.56/7.44 [31]~E(x311,x312)+E(f23(x313,x314,x311),f23(x313,x314,x312))
% 7.56/7.44 [32]~E(x321,x322)+E(f32(x321,x323),f32(x322,x323))
% 7.56/7.44 [33]~E(x331,x332)+E(f32(x333,x331),f32(x333,x332))
% 7.56/7.44 [34]~E(x341,x342)+E(f34(x341,x343),f34(x342,x343))
% 7.56/7.44 [35]~E(x351,x352)+E(f34(x353,x351),f34(x353,x352))
% 7.56/7.44 [36]~E(x361,x362)+E(f7(x361,x363,x364),f7(x362,x363,x364))
% 7.56/7.44 [37]~E(x371,x372)+E(f7(x373,x371,x374),f7(x373,x372,x374))
% 7.56/7.44 [38]~E(x381,x382)+E(f7(x383,x384,x381),f7(x383,x384,x382))
% 7.56/7.44 [39]~E(x391,x392)+E(f8(x391,x393,x394),f8(x392,x393,x394))
% 7.56/7.44 [40]~E(x401,x402)+E(f8(x403,x401,x404),f8(x403,x402,x404))
% 7.56/7.44 [41]~E(x411,x412)+E(f8(x413,x414,x411),f8(x413,x414,x412))
% 7.56/7.44 [42]~E(x421,x422)+E(f41(x421,x423),f41(x422,x423))
% 7.56/7.44 [43]~E(x431,x432)+E(f41(x433,x431),f41(x433,x432))
% 7.56/7.44 [44]~E(x441,x442)+E(f24(x441),f24(x442))
% 7.56/7.44 [45]~E(x451,x452)+E(f28(x451,x453),f28(x452,x453))
% 7.56/7.44 [46]~E(x461,x462)+E(f28(x463,x461),f28(x463,x462))
% 7.56/7.44 [47]~E(x471,x472)+E(f33(x471,x473,x474,x475),f33(x472,x473,x474,x475))
% 7.56/7.44 [48]~E(x481,x482)+E(f33(x483,x481,x484,x485),f33(x483,x482,x484,x485))
% 7.56/7.44 [49]~E(x491,x492)+E(f33(x493,x494,x491,x495),f33(x493,x494,x492,x495))
% 7.56/7.44 [50]~E(x501,x502)+E(f33(x503,x504,x505,x501),f33(x503,x504,x505,x502))
% 7.56/7.44 [51]~E(x511,x512)+E(f35(x511,x513),f35(x512,x513))
% 7.56/7.44 [52]~E(x521,x522)+E(f35(x523,x521),f35(x523,x522))
% 7.56/7.44 [53]~E(x531,x532)+E(f36(x531,x533),f36(x532,x533))
% 7.56/7.44 [54]~E(x541,x542)+E(f36(x543,x541),f36(x543,x542))
% 7.56/7.44 [55]~E(x551,x552)+E(f10(x551),f10(x552))
% 7.56/7.44 [56]~E(x561,x562)+E(f19(x561,x563),f19(x562,x563))
% 7.56/7.44 [57]~E(x571,x572)+E(f19(x573,x571),f19(x573,x572))
% 7.56/7.44 [58]~E(x581,x582)+E(f31(x581),f31(x582))
% 7.56/7.44 [59]~E(x591,x592)+E(f6(x591),f6(x592))
% 7.56/7.44 [60]~P1(x601)+P1(x602)+~E(x601,x602)
% 7.56/7.44 [61]P7(x612,x613,x614)+~E(x611,x612)+~P7(x611,x613,x614)
% 7.56/7.44 [62]P7(x623,x622,x624)+~E(x621,x622)+~P7(x623,x621,x624)
% 7.56/7.44 [63]P7(x633,x634,x632)+~E(x631,x632)+~P7(x633,x634,x631)
% 7.56/7.44 [64]~P27(x641)+P27(x642)+~E(x641,x642)
% 7.56/7.44 [65]P6(x652,x653,x654)+~E(x651,x652)+~P6(x651,x653,x654)
% 7.56/7.44 [66]P6(x663,x662,x664)+~E(x661,x662)+~P6(x663,x661,x664)
% 7.56/7.44 [67]P6(x673,x674,x672)+~E(x671,x672)+~P6(x673,x674,x671)
% 7.56/7.44 [68]~P18(x681)+P18(x682)+~E(x681,x682)
% 7.56/7.44 [69]~P8(x691)+P8(x692)+~E(x691,x692)
% 7.56/7.44 [70]~P19(x701)+P19(x702)+~E(x701,x702)
% 7.56/7.44 [71]~P48(x711)+P48(x712)+~E(x711,x712)
% 7.56/7.44 [72]~P33(x721)+P33(x722)+~E(x721,x722)
% 7.56/7.44 [73]~P37(x731)+P37(x732)+~E(x731,x732)
% 7.56/7.44 [74]~P47(x741)+P47(x742)+~E(x741,x742)
% 7.56/7.44 [75]~P4(x751)+P4(x752)+~E(x751,x752)
% 7.56/7.44 [76]~P59(x761)+P59(x762)+~E(x761,x762)
% 7.56/7.44 [77]~P9(x771)+P9(x772)+~E(x771,x772)
% 7.56/7.44 [78]~P28(x781)+P28(x782)+~E(x781,x782)
% 7.56/7.44 [79]~P52(x791)+P52(x792)+~E(x791,x792)
% 7.56/7.44 [80]~P44(x801)+P44(x802)+~E(x801,x802)
% 7.56/7.44 [81]~P34(x811)+P34(x812)+~E(x811,x812)
% 7.56/7.44 [82]~P29(x821)+P29(x822)+~E(x821,x822)
% 7.56/7.44 [83]~P49(x831)+P49(x832)+~E(x831,x832)
% 7.56/7.44 [84]~P61(x841)+P61(x842)+~E(x841,x842)
% 7.56/7.44 [85]~P23(x851)+P23(x852)+~E(x851,x852)
% 7.56/7.44 [86]~P41(x861)+P41(x862)+~E(x861,x862)
% 7.56/7.44 [87]~P32(x871)+P32(x872)+~E(x871,x872)
% 7.56/7.44 [88]~P68(x881)+P68(x882)+~E(x881,x882)
% 7.56/7.44 [89]~P55(x891)+P55(x892)+~E(x891,x892)
% 7.56/7.44 [90]~P24(x901)+P24(x902)+~E(x901,x902)
% 7.56/7.44 [91]~P38(x911)+P38(x912)+~E(x911,x912)
% 7.56/7.44 [92]~P51(x921)+P51(x922)+~E(x921,x922)
% 7.56/7.44 [93]~P45(x931)+P45(x932)+~E(x931,x932)
% 7.56/7.44 [94]~P39(x941)+P39(x942)+~E(x941,x942)
% 7.56/7.44 [95]~P15(x951)+P15(x952)+~E(x951,x952)
% 7.56/7.44 [96]~P30(x961)+P30(x962)+~E(x961,x962)
% 7.56/7.44 [97]~P42(x971)+P42(x972)+~E(x971,x972)
% 7.56/7.44 [98]~P70(x981)+P70(x982)+~E(x981,x982)
% 7.56/7.44 [99]~P2(x991)+P2(x992)+~E(x991,x992)
% 7.56/7.44 [100]~P31(x1001)+P31(x1002)+~E(x1001,x1002)
% 7.56/7.44 [101]~P35(x1011)+P35(x1012)+~E(x1011,x1012)
% 7.56/7.44 [102]~P67(x1021)+P67(x1022)+~E(x1021,x1022)
% 7.56/7.44 [103]~P57(x1031)+P57(x1032)+~E(x1031,x1032)
% 7.56/7.44 [104]~P36(x1041)+P36(x1042)+~E(x1041,x1042)
% 7.56/7.44 [105]~P25(x1051)+P25(x1052)+~E(x1051,x1052)
% 7.56/7.44 [106]~P54(x1061)+P54(x1062)+~E(x1061,x1062)
% 7.56/7.44 [107]~P20(x1071)+P20(x1072)+~E(x1071,x1072)
% 7.56/7.44 [108]~P5(x1081)+P5(x1082)+~E(x1081,x1082)
% 7.56/7.44 [109]~P26(x1091)+P26(x1092)+~E(x1091,x1092)
% 7.56/7.44 [110]~P60(x1101)+P60(x1102)+~E(x1101,x1102)
% 7.56/7.44 [111]~P63(x1111)+P63(x1112)+~E(x1111,x1112)
% 7.56/7.44 [112]~P13(x1121)+P13(x1122)+~E(x1121,x1122)
% 7.56/7.44 [113]~P43(x1131)+P43(x1132)+~E(x1131,x1132)
% 7.56/7.44 [114]~P10(x1141)+P10(x1142)+~E(x1141,x1142)
% 7.56/7.44 [115]~P22(x1151)+P22(x1152)+~E(x1151,x1152)
% 7.56/7.44 [116]~P40(x1161)+P40(x1162)+~E(x1161,x1162)
% 7.56/7.44 [117]~P16(x1171)+P16(x1172)+~E(x1171,x1172)
% 7.56/7.44 [118]~P17(x1181)+P17(x1182)+~E(x1181,x1182)
% 7.56/7.44 [119]~P56(x1191)+P56(x1192)+~E(x1191,x1192)
% 7.56/7.44 [120]~P53(x1201)+P53(x1202)+~E(x1201,x1202)
% 7.56/7.44 [121]~P66(x1211)+P66(x1212)+~E(x1211,x1212)
% 7.56/7.44 [122]~P3(x1221)+P3(x1222)+~E(x1221,x1222)
% 7.56/7.44 [123]~P64(x1231)+P64(x1232)+~E(x1231,x1232)
% 7.56/7.44 [124]~P11(x1241)+P11(x1242)+~E(x1241,x1242)
% 7.56/7.44 [125]~P46(x1251)+P46(x1252)+~E(x1251,x1252)
% 7.56/7.44 [126]~P62(x1261)+P62(x1262)+~E(x1261,x1262)
% 7.56/7.44 [127]~P14(x1271)+P14(x1272)+~E(x1271,x1272)
% 7.56/7.44 [128]~P65(x1281)+P65(x1282)+~E(x1281,x1282)
% 7.56/7.44 [129]~P12(x1291)+P12(x1292)+~E(x1291,x1292)
% 7.56/7.44 [130]~P21(x1301)+P21(x1302)+~E(x1301,x1302)
% 7.56/7.44 [131]~P69(x1311)+P69(x1312)+~E(x1311,x1312)
% 7.56/7.44 [132]~P58(x1321)+P58(x1322)+~E(x1321,x1322)
% 7.56/7.44 [133]~P50(x1331)+P50(x1332)+~E(x1331,x1332)
% 7.56/7.44
% 7.56/7.44 %-------------------------------------------
% 7.56/7.44 cnf(1792,plain,
% 7.56/7.44 (~P7(a39,f13(a39,x17921,x17922),x17922)),
% 7.56/7.44 inference(rename_variables,[],[551])).
% 7.56/7.44 cnf(1797,plain,
% 7.56/7.44 (P6(a39,x17971,f13(a39,x17972,x17971))),
% 7.56/7.44 inference(rename_variables,[],[398])).
% 7.56/7.44 cnf(1800,plain,
% 7.56/7.44 (P6(a39,x18001,f13(a39,x18002,x18001))),
% 7.56/7.44 inference(rename_variables,[],[398])).
% 7.56/7.44 cnf(1805,plain,
% 7.56/7.44 (P7(a39,x18051,f13(a39,f13(a39,x18052,x18051),f3(a39)))),
% 7.56/7.44 inference(rename_variables,[],[445])).
% 7.56/7.44 cnf(1808,plain,
% 7.56/7.44 (P6(a39,x18081,f13(a39,x18082,x18081))),
% 7.56/7.44 inference(rename_variables,[],[398])).
% 7.56/7.44 cnf(1811,plain,
% 7.56/7.44 (P6(a39,x18111,f13(a39,x18112,x18111))),
% 7.56/7.44 inference(rename_variables,[],[398])).
% 7.56/7.44 cnf(1814,plain,
% 7.56/7.44 (~P7(a39,f13(a39,x18141,x18142),x18141)),
% 7.56/7.44 inference(rename_variables,[],[552])).
% 7.56/7.44 cnf(1817,plain,
% 7.56/7.44 (~P7(a39,x18171,x18171)),
% 7.56/7.44 inference(rename_variables,[],[537])).
% 7.56/7.44 cnf(1820,plain,
% 7.56/7.44 (~P7(a39,f13(a39,x18201,x18202),x18202)),
% 7.56/7.44 inference(rename_variables,[],[551])).
% 7.56/7.44 cnf(1823,plain,
% 7.56/7.44 (~P7(a39,f13(a39,x18231,x18232),x18232)),
% 7.56/7.44 inference(rename_variables,[],[551])).
% 7.56/7.44 cnf(1826,plain,
% 7.56/7.44 (~P6(a39,f13(a39,x18261,f3(a39)),x18261)),
% 7.56/7.44 inference(rename_variables,[],[555])).
% 7.56/7.44 cnf(1829,plain,
% 7.56/7.44 (~P6(a39,f13(a39,x18291,f3(a39)),x18291)),
% 7.56/7.44 inference(rename_variables,[],[555])).
% 7.56/7.44 cnf(1832,plain,
% 7.56/7.44 (~P7(a39,f13(a39,x18321,x18322),x18321)),
% 7.56/7.44 inference(rename_variables,[],[552])).
% 7.56/7.44 cnf(1846,plain,
% 7.56/7.44 (~P7(a38,f13(a38,f9(a38,x18461),f3(a38)),x18461)),
% 7.56/7.44 inference(rename_variables,[],[557])).
% 7.56/7.44 cnf(1851,plain,
% 7.56/7.44 (~E(f13(a39,x18511,f3(a39)),x18511)),
% 7.56/7.44 inference(rename_variables,[],[544])).
% 7.56/7.44 cnf(1864,plain,
% 7.56/7.44 (~E(f13(a39,x18641,f3(a39)),x18641)),
% 7.56/7.44 inference(rename_variables,[],[544])).
% 7.56/7.44 cnf(1869,plain,
% 7.56/7.44 (~E(f13(a39,x18691,f3(a39)),x18691)),
% 7.56/7.44 inference(rename_variables,[],[544])).
% 7.56/7.44 cnf(1879,plain,
% 7.56/7.44 (~E(f13(a1,x18791,x18791),f13(a1,f13(a1,f3(a1),x18792),x18792))),
% 7.56/7.44 inference(rename_variables,[],[559])).
% 7.56/7.44 cnf(1892,plain,
% 7.56/7.44 (~E(f13(a39,x18921,f3(a39)),f2(a39))),
% 7.56/7.44 inference(rename_variables,[],[550])).
% 7.56/7.44 cnf(1898,plain,
% 7.56/7.44 (P6(a38,x18981,f17(f13(a38,f30(f30(f12(a38),x18981),x18981),f30(f30(f12(a38),x18982),x18982))))),
% 7.56/7.44 inference(rename_variables,[],[475])).
% 7.56/7.44 cnf(1901,plain,
% 7.56/7.44 (E(f11(a39,f13(a39,x19011,x19012),x19012),x19011)),
% 7.56/7.44 inference(rename_variables,[],[401])).
% 7.56/7.44 cnf(1904,plain,
% 7.56/7.44 (~E(f13(a39,x19041,f3(a39)),f2(a39))),
% 7.56/7.44 inference(rename_variables,[],[550])).
% 7.56/7.44 cnf(1907,plain,
% 7.56/7.44 (~E(f13(a39,x19071,f3(a39)),x19071)),
% 7.56/7.44 inference(rename_variables,[],[544])).
% 7.56/7.44 cnf(1910,plain,
% 7.56/7.44 (~P6(a39,f13(a39,x19101,f3(a39)),x19101)),
% 7.56/7.44 inference(rename_variables,[],[555])).
% 7.56/7.44 cnf(1913,plain,
% 7.56/7.44 (E(f18(a1,x19131),x19131)),
% 7.56/7.44 inference(rename_variables,[],[341])).
% 7.56/7.44 cnf(1916,plain,
% 7.56/7.44 (~E(f13(a39,x19161,f3(a39)),x19161)),
% 7.56/7.44 inference(rename_variables,[],[544])).
% 7.56/7.44 cnf(1919,plain,
% 7.56/7.44 (E(f18(a1,x19191),x19191)),
% 7.56/7.44 inference(rename_variables,[],[341])).
% 7.56/7.44 cnf(1921,plain,
% 7.56/7.44 (P6(a1,x19211,x19211)),
% 7.56/7.44 inference(rename_variables,[],[366])).
% 7.56/7.44 cnf(1923,plain,
% 7.56/7.44 (P6(a38,x19231,x19231)),
% 7.56/7.44 inference(rename_variables,[],[364])).
% 7.56/7.44 cnf(1926,plain,
% 7.56/7.44 (~P7(a38,f13(a38,f9(a38,x19261),f3(a38)),x19261)),
% 7.56/7.44 inference(rename_variables,[],[557])).
% 7.56/7.44 cnf(1936,plain,
% 7.56/7.44 (P6(a39,f2(a39),x19361)),
% 7.56/7.44 inference(rename_variables,[],[375])).
% 7.56/7.44 cnf(1959,plain,
% 7.56/7.44 (P7(a39,x19591,f13(a39,f13(a39,x19592,x19591),f3(a39)))),
% 7.56/7.44 inference(rename_variables,[],[445])).
% 7.56/7.44 cnf(1962,plain,
% 7.56/7.44 (P7(a39,x19621,f13(a39,x19621,f3(a39)))),
% 7.56/7.44 inference(rename_variables,[],[406])).
% 7.56/7.44 cnf(1965,plain,
% 7.56/7.44 (~E(f13(a39,x19651,f3(a39)),f2(a39))),
% 7.56/7.44 inference(rename_variables,[],[550])).
% 7.56/7.44 cnf(1968,plain,
% 7.56/7.44 (P7(a39,x19681,f13(a39,x19681,f3(a39)))),
% 7.56/7.44 inference(rename_variables,[],[406])).
% 7.56/7.44 cnf(1969,plain,
% 7.56/7.44 (~P7(a39,x19691,x19691)),
% 7.56/7.44 inference(rename_variables,[],[537])).
% 7.56/7.44 cnf(1972,plain,
% 7.56/7.44 (P6(a38,x19721,x19721)),
% 7.56/7.44 inference(rename_variables,[],[364])).
% 7.56/7.44 cnf(1975,plain,
% 7.56/7.44 (P6(a38,x19751,x19751)),
% 7.56/7.44 inference(rename_variables,[],[364])).
% 7.56/7.44 cnf(1978,plain,
% 7.56/7.44 (P7(a39,x19781,f13(a39,x19781,f3(a39)))),
% 7.56/7.44 inference(rename_variables,[],[406])).
% 7.56/7.44 cnf(1981,plain,
% 7.56/7.44 (P6(a39,x19811,f13(a39,x19812,x19811))),
% 7.56/7.44 inference(rename_variables,[],[398])).
% 7.56/7.44 cnf(1985,plain,
% 7.56/7.44 (P7(a39,x19851,f13(a39,x19851,f3(a39)))),
% 7.56/7.44 inference(rename_variables,[],[406])).
% 7.56/7.44 cnf(1990,plain,
% 7.56/7.44 (E(f11(a39,x19901,f13(a39,x19901,x19902)),f2(a39))),
% 7.56/7.44 inference(rename_variables,[],[405])).
% 7.56/7.44 cnf(1993,plain,
% 7.56/7.44 (P7(a39,x19931,f13(a39,x19931,f3(a39)))),
% 7.56/7.44 inference(rename_variables,[],[406])).
% 7.56/7.44 cnf(1994,plain,
% 7.56/7.44 (~E(f13(a39,x19941,f3(a39)),x19941)),
% 7.56/7.44 inference(rename_variables,[],[544])).
% 7.56/7.44 cnf(1997,plain,
% 7.56/7.44 (E(f18(a1,x19971),x19971)),
% 7.56/7.44 inference(rename_variables,[],[341])).
% 7.56/7.44 cnf(2004,plain,
% 7.56/7.44 (~P7(a38,f13(a38,f9(a38,x20041),f3(a38)),x20041)),
% 7.56/7.44 inference(rename_variables,[],[557])).
% 7.56/7.44 cnf(2011,plain,
% 7.56/7.44 (~P7(a39,x20111,f2(a39))),
% 7.56/7.44 inference(rename_variables,[],[542])).
% 7.56/7.44 cnf(2021,plain,
% 7.56/7.44 (~P6(a39,f13(a39,x20211,f3(a39)),x20211)),
% 7.56/7.44 inference(rename_variables,[],[555])).
% 7.56/7.44 cnf(2026,plain,
% 7.56/7.44 (~E(f13(a39,x20261,f3(a39)),x20261)),
% 7.56/7.44 inference(rename_variables,[],[544])).
% 7.56/7.44 cnf(2027,plain,
% 7.56/7.44 (P6(a39,f2(a39),x20271)),
% 7.56/7.44 inference(rename_variables,[],[375])).
% 7.56/7.44 cnf(2036,plain,
% 7.56/7.44 (E(f30(f30(f22(a16),f10(x20361)),f18(a39,f13(a1,f13(a1,f13(a1,f3(a1),a14),a14),f13(a1,f13(a1,f3(a1),a14),a14)))),x20361)),
% 7.56/7.44 inference(rename_variables,[],[485])).
% 7.56/7.44 cnf(2059,plain,
% 7.56/7.44 (~E(f13(a39,x20591,f3(a39)),x20591)),
% 7.56/7.44 inference(rename_variables,[],[544])).
% 7.56/7.44 cnf(2062,plain,
% 7.56/7.44 (P7(a39,x20621,f13(a39,x20621,f3(a39)))),
% 7.56/7.44 inference(rename_variables,[],[406])).
% 7.56/7.44 cnf(2063,plain,
% 7.56/7.44 (~P7(a39,x20631,f2(a39))),
% 7.56/7.44 inference(rename_variables,[],[542])).
% 7.56/7.44 cnf(2070,plain,
% 7.56/7.44 (P6(a39,x20701,x20701)),
% 7.56/7.44 inference(rename_variables,[],[365])).
% 7.56/7.44 cnf(2071,plain,
% 7.56/7.44 (P6(a39,f2(a39),x20711)),
% 7.56/7.44 inference(rename_variables,[],[375])).
% 7.56/7.44 cnf(2080,plain,
% 7.56/7.44 (E(f13(a39,x20801,x20802),f13(a39,x20802,x20801))),
% 7.56/7.44 inference(rename_variables,[],[390])).
% 7.56/7.44 cnf(2083,plain,
% 7.56/7.44 (E(f13(a39,x20831,x20832),f13(a39,x20832,x20831))),
% 7.56/7.45 inference(rename_variables,[],[390])).
% 7.56/7.45 cnf(2086,plain,
% 7.56/7.45 (P6(a38,x20861,x20861)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2095,plain,
% 7.56/7.45 (~P7(a38,f13(a38,f9(a38,x20951),f3(a38)),x20951)),
% 7.56/7.45 inference(rename_variables,[],[557])).
% 7.56/7.45 cnf(2098,plain,
% 7.56/7.45 (~E(f13(a1,x20981,x20981),a15)),
% 7.56/7.45 inference(rename_variables,[],[535])).
% 7.56/7.45 cnf(2101,plain,
% 7.56/7.45 (~E(f13(a39,x21011,f3(a39)),x21011)),
% 7.56/7.45 inference(rename_variables,[],[544])).
% 7.56/7.45 cnf(2104,plain,
% 7.56/7.45 (~P7(a38,f13(a38,f9(a38,x21041),f3(a38)),x21041)),
% 7.56/7.45 inference(rename_variables,[],[557])).
% 7.56/7.45 cnf(2113,plain,
% 7.56/7.45 (~P7(a38,f13(a38,f9(a38,x21131),f3(a38)),x21131)),
% 7.56/7.45 inference(rename_variables,[],[557])).
% 7.56/7.45 cnf(2120,plain,
% 7.56/7.45 (P6(a39,x21201,f13(a39,x21202,x21201))),
% 7.56/7.45 inference(rename_variables,[],[398])).
% 7.56/7.45 cnf(2123,plain,
% 7.56/7.45 (P6(a39,x21231,f13(a39,x21232,x21231))),
% 7.56/7.45 inference(rename_variables,[],[398])).
% 7.56/7.45 cnf(2126,plain,
% 7.56/7.45 (~P7(a39,x21261,f2(a39))),
% 7.56/7.45 inference(rename_variables,[],[542])).
% 7.56/7.45 cnf(2129,plain,
% 7.56/7.45 (~P7(a39,x21291,f2(a39))),
% 7.56/7.45 inference(rename_variables,[],[542])).
% 7.56/7.45 cnf(2150,plain,
% 7.56/7.45 (E(f11(a1,x21501,a14),x21501)),
% 7.56/7.45 inference(rename_variables,[],[361])).
% 7.56/7.45 cnf(2154,plain,
% 7.56/7.45 (P6(a39,f2(a39),x21541)),
% 7.56/7.45 inference(rename_variables,[],[375])).
% 7.56/7.45 cnf(2155,plain,
% 7.56/7.45 (P6(a39,x21551,x21551)),
% 7.56/7.45 inference(rename_variables,[],[365])).
% 7.56/7.45 cnf(2158,plain,
% 7.56/7.45 (~P7(a38,f13(a38,f9(a38,x21581),f3(a38)),x21581)),
% 7.56/7.45 inference(rename_variables,[],[557])).
% 7.56/7.45 cnf(2159,plain,
% 7.56/7.45 (P6(a38,x21591,x21591)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2162,plain,
% 7.56/7.45 (~P7(a39,x21621,x21621)),
% 7.56/7.45 inference(rename_variables,[],[537])).
% 7.56/7.45 cnf(2163,plain,
% 7.56/7.45 (P7(a39,x21631,f13(a39,x21631,f3(a39)))),
% 7.56/7.45 inference(rename_variables,[],[406])).
% 7.56/7.45 cnf(2166,plain,
% 7.56/7.45 (~P7(a38,f13(a38,f9(a38,x21661),f3(a38)),x21661)),
% 7.56/7.45 inference(rename_variables,[],[557])).
% 7.56/7.45 cnf(2169,plain,
% 7.56/7.45 (P6(a39,f2(a39),x21691)),
% 7.56/7.45 inference(rename_variables,[],[375])).
% 7.56/7.45 cnf(2172,plain,
% 7.56/7.45 (P6(a39,x21721,x21721)),
% 7.56/7.45 inference(rename_variables,[],[365])).
% 7.56/7.45 cnf(2175,plain,
% 7.56/7.45 (~P7(a38,f13(a38,f9(a38,x21751),f3(a38)),x21751)),
% 7.56/7.45 inference(rename_variables,[],[557])).
% 7.56/7.45 cnf(2185,plain,
% 7.56/7.45 (E(f11(a1,x21851,a14),x21851)),
% 7.56/7.45 inference(rename_variables,[],[361])).
% 7.56/7.45 cnf(2197,plain,
% 7.56/7.45 (~E(f13(a39,x21971,f3(a39)),x21971)),
% 7.56/7.45 inference(rename_variables,[],[544])).
% 7.56/7.45 cnf(2202,plain,
% 7.56/7.45 (P7(a39,x22021,f13(a39,x22021,f3(a39)))),
% 7.56/7.45 inference(rename_variables,[],[406])).
% 7.56/7.45 cnf(2205,plain,
% 7.56/7.45 (E(f30(f30(f12(a38),x22051),x22052),f30(f30(f12(a38),x22052),x22051))),
% 7.56/7.45 inference(rename_variables,[],[387])).
% 7.56/7.45 cnf(2208,plain,
% 7.56/7.45 (E(f30(f30(f12(a38),x22081),x22082),f30(f30(f12(a38),x22082),x22081))),
% 7.56/7.45 inference(rename_variables,[],[387])).
% 7.56/7.45 cnf(2211,plain,
% 7.56/7.45 (~P7(a38,f13(a38,f9(a38,x22111),f3(a38)),x22111)),
% 7.56/7.45 inference(rename_variables,[],[557])).
% 7.56/7.45 cnf(2216,plain,
% 7.56/7.45 (P6(a38,x22161,x22161)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2221,plain,
% 7.56/7.45 (P6(a38,x22211,x22211)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2224,plain,
% 7.56/7.45 (P6(a38,x22241,f17(f13(a38,f30(f30(f12(a38),x22241),x22241),f30(f30(f12(a38),x22242),x22242))))),
% 7.56/7.45 inference(rename_variables,[],[475])).
% 7.56/7.45 cnf(2253,plain,
% 7.56/7.45 (~E(f13(a39,x22531,f3(a39)),x22531)),
% 7.56/7.45 inference(rename_variables,[],[544])).
% 7.56/7.45 cnf(2271,plain,
% 7.56/7.45 (~E(f13(a39,x22711,f3(a39)),x22711)),
% 7.56/7.45 inference(rename_variables,[],[544])).
% 7.56/7.45 cnf(2280,plain,
% 7.56/7.45 (P6(a38,x22801,x22801)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2285,plain,
% 7.56/7.45 (P6(a38,x22851,x22851)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2291,plain,
% 7.56/7.45 (P6(a38,x22911,x22911)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2294,plain,
% 7.56/7.45 (P6(a38,x22941,x22941)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2297,plain,
% 7.56/7.45 (P6(a38,x22971,x22971)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2300,plain,
% 7.56/7.45 (P6(a38,x23001,x23001)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2304,plain,
% 7.56/7.45 (P6(a38,x23041,x23041)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2307,plain,
% 7.56/7.45 (P6(a38,x23071,x23071)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2308,plain,
% 7.56/7.45 (P6(a38,x23081,x23081)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2311,plain,
% 7.56/7.45 (P6(a38,x23111,x23111)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2312,plain,
% 7.56/7.45 (P6(a38,x23121,x23121)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2319,plain,
% 7.56/7.45 (P6(a38,x23191,x23191)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2379,plain,
% 7.56/7.45 (P6(a38,x23791,x23791)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2382,plain,
% 7.56/7.45 (P7(a39,x23821,f13(a39,x23821,f3(a39)))),
% 7.56/7.45 inference(rename_variables,[],[406])).
% 7.56/7.45 cnf(2387,plain,
% 7.56/7.45 (P6(a38,x23871,x23871)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2390,plain,
% 7.56/7.45 (P6(a38,x23901,x23901)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2401,plain,
% 7.56/7.45 (~E(f13(a39,x24011,f3(a39)),x24011)),
% 7.56/7.45 inference(rename_variables,[],[544])).
% 7.56/7.45 cnf(2404,plain,
% 7.56/7.45 (~E(f13(a39,x24041,f3(a39)),x24041)),
% 7.56/7.45 inference(rename_variables,[],[544])).
% 7.56/7.45 cnf(2415,plain,
% 7.56/7.45 (~E(f13(a39,x24151,f3(a39)),x24151)),
% 7.56/7.45 inference(rename_variables,[],[544])).
% 7.56/7.45 cnf(2422,plain,
% 7.56/7.45 (~P7(a39,x24221,x24221)),
% 7.56/7.45 inference(rename_variables,[],[537])).
% 7.56/7.45 cnf(2441,plain,
% 7.56/7.45 (P6(a38,x24411,x24411)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2444,plain,
% 7.56/7.45 (P6(a38,x24441,x24441)),
% 7.56/7.45 inference(rename_variables,[],[364])).
% 7.56/7.45 cnf(2642,plain,
% 7.56/7.45 ($false),
% 7.56/7.45 inference(scs_inference,[],[560,364,1923,1972,1975,2086,2159,2216,2221,2280,2285,2291,2294,2297,2300,2304,2308,2312,2319,2379,2387,2390,2441,2444,2311,2307,365,2070,2155,2172,366,1921,537,1817,1969,2162,2422,135,136,143,144,149,152,153,156,159,160,174,175,176,177,178,179,183,185,190,194,203,207,211,220,221,227,228,229,230,231,232,239,241,242,243,244,248,249,250,272,273,276,278,296,297,308,312,314,320,321,326,328,329,355,523,531,532,375,1936,2027,2071,2154,2169,542,2011,2063,2126,2129,370,371,538,539,134,339,386,343,344,345,382,384,527,528,415,337,403,451,491,492,493,479,481,506,341,1913,1919,1997,360,361,2150,2185,398,1797,1800,1808,1811,1981,2120,2123,400,551,1792,1820,1823,552,1814,1832,535,2098,390,2080,2083,406,1962,1968,1978,1985,1993,2062,2163,2202,2382,555,1826,1829,1910,2021,401,1901,402,379,544,1851,1864,1869,1907,1916,1994,2026,2059,2101,2197,2253,2271,2401,2404,2415,445,1805,1959,446,557,1846,1926,2004,2095,2104,2113,2158,2166,2175,2211,405,1990,550,1892,1904,1965,367,368,559,1879,413,387,2205,2208,475,1898,2224,485,2036,490,509,520,2,785,780,737,705,690,689,684,602,696,874,800,1134,1086,1080,1075,1074,1073,1012,999,998,997,996,995,944,870,787,1718,882,855,854,725,692,607,590,580,579,578,577,564,563,562,859,954,14,13,7,1364,1355,1352,1145,875,872,862,796,1007,599,1254,1756,1749,95,67,66,63,62,3,898,896,879,878,877,804,802,791,757,745,718,717,622,620,1135,1123,629,1189,923,1719,1290,1289,1076,1002,729,1130,593,726,1368,1167,1166,1163,1034,943,1770,1376,1375,952,951,847,807,730,727,724,589,1121,1119,1118,1117,885,733,646,645,1530,1700,1699,1694,1693,1683,1682,1663,1662,1716,1704,1702,1698,1696,1661,1660,974,973,972,971,970,969,968,967,910,823,817,815,769,932,930,913,912,1553,977,976,922,1122,1155,1154,1153,1152,1151,1313,1312,1311,1310,1098,1096,742,741,671,670,1327,1332,861,860,1417,1416,1402,1400,1394,1392,1247,1246,1245,1244,1241,1240,1235,1234,1233,1232,1213,1211,1196,849,848,846,845,843,842,1388,1301,1300,1299,1298,1231,1230,1229,1228,1499,1493,1491,1489,1603,1598,772,1534,1050,784,739,738,615,605,699,609,1043,1133,1082,1017,945,899,778,711,691,663,618,617,587,586,585,1761,1760,1744,1743,1739,1713,840,831,830,829,746,698,697,694,675,674,597,596,594,572,571,561,1726,1054,1053,975,858,857,856,839,837,836,834,953,928,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,12,11,10,9,8,6,5,4,1750,1733,1731,1730,1723,1710,1709,1687,1685,1638,1574,1538,1537,1536,1362,1342,1340,1339,1314,1274,1273,1147,1146,1142,1141,1140,1139,1138,1137,1132,1094,1093,1079,1065,1064,1063,1062,1061,1036,1031,1030,1008,983,981,980,979,938,937,936,917,916,915,906,880,876,871,869,868,863,813,812,810,809,798,789,750,749,748,747,706]),
% 7.56/7.45 ['proof']).
% 7.56/7.45 % SZS output end Proof
% 7.56/7.45 % Total time :5.990000s
%------------------------------------------------------------------------------