TSTP Solution File: SWW216+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW216+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 : n019.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 00:13:09 EDT 2023
% Result : Theorem 1.87s 2.00s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW216+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.17/0.35 % Computer : n019.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sun Aug 27 22:55:13 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 1.84/1.92 %-------------------------------------------
% 1.84/1.92 % File :CSE---1.6
% 1.84/1.92 % Problem :theBenchmark
% 1.84/1.92 % Transform :cnf
% 1.84/1.92 % Format :tptp:raw
% 1.84/1.92 % Command :java -jar mcs_scs.jar %d %s
% 1.84/1.93
% 1.84/1.93 % Result :Theorem 0.660000s
% 1.84/1.93 % Output :CNFRefutation 0.660000s
% 1.84/1.93 %-------------------------------------------
% 1.84/1.93 %------------------------------------------------------------------------------
% 1.84/1.93 % File : SWW216+1 : TPTP v8.1.2. Released v5.2.0.
% 1.84/1.93 % Domain : Software Verification
% 1.84/1.93 % Problem : Fundamental Theorem of Algebra 437039, 1000 axioms selected
% 1.84/1.93 % Version : Especial.
% 1.84/1.93 % English :
% 1.84/1.93
% 1.84/1.93 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 1.84/1.93 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 1.84/1.93 % Source : [Bla11]
% 1.84/1.93 % Names : fta_437039.1000.p [Bla11]
% 1.84/1.93
% 1.84/1.93 % Status : Theorem
% 1.84/1.93 % Rating : 0.25 v7.5.0, 0.28 v7.4.0, 0.27 v7.3.0, 0.28 v7.1.0, 0.26 v7.0.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.36 v6.1.0, 0.40 v6.0.0, 0.35 v5.5.0, 0.48 v5.4.0, 0.57 v5.3.0, 0.63 v5.2.0
% 1.84/1.93 % Syntax : Number of formulae : 1250 ( 410 unt; 0 def)
% 1.84/1.93 % Number of atoms : 3071 ( 745 equ)
% 1.84/1.93 % Maximal formula atoms : 10 ( 2 avg)
% 1.84/1.93 % Number of connectives : 2014 ( 193 ~; 52 |; 154 &)
% 1.84/1.93 % ( 278 <=>;1337 =>; 0 <=; 0 <~>)
% 1.84/1.93 % Maximal formula depth : 13 ( 4 avg)
% 1.84/1.93 % Maximal term depth : 11 ( 1 avg)
% 1.84/1.93 % Number of predicates : 79 ( 78 usr; 0 prp; 1-4 aty)
% 1.84/1.93 % Number of functors : 33 ( 33 usr; 14 con; 0-3 aty)
% 1.84/1.93 % Number of variables : 2481 (2476 !; 5 ?)
% 1.84/1.93 % SPC : FOF_THM_RFO_SEQ
% 1.84/1.93
% 1.84/1.93 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 1.84/1.93 % 2011-03-01 11:34:48
% 1.84/1.93 %------------------------------------------------------------------------------
% 1.84/1.93 %----Relevant facts (996)
% 1.84/1.93 fof(fact_ext,axiom,
% 1.84/1.93 ! [V_g_2,V_f_2] :
% 1.84/1.93 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 1.84/1.93 => V_f_2 = V_g_2 ) ).
% 1.84/1.93
% 1.84/1.93 fof(fact_m_I1_J,axiom,
% 1.84/1.93 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ).
% 1.84/1.93
% 1.84/1.93 fof(fact_H_I3_J,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_assms,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_H_I1_J,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_H_I2_J,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_dm_I2_J,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____),v_e) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_d_I3_J,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_dm_I1_J,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____)) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_em0,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__mult__commute,axiom,
% 1.84/1.94 ! [V_w,V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w),V_z) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__mult__assoc,axiom,
% 1.84/1.94 ! [V_z3,V_z2,V_z1] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_z2)),V_z3) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_z3)) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_d_I1_J,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_times_Oidem,axiom,
% 1.84/1.94 ! [V_a,T_a] :
% 1.84/1.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a) = V_a ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_mult__idem,axiom,
% 1.84/1.94 ! [V_x,T_a] :
% 1.84/1.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x) = V_x ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 1.84/1.94 ! [V_b,V_a,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_mult__left__idem,axiom,
% 1.84/1.94 ! [V_b,V_a,T_a] :
% 1.84/1.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 1.84/1.94 ! [V_ry,V_rx,V_lx,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ry)) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_d_I2_J,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_one0,axiom,
% 1.84/1.94 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__zero__not__eq__one,axiom,
% 1.84/1.94 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 1.84/1.94 ! [V_a,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 1.84/1.94 ! [V_a,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 1.84/1.94 ! [V_a,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 1.84/1.94 ! [V_a,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__mult__1,axiom,
% 1.84/1.94 ! [V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__mult__left__cancel,axiom,
% 1.84/1.94 ! [V_b_2,V_a_2,V_ca_2] :
% 1.84/1.94 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.84/1.94 => ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_a_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_b_2)
% 1.84/1.94 <=> V_a_2 = V_b_2 ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__mult__right__cancel,axiom,
% 1.84/1.94 ! [V_b_2,V_a_2,V_ca_2] :
% 1.84/1.94 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.84/1.94 => ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2),V_ca_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2),V_ca_2)
% 1.84/1.94 <=> V_a_2 = V_b_2 ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__mult__less__mono2,axiom,
% 1.84/1.94 ! [V_y,V_x,V_z] :
% 1.84/1.94 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.84/1.94 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_y)) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__mult__order,axiom,
% 1.84/1.94 ! [V_y,V_x] :
% 1.84/1.94 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.84/1.94 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_real__mult__less__iff1,axiom,
% 1.84/1.94 ! [V_y_2,V_x_2,V_za_2] :
% 1.84/1.94 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))
% 1.84/1.94 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 1.84/1.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),V_ry)) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 1.84/1.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_ry)) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 1.84/1.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 1.84/1.94 ! [V_rx,V_ly,V_lx,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),V_ly) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 1.84/1.94 ! [V_rx,V_ly,V_lx,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),V_rx)) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 1.84/1.94 ! [V_ry,V_rx,V_lx,T_a] :
% 1.84/1.94 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.84/1.94 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),V_ry) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 1.84/1.94 ~ ! [B_d] :
% 1.84/1.94 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.84/1.94 => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096,axiom,
% 1.84/1.94 ? [B_e] :
% 1.84/1.94 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
% 1.84/1.94 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.84/1.94 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_divide__strict__left__mono__neg,axiom,
% 1.84/1.94 ! [V_c,V_b,V_a,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_divide__strict__left__mono,axiom,
% 1.84/1.94 ! [V_c,V_a,V_b,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_neg__divide__less__eq,axiom,
% 1.84/1.94 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
% 1.84/1.94 <=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_neg__less__divide__eq,axiom,
% 1.84/1.94 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
% 1.84/1.94 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_mult__imp__less__div__pos,axiom,
% 1.84/1.94 ! [V_x,V_z,V_y,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y),V_x)
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_mult__imp__div__pos__less,axiom,
% 1.84/1.94 ! [V_z,V_x,V_y,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y))
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_pos__divide__less__eq,axiom,
% 1.84/1.94 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
% 1.84/1.94 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_pos__less__divide__eq,axiom,
% 1.84/1.94 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
% 1.84/1.94 <=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_divide__less__eq,axiom,
% 1.84/1.94 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
% 1.84/1.94 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
% 1.84/1.94 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.84/1.94 => ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
% 1.84/1.94 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_less__divide__eq,axiom,
% 1.84/1.94 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
% 1.84/1.94 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
% 1.84/1.94 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.84/1.94 => ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
% 1.84/1.94 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.94 => c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_times__divide__times__eq,axiom,
% 1.84/1.94 ! [V_w,V_z,V_y,V_x,T_a] :
% 1.84/1.94 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.84/1.94 => 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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_w)) ) ).
% 1.84/1.94
% 1.84/1.94 fof(fact_divide__strict__right__mono__neg,axiom,
% 1.84/1.94 ! [V_c,V_a,V_b,T_a] :
% 1.84/1.94 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.94 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__strict__right__mono,axiom,
% 1.84/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.84/1.95 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.84/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__neg__neg,axiom,
% 1.84/1.95 ! [V_y,V_x,T_a] :
% 1.84/1.95 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__neg__pos,axiom,
% 1.84/1.95 ! [V_y,V_x,T_a] :
% 1.84/1.95 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.84/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__pos__neg,axiom,
% 1.84/1.95 ! [V_y,V_x,T_a] :
% 1.84/1.95 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__pos__pos,axiom,
% 1.84/1.95 ! [V_y,V_x,T_a] :
% 1.84/1.95 ( class_Fields_Olinordered__field(T_a)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.84/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__less__0__iff,axiom,
% 1.84/1.95 ! [V_b_2,V_a_2,T_a] :
% 1.84/1.95 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.95 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.84/1.95 & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.84/1.95 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.95 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_zero__less__divide__iff,axiom,
% 1.84/1.95 ! [V_b_2,V_a_2,T_a] :
% 1.84/1.95 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.84/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
% 1.84/1.95 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.84/1.95 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.84/1.95 | ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.84/1.95 & c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_frac__eq__eq,axiom,
% 1.84/1.95 ! [V_wa_2,V_x_2,V_za_2,V_y_2,T_a] :
% 1.84/1.95 ( class_Fields_Ofield(T_a)
% 1.84/1.95 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => ( V_za_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => ( c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)
% 1.84/1.95 <=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2) ) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_mult__divide__mult__cancel__left,axiom,
% 1.84/1.95 ! [V_b,V_a,V_c,T_a] :
% 1.84/1.95 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.84/1.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_mult__divide__mult__cancel__right,axiom,
% 1.84/1.95 ! [V_b,V_a,V_c,T_a] :
% 1.84/1.95 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.84/1.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__eq__eq,axiom,
% 1.84/1.95 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 1.84/1.95 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.84/1.95 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_a_2
% 1.84/1.95 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) )
% 1.84/1.95 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_eq__divide__eq,axiom,
% 1.84/1.95 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 1.84/1.95 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.84/1.95 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
% 1.84/1.95 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) = V_b_2 )
% 1.84/1.95 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_not__real__square__gt__zero,axiom,
% 1.84/1.95 ! [V_x_2] :
% 1.84/1.95 ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2))
% 1.84/1.95 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_right__inverse__eq,axiom,
% 1.84/1.95 ! [V_a_2,V_b_2,T_a] :
% 1.84/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.84/1.95 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
% 1.84/1.95 <=> V_a_2 = V_b_2 ) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__self,axiom,
% 1.84/1.95 ! [V_a,T_a] :
% 1.84/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.84/1.95 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.84/1.95
% 1.84/1.95 fof(fact_divide__self__if,axiom,
% 1.84/1.95 ! [V_a,T_a] :
% 1.84/1.95 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.84/1.95 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.84/1.95 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.84/1.95 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_eq__divide__imp,axiom,
% 1.87/1.95 ! [V_b,V_a,V_c,T_a] :
% 1.87/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 => ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c) = V_b
% 1.87/1.95 => V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divide__eq__imp,axiom,
% 1.87/1.95 ! [V_a,V_b,V_c,T_a] :
% 1.87/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.95 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 => ( V_b = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c)
% 1.87/1.95 => c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_nonzero__divide__eq__eq,axiom,
% 1.87/1.95 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 1.87/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.95 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_a_2
% 1.87/1.95 <=> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_nonzero__eq__divide__eq,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.95 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
% 1.87/1.95 <=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_less__1__mult,axiom,
% 1.87/1.95 ! [V_n,V_m,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_m),V_n)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_zero__less__one,axiom,
% 1.87/1.95 ! [T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_not__one__less__zero,axiom,
% 1.87/1.95 ! [T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.95 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_linorder__neqE__linordered__idom,axiom,
% 1.87/1.95 ! [V_y,V_x,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.95 => ( V_x != V_y
% 1.87/1.95 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divisors__zero,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Ono__zero__divisors(T_a)
% 1.87/1.95 => ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_no__zero__divisors,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Ono__zero__divisors(T_a)
% 1.87/1.95 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__eq__0__iff,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.95 ( class_Rings_Oring__no__zero__divisors(T_a)
% 1.87/1.95 => ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.95 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__zero__right,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Rings_Omult__zero(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__zero__left,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Rings_Omult__zero(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_one__neq__zero,axiom,
% 1.87/1.95 ! [T_a] :
% 1.87/1.95 ( class_Rings_Ozero__neq__one(T_a)
% 1.87/1.95 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_zero__neq__one,axiom,
% 1.87/1.95 ! [T_a] :
% 1.87/1.95 ( class_Rings_Ozero__neq__one(T_a)
% 1.87/1.95 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divide__zero__left,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.95 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divide__zero,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.87/1.95 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_times__divide__eq__right,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.95 => 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_c) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divide__1,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.95 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_real__divide__square__eq,axiom,
% 1.87/1.95 ! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_a),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) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__strict__left__mono__neg,axiom,
% 1.87/1.95 ! [V_c,V_a,V_b,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__strict__right__mono__neg,axiom,
% 1.87/1.95 ! [V_c,V_a,V_b,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_comm__mult__strict__left__mono,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__strict__left__mono,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__strict__right__mono,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__neg__neg,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__neg__pos,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__less__cancel__left__neg,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))
% 1.87/1.95 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_zero__less__mult__pos2,axiom,
% 1.87/1.95 ! [V_a,V_b,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_zero__less__mult__pos,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__pos__neg2,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__pos__neg,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__pos__pos,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__less__cancel__left__pos,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))
% 1.87/1.95 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__less__cancel__left__disj,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))
% 1.87/1.95 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.95 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 1.87/1.95 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__less__cancel__right__disj,axiom,
% 1.87/1.95 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))
% 1.87/1.95 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.95 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 1.87/1.95 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_not__square__less__zero,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring(T_a)
% 1.87/1.95 => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_d1_I2_J,axiom,
% 1.87/1.95 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divide_Ozero,axiom,
% 1.87/1.95 ! [V_y,T_a] :
% 1.87/1.95 ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.95 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult_Ocomm__neutral,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__1__right,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__1,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__1__left,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__right_Ozero,axiom,
% 1.87/1.95 ! [V_x,T_a] :
% 1.87/1.95 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult_Ozero__right,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__left_Ozero,axiom,
% 1.87/1.95 ! [V_y,T_a] :
% 1.87/1.95 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult_Ozero__left,axiom,
% 1.87/1.95 ! [V_b,T_a] :
% 1.87/1.95 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.95 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_real__le__refl,axiom,
% 1.87/1.95 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_real__le__linear,axiom,
% 1.87/1.95 ! [V_w,V_z] :
% 1.87/1.95 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.87/1.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_real__le__trans,axiom,
% 1.87/1.95 ! [V_k,V_j,V_i] :
% 1.87/1.95 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_real__le__antisym,axiom,
% 1.87/1.95 ! [V_w,V_z] :
% 1.87/1.95 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 1.87/1.95 => V_z = V_w ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_real__less__def,axiom,
% 1.87/1.95 ! [V_y_2,V_x_2] :
% 1.87/1.95 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.87/1.95 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.87/1.95 & V_x_2 != V_y_2 ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_less__eq__real__def,axiom,
% 1.87/1.95 ! [V_y_2,V_x_2] :
% 1.87/1.95 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.87/1.95 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 1.87/1.95 | V_x_2 = V_y_2 ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_split__mult__neg__le,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.87/1.95 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.87/1.95 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_split__mult__pos__le,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__ring(T_a)
% 1.87/1.95 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 1.87/1.95 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__mono,axiom,
% 1.87/1.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)) ) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__mono_H,axiom,
% 1.87/1.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)) ) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__left__mono__neg,axiom,
% 1.87/1.95 ! [V_c,V_a,V_b,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__ring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__right__mono__neg,axiom,
% 1.87/1.95 ! [V_c,V_a,V_b,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__ring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_comm__mult__left__mono,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__comm__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__left__mono,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__right__mono,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__nonpos__nonpos,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__ring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__nonpos__nonneg,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__nonneg__nonpos2,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__nonneg__nonpos,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__nonneg__nonneg,axiom,
% 1.87/1.95 ! [V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Oordered__cancel__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__le__0__iff,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.87/1.95 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_zero__le__mult__iff,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_b_2))
% 1.87/1.95 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.87/1.95 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_zero__le__square,axiom,
% 1.87/1.95 ! [V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring(T_a)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_zero__le__one,axiom,
% 1.87/1.95 ! [T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_not__one__le__zero,axiom,
% 1.87/1.95 ! [T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.95 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divide__right__mono__neg,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divide__right__mono,axiom,
% 1.87/1.95 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_divide__le__0__iff,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.95 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.87/1.95 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_zero__le__divide__iff,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.95 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
% 1.87/1.95 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 1.87/1.95 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_real__0__le__divide__iff,axiom,
% 1.87/1.95 ! [V_y_2,V_x_2] :
% 1.87/1.95 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.87/1.95 <=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) )
% 1.87/1.95 & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__le__cancel__left__pos,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))
% 1.87/1.95 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__le__cancel__left__neg,axiom,
% 1.87/1.95 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_b_2))
% 1.87/1.95 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__strict__mono,axiom,
% 1.87/1.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)) ) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__strict__mono_H,axiom,
% 1.87/1.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)) ) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__less__le__imp__less,axiom,
% 1.87/1.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)) ) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__le__less__imp__less,axiom,
% 1.87/1.95 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)) ) ) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__right__less__imp__less,axiom,
% 1.87/1.95 ! [V_b,V_c,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__less__imp__less__right,axiom,
% 1.87/1.95 ! [V_b,V_c,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__left__less__imp__less,axiom,
% 1.87/1.95 ! [V_b,V_a,V_c,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__less__imp__less__left,axiom,
% 1.87/1.95 ! [V_b,V_a,V_c,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__right__le__imp__le,axiom,
% 1.87/1.95 ! [V_b,V_c,V_a,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.95 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.95
% 1.87/1.95 fof(fact_mult__left__le__imp__le,axiom,
% 1.87/1.95 ! [V_b,V_a,V_c,T_a] :
% 1.87/1.95 ( class_Rings_Olinordered__semiring__strict(T_a)
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b))
% 1.87/1.95 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_mult__left__le__one__le,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_x),V_x) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_mult__right__le__one__le,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_x) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide__nonpos__neg,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide__nonpos__pos,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_frac__le,axiom,
% 1.87/1.96 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_frac__less,axiom,
% 1.87/1.96 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_frac__less2,axiom,
% 1.87/1.96 ! [V_z,V_w,V_y,V_x,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide__nonneg__neg,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide__nonneg__pos,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_zero__reorient,axiom,
% 1.87/1.96 ! [V_x_2,T_a] :
% 1.87/1.96 ( class_Groups_Ozero(T_a)
% 1.87/1.96 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 1.87/1.96 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_real__mult__le__cancel__iff1,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,V_za_2] :
% 1.87/1.96 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_real__mult__le__cancel__iff2,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,V_za_2] :
% 1.87/1.96 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_y_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oab__semigroup__mult(T_a)
% 1.87/1.96 => hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)),V_c) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_one__reorient,axiom,
% 1.87/1.96 ! [V_x_2,T_a] :
% 1.87/1.96 ( class_Groups_Oone(T_a)
% 1.87/1.96 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 1.87/1.96 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_le__divide__eq,axiom,
% 1.87/1.96 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
% 1.87/1.96 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
% 1.87/1.96 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.96 => ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
% 1.87/1.96 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide__le__eq,axiom,
% 1.87/1.96 ! [V_a_2,V_ca_2,V_b_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
% 1.87/1.96 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
% 1.87/1.96 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.96 => ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
% 1.87/1.96 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_pos__le__divide__eq,axiom,
% 1.87/1.96 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_pos__divide__le__eq,axiom,
% 1.87/1.96 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_mult__imp__div__pos__le,axiom,
% 1.87/1.96 ! [V_z,V_x,V_y,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_mult__imp__le__div__pos,axiom,
% 1.87/1.96 ! [V_x,V_z,V_y,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y),V_x)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_neg__le__divide__eq,axiom,
% 1.87/1.96 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_neg__divide__le__eq,axiom,
% 1.87/1.96 ! [V_a_2,V_b_2,V_ca_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide__left__mono,axiom,
% 1.87/1.96 ! [V_c,V_a,V_b,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide__left__mono__neg,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__refl,axiom,
% 1.87/1.96 ! [V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__not__less,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__not__le,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__le__less__linear,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__le,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.87/1.96 & V_x_2 != V_y_2 ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_less__le__not__le,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.87/1.96 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__le__less,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 | V_x_2 = V_y_2 ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_leI,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_not__leE,axiom,
% 1.87/1.96 ! [V_x,V_y,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_le__fun__def,axiom,
% 1.87/1.96 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.87/1.96 ( class_Orderings_Oord(T_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.87/1.96 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__linear,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__eq__iff,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( V_x_2 = V_y_2
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.87/1.96 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__eq__refl,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( V_x = V_y
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_le__funD,axiom,
% 1.87/1.96 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.87/1.96 ( class_Orderings_Oord(T_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__antisym__conv,axiom,
% 1.87/1.96 ! [V_x_2,V_y_2,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_ord__eq__le__trans,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oord(T_a)
% 1.87/1.96 => ( V_a = V_b
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I3_J,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( V_a = V_b
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_ord__le__eq__trans,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oord(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.96 => ( V_b = V_c
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I4_J,axiom,
% 1.87/1.96 ! [V_c,V_a,V_b,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.87/1.96 => ( V_b = V_c
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__antisym,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.87/1.96 => V_x = V_y ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__trans,axiom,
% 1.87/1.96 ! [V_z,V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I5_J,axiom,
% 1.87/1.96 ! [V_x,V_y,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 => V_x = V_y ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I6_J,axiom,
% 1.87/1.96 ! [V_z,V_x,V_y,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_le__funE,axiom,
% 1.87/1.96 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 1.87/1.96 ( class_Orderings_Oord(T_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__le__cases,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__cases,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => ( V_x != V_y
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__asym,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I10_J,axiom,
% 1.87/1.96 ! [V_z,V_x,V_y,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__trans,axiom,
% 1.87/1.96 ! [V_z,V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I2_J,axiom,
% 1.87/1.96 ! [V_c,V_a,V_b,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.87/1.96 => ( V_b = V_c
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_ord__less__eq__trans,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oord(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.96 => ( V_b = V_c
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I1_J,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( V_a = V_b
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_ord__eq__less__trans,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oord(T_a)
% 1.87/1.96 => ( V_a = V_b
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I9_J,axiom,
% 1.87/1.96 ! [V_a,V_b,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 1.87/1.96 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__asym_H,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.96 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__imp__not__eq2,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => V_y != V_x ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__imp__not__eq,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => V_x != V_y ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__imp__not__less,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__not__sym,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_less__imp__neq,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => V_x != V_y ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__neqE,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( V_x != V_y
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__antisym__conv3,axiom,
% 1.87/1.96 ! [V_x_2,V_y_2,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__less__linear,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 | V_x = V_y
% 1.87/1.96 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_not__less__iff__gr__or__eq,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 1.87/1.96 | V_x_2 = V_y_2 ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__neq__iff,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( V_x_2 != V_y_2
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__irrefl,axiom,
% 1.87/1.96 ! [V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I8_J,axiom,
% 1.87/1.96 ! [V_z,V_x,V_y,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__le__less__trans,axiom,
% 1.87/1.96 ! [V_z,V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I7_J,axiom,
% 1.87/1.96 ! [V_z,V_x,V_y,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__le__trans,axiom,
% 1.87/1.96 ! [V_z,V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I11_J,axiom,
% 1.87/1.96 ! [V_a,V_b,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.87/1.96 => ( V_a != V_b
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__le__neq__trans,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.96 => ( V_a != V_b
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__le__imp__less__or__eq,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 | V_x = V_y ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__antisym__conv2,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__less__imp__le,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Orderings_Opreorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_leD,axiom,
% 1.87/1.96 ! [V_x,V_y,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 1.87/1.96 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_xt1_I12_J,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( V_a != V_b
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_order__neq__le__trans,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Orderings_Oorder(T_a)
% 1.87/1.96 => ( V_a != V_b
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_linorder__antisym__conv1,axiom,
% 1.87/1.96 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.96 ( class_Orderings_Olinorder(T_a)
% 1.87/1.96 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 1.87/1.96 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_field__le__mult__one__interval,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( ! [B_z] :
% 1.87/1.96 ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,B_z),V_x),V_y) ) )
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_convex__bound__lt,axiom,
% 1.87/1.96 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.87/1.96 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_convex__bound__le,axiom,
% 1.87/1.96 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__semiring__1(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 1.87/1.96 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_one__le__inverse__iff,axiom,
% 1.87/1.96 ! [V_x_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.87/1.96 & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__less__1__iff,axiom,
% 1.87/1.96 ! [V_x_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 | c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_one__le__inverse,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__1__pos,axiom,
% 1.87/1.96 ! [V_a_2,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.96 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__pos,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.96 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_less__fun__def,axiom,
% 1.87/1.96 ! [V_g_2,V_f_2,T_a,T_b] :
% 1.87/1.96 ( class_Orderings_Oord(T_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.87/1.96 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 1.87/1.96 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__inverse__eq,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__sgn,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.96 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__eq__iff__eq,axiom,
% 1.87/1.96 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.87/1.96 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)
% 1.87/1.96 <=> V_a_2 = V_b_2 ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__eq__imp__eq,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.87/1.96 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 1.87/1.96 => V_a = V_b ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 1.87/1.96 ! [V_c,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 1.87/1.96 ! [V_d,V_c,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 1.87/1.96 ! [V_d,V_c,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 1.87/1.96 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oab__semigroup__add(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__left__cancel,axiom,
% 1.87/1.96 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 1.87/1.96 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.87/1.96 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2)
% 1.87/1.96 <=> V_b_2 = V_ca_2 ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__right__cancel,axiom,
% 1.87/1.96 ! [V_ca_2,V_a_2,V_b_2,T_a] :
% 1.87/1.96 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.87/1.96 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2)
% 1.87/1.96 <=> V_b_2 = V_ca_2 ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__left__imp__eq,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.87/1.96 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.87/1.96 => V_b = V_c ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__imp__eq,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 1.87/1.96 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 1.87/1.96 => V_b = V_c ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__right__imp__eq,axiom,
% 1.87/1.96 ! [V_c,V_a,V_b,T_a] :
% 1.87/1.96 ( class_Groups_Ocancel__semigroup__add(T_a)
% 1.87/1.96 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 1.87/1.96 => V_b = V_c ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__add,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Ofield(T_a)
% 1.87/1.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_division__ring__inverse__add,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_field__inverse__zero,axiom,
% 1.87/1.96 ! [T_a] :
% 1.87/1.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_nonzero__inverse__eq__imp__eq,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
% 1.87/1.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => V_a = V_b ) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__zero__imp__zero,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_nonzero__inverse__inverse__eq,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_nonzero__imp__inverse__nonzero,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__nonzero__iff__nonzero,axiom,
% 1.87/1.96 ! [V_a_2,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.87/1.96 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__zero,axiom,
% 1.87/1.96 ! [T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__mult__distrib,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__eq__1__iff,axiom,
% 1.87/1.96 ! [V_x_2,T_a] :
% 1.87/1.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.96 => ( c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.96 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__1,axiom,
% 1.87/1.96 ! [T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__divide,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_INVERSE__ZERO,axiom,
% 1.87/1.96 c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add_Ocomm__neutral,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__0__right,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Groups_Omonoid__add(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_double__zero__sym,axiom,
% 1.87/1.96 ! [V_a_2,T_a] :
% 1.87/1.96 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.96 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 1.87/1.96 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__0,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Groups_Ocomm__monoid__add(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__0__left,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Groups_Omonoid__add(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__0__iff,axiom,
% 1.87/1.96 ! [V_a_2,V_b_2,T_a] :
% 1.87/1.96 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.87/1.96 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
% 1.87/1.96 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__le__imp__le__left,axiom,
% 1.87/1.96 ! [V_b,V_a,V_c,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__le__imp__le__right,axiom,
% 1.87/1.96 ! [V_b,V_c,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__mono,axiom,
% 1.87/1.96 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__left__mono,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__right__mono,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__le__cancel__left,axiom,
% 1.87/1.96 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__le__cancel__right,axiom,
% 1.87/1.96 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__less__cancel__right,axiom,
% 1.87/1.96 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__less__cancel__left,axiom,
% 1.87/1.96 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__strict__right__mono,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__strict__left__mono,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__strict__mono,axiom,
% 1.87/1.96 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__less__imp__less__right,axiom,
% 1.87/1.96 ! [V_b,V_c,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__less__imp__less__left,axiom,
% 1.87/1.96 ! [V_b,V_a,V_c,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_mult_Oadd__right,axiom,
% 1.87/1.96 ! [V_b_H,V_b,V_a,T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.96 => 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b_H)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_mult__right_Oadd,axiom,
% 1.87/1.96 ! [V_y,V_x,V_xa,T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.96 => 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(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_y)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_mult_Oadd__left,axiom,
% 1.87/1.96 ! [V_b,V_a_H,V_a,T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.96 => 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_H),V_b)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_mult__left_Oadd,axiom,
% 1.87/1.96 ! [V_ya,V_y,V_x,T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.96 => 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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_ya),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_ya)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 1.87/1.96 ! [V_z,V_y,V_x,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => 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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_crossproduct__noteq,axiom,
% 1.87/1.96 ! [V_db_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 1.87/1.96 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.87/1.96 => ( ( V_a_2 != V_b_2
% 1.87/1.96 & V_ca_2 != V_db_2 )
% 1.87/1.96 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 1.87/1.96 ! [V_b,V_m,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_m)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_crossproduct__eq,axiom,
% 1.87/1.96 ! [V_za_2,V_x_2,V_y_2,V_wa_2,T_a] :
% 1.87/1.96 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.87/1.96 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_y_2))
% 1.87/1.96 <=> ( V_wa_2 = V_x_2
% 1.87/1.96 | V_y_2 = V_za_2 ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_comm__semiring__class_Odistrib,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Ocomm__semiring(T_a)
% 1.87/1.96 => 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_combine__common__factor,axiom,
% 1.87/1.96 ! [V_c,V_b,V_e,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Osemiring(T_a)
% 1.87/1.96 => c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide_Oadd,axiom,
% 1.87/1.96 ! [V_ya,V_y,V_x,T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__divide__distrib,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_real__add__left__mono,axiom,
% 1.87/1.96 ! [V_z,V_y,V_x] :
% 1.87/1.96 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_real__add__mult__distrib,axiom,
% 1.87/1.96 ! [V_w,V_z2,V_z1] : 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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_w)) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__zero__iff,axiom,
% 1.87/1.96 ! [V_x_2,T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.87/1.96 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__zero,axiom,
% 1.87/1.96 ! [T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.87/1.96 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn0,axiom,
% 1.87/1.96 ! [T_a] :
% 1.87/1.96 ( class_Groups_Osgn__if(T_a)
% 1.87/1.96 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__0__0,axiom,
% 1.87/1.96 ! [V_a_2,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.96 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__mult,axiom,
% 1.87/1.96 ! [V_y,V_x,T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 1.87/1.96 => c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__times,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.96 => c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_sgn__one,axiom,
% 1.87/1.96 ! [T_a] :
% 1.87/1.96 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 1.87/1.96 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
% 1.87/1.96 ! [V_a_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
% 1.87/1.96 ! [V_a_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__less__imp__less__neg,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__less__imp__less,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__negative__imp__negative,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_less__imp__inverse__less__neg,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_less__imp__inverse__less,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_negative__imp__inverse__negative,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__positive__imp__positive,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
% 1.87/1.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_positive__imp__inverse__positive,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__negative__iff__negative,axiom,
% 1.87/1.96 ! [V_a_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__positive__iff__positive,axiom,
% 1.87/1.96 ! [V_a_2,T_a] :
% 1.87/1.96 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2))
% 1.87/1.96 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_nonzero__inverse__mult__distrib,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__unique,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_field__divide__inverse,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Fields_Ofield(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_divide__inverse,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_field__class_Onormalizing__field__rules_I2_J,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Fields_Ofield(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_inverse__eq__divide,axiom,
% 1.87/1.96 ! [V_a,T_a] :
% 1.87/1.96 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.96 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__nonpos__nonpos,axiom,
% 1.87/1.96 ! [V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__increasing2,axiom,
% 1.87/1.96 ! [V_a,V_b,V_c,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 1.87/1.96 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.87/1.96
% 1.87/1.96 fof(fact_add__increasing,axiom,
% 1.87/1.96 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.96 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.96 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__nonneg__eq__0__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 1.87/1.97 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__nonneg__nonneg,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__neg__neg,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__pos__pos,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_pos__add__strict,axiom,
% 1.87/1.97 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__less__le__mono,axiom,
% 1.87/1.97 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__le__less__mono,axiom,
% 1.87/1.97 ! [V_d,V_c,V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__scale__eq__noteq,axiom,
% 1.87/1.97 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 1.87/1.97 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 1.87/1.97 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => ( ( V_a = V_b
% 1.87/1.97 & V_c != V_d )
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_d)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__add__one,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 1.87/1.97 ! [V_m,V_a,T_a] :
% 1.87/1.97 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),V_m) = 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) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 1.87/1.97 ! [V_a,V_m,T_a] :
% 1.87/1.97 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m)) = 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) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 1.87/1.97 ! [V_m,T_a] :
% 1.87/1.97 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = 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) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide__real__def,axiom,
% 1.87/1.97 ! [V_y,V_x] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_y)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__divide__def,axiom,
% 1.87/1.97 ! [V_S,V_R] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_R,V_S) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_R),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_S)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__two__squares__add__zero__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_sgn__less,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_sgn__greater,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_inverse__le__imp__le__neg,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_inverse__le__imp__le,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__imp__inverse__le__neg,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__imp__inverse__le,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_inverse__le__1__iff,axiom,
% 1.87/1.97 ! [V_x_2,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.87/1.97 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 | c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_one__less__inverse,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_one__less__inverse__iff,axiom,
% 1.87/1.97 ! [V_x_2,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
% 1.87/1.97 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 1.87/1.97 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_field__inverse,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Fields_Ofield(T_a)
% 1.87/1.97 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_left__inverse,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.97 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_right__inverse,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.97 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_nonzero__inverse__eq__divide,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.97 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__nonpos__neg,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__neg__nonpos,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__strict__increasing2,axiom,
% 1.87/1.97 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__strict__increasing,axiom,
% 1.87/1.97 ! [V_c,V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__nonneg__pos,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__pos__nonneg,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zero__less__two,axiom,
% 1.87/1.97 ! [T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__frac__eq,axiom,
% 1.87/1.97 ! [V_w,V_x,V_z,V_y,T_a] :
% 1.87/1.97 ( class_Fields_Ofield(T_a)
% 1.87/1.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => 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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_w),V_y)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_z)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide__add__eq__iff,axiom,
% 1.87/1.97 ! [V_y,V_x,V_z,T_a] :
% 1.87/1.97 ( class_Fields_Ofield(T_a)
% 1.87/1.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => 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(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_z) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__frac__num,axiom,
% 1.87/1.97 ! [V_z,V_x,V_y,T_a] :
% 1.87/1.97 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => 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(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__divide__eq__iff,axiom,
% 1.87/1.97 ! [V_y,V_x,V_z,T_a] :
% 1.87/1.97 ( class_Fields_Ofield(T_a)
% 1.87/1.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => 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(c_Groups_Otimes__class_Otimes(T_a,V_z),V_x),V_y),V_z) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__num__frac,axiom,
% 1.87/1.97 ! [V_x,V_z,V_y,T_a] :
% 1.87/1.97 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => 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(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__mult__inverse__left,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_gt__half__sum,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__half__sum,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__sgn__pos,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_not__sum__squares__lt__zero,axiom,
% 1.87/1.97 ! [V_y,V_x,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__ring(T_a)
% 1.87/1.97 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_sum__squares__gt__zero__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)))
% 1.87/1.97 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_sum__squares__le__zero__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_sum__squares__ge__zero,axiom,
% 1.87/1.97 ! [V_y,V_x,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__ring(T_a)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_y))) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__mult__inverse__cancel2,axiom,
% 1.87/1.97 ! [V_u,V_y,V_x1,V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1))) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__mult__inverse__cancel,axiom,
% 1.87/1.97 ! [V_u,V_y,V_x1,V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_sum__squares__eq__zero__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__ring__strict(T_a)
% 1.87/1.97 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_even__less__0__iff,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_double__eq__0__iff,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_field__le__epsilon,axiom,
% 1.87/1.97 ! [V_y,V_x,T_a] :
% 1.87/1.97 ( class_Fields_Olinordered__field(T_a)
% 1.87/1.97 => ( ! [B_e] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_e)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,B_e)) )
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__add__one__self__le__self,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__mult,axiom,
% 1.87/1.97 ! [V_y,V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.87/1.97 => hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),hAPP(c_Transcendental_Oln,V_y)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__less__cancel__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__inj__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
% 1.87/1.97 => ( hAPP(c_Transcendental_Oln,V_x_2) = hAPP(c_Transcendental_Oln,V_y_2)
% 1.87/1.97 <=> V_x_2 = V_y_2 ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__less__self,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),V_x) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__one,axiom,
% 1.87/1.97 hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__le__cancel__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__ge__zero,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__gt__zero__imp__gt__one,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x))
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__less__zero,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__less__zero__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__eq__zero__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => ( hAPP(c_Transcendental_Oln,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 <=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__gt__zero__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__gt__zero,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__ge__zero__imp__ge__one,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x))
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__ge__zero__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide__le__eq__number__of1,axiom,
% 1.87/1.97 ! [V_a_2,V_wa_2,V_b_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( 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_wa_2)),V_a_2)
% 1.87/1.97 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide__le__eq__number__of,axiom,
% 1.87/1.97 ! [V_wa_2,V_ca_2,V_b_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__divide__eq__number__of,axiom,
% 1.87/1.97 ! [V_ca_2,V_b_2,V_wa_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
% 1.87/1.97 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__divide__eq__number__of1,axiom,
% 1.87/1.97 ! [V_wa_2,V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( 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_wa_2)))
% 1.87/1.97 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_DERIV__ln__divide,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__number__of__left,axiom,
% 1.87/1.97 ! [V_z,V_w,V_v,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__number__of__eq,axiom,
% 1.87/1.97 ! [V_w,V_v,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_number__of__add,axiom,
% 1.87/1.97 ! [V_w,V_v,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__number__of,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_eq__number__of,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 & class_Int_Oring__char__0(T_a) )
% 1.87/1.97 => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
% 1.87/1.97 <=> V_x_2 = V_y_2 ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_number__of__reorient,axiom,
% 1.87/1.97 ! [V_x_2,V_wa_2,T_a] :
% 1.87/1.97 ( class_Int_Onumber(T_a)
% 1.87/1.97 => ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
% 1.87/1.97 <=> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_mult__number__of__left,axiom,
% 1.87/1.97 ! [V_z,V_w,V_v,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))),V_z) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_arith__simps_I32_J,axiom,
% 1.87/1.97 ! [V_w,V_v,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_number__of__mult,axiom,
% 1.87/1.97 ! [V_w,V_v,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)) = 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)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__number__of,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__number__of__eq__not__less,axiom,
% 1.87/1.97 ! [V_wa_2,V_v_2,T_a] :
% 1.87/1.97 ( ( class_Int_Onumber(T_a)
% 1.87/1.97 & class_Orderings_Olinorder(T_a) )
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 <=> ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_left__distrib__number__of,axiom,
% 1.87/1.97 ! [V_v,V_b,V_a,T_b] :
% 1.87/1.97 ( ( class_Int_Onumber(T_b)
% 1.87/1.97 & class_Rings_Osemiring(T_b) )
% 1.87/1.97 => 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(c_Groups_Otimes__class_Otimes(T_b,V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_b,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_right__distrib__number__of,axiom,
% 1.87/1.97 ! [V_c,V_b,V_v,T_b] :
% 1.87/1.97 ( ( class_Int_Onumber(T_b)
% 1.87/1.97 & class_Rings_Osemiring(T_b) )
% 1.87/1.97 => 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(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_eq__divide__eq__number__of1,axiom,
% 1.87/1.97 ! [V_wa_2,V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 <=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_b_2 )
% 1.87/1.97 & ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_eq__divide__eq__number__of,axiom,
% 1.87/1.97 ! [V_ca_2,V_b_2,V_wa_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
% 1.87/1.97 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2) = V_b_2 )
% 1.87/1.97 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide__eq__eq__number__of,axiom,
% 1.87/1.97 ! [V_wa_2,V_ca_2,V_b_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)
% 1.87/1.97 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2) )
% 1.87/1.97 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide__eq__eq__number__of1,axiom,
% 1.87/1.97 ! [V_a_2,V_wa_2,V_b_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_a_2
% 1.87/1.97 <=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
% 1.87/1.97 & ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_inverse__eq__divide__number__of,axiom,
% 1.87/1.97 ! [V_w,T_b] :
% 1.87/1.97 ( ( class_Int_Onumber(T_b)
% 1.87/1.97 & class_Rings_Odivision__ring(T_b) )
% 1.87/1.97 => c_Rings_Oinverse__class_Oinverse(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)) = c_Rings_Oinverse__class_Odivide(T_b,c_Groups_Oone__class_Oone(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide__less__eq__number__of1,axiom,
% 1.87/1.97 ! [V_a_2,V_wa_2,V_b_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( 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_wa_2)),V_a_2)
% 1.87/1.97 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide__less__eq__number__of,axiom,
% 1.87/1.97 ! [V_wa_2,V_ca_2,V_b_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__divide__eq__number__of,axiom,
% 1.87/1.97 ! [V_ca_2,V_b_2,V_wa_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
% 1.87/1.97 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__divide__eq__number__of1,axiom,
% 1.87/1.97 ! [V_wa_2,V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.97 & class_Int_Onumber(T_a) )
% 1.87/1.97 => ( 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_wa_2)))
% 1.87/1.97 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_DERIV__ln,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.97 => c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_DERIV__cmult__Id,axiom,
% 1.87/1.97 ! [V_x_2,V_ca_2,T_a] :
% 1.87/1.97 ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.97 => c_Deriv_Oderiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_x_2,V_ca_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_number__of__succ,axiom,
% 1.87/1.97 ! [V_k,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_sgn__real__def,axiom,
% 1.87/1.97 ! [V_a] :
% 1.87/1.97 ( ( V_a = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 1.87/1.97 & ( V_a != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.87/1.97 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 1.87/1.97 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__sgn__def,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( ( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 1.87/1.97 & ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
% 1.87/1.97 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__ge__add__one__self__aux,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__less__mono,axiom,
% 1.87/1.97 ! [V_y,V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_plus__numeral__code_I9_J,axiom,
% 1.87/1.97 ! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__number__of__int__code,axiom,
% 1.87/1.97 ! [V_l_2,V_k_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_times__numeral__code_I5_J,axiom,
% 1.87/1.97 ! [V_w,V_v] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__number__of__mult,axiom,
% 1.87/1.97 ! [V_z,V_w,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))),V_z) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_z) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_number__of__minus,axiom,
% 1.87/1.97 ! [V_w,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_arith__simps_I30_J,axiom,
% 1.87/1.97 ! [V_w,T_a] :
% 1.87/1.97 ( class_Int_Onumber__ring(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__eq__number__of__int__code,axiom,
% 1.87/1.97 ! [V_l_2,V_k_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_sgn__minus,axiom,
% 1.87/1.97 ! [V_x,T_a] :
% 1.87/1.97 ( class_RealVector_Oreal__normed__vector(T_a)
% 1.87/1.97 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__le__cancel__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__minus,axiom,
% 1.87/1.97 ! [V_x,T_a] :
% 1.87/1.97 ( ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.97 & class_SEQ_Obanach(T_a) )
% 1.87/1.97 => hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__inj__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)
% 1.87/1.97 <=> V_x_2 = V_y_2 ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__zero,axiom,
% 1.87/1.97 ! [T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__0__equal__iff__equal,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
% 1.87/1.97 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_equal__neg__zero,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
% 1.87/1.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__equal__0__iff__equal,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__equal__zero,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
% 1.87/1.97 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__minus__iff,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__le__iff,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__le__iff__le,axiom,
% 1.87/1.97 ! [V_a_2,V_b_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__imp__neg__le,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_compl__mono,axiom,
% 1.87/1.97 ! [V_y,V_x,T_a] :
% 1.87/1.97 ( class_Lattices_Oboolean__algebra(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_compl__le__compl__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( class_Lattices_Oboolean__algebra(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__less__iff__less,axiom,
% 1.87/1.97 ! [V_a_2,V_b_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__less__iff,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__minus__iff,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_square__eq__iff,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Rings_Oidom(T_a)
% 1.87/1.97 => ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_b_2)
% 1.87/1.97 <=> ( V_a_2 = V_b_2
% 1.87/1.97 | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__mult__minus,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Rings_Oring(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__mult__commute,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Rings_Oring(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__mult__left,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Rings_Oring(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__mult__right,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Rings_Oring(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_mult__left_Ominus,axiom,
% 1.87/1.97 ! [V_y,V_x,T_a] :
% 1.87/1.97 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_mult_Ominus__left,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_mult__right_Ominus,axiom,
% 1.87/1.97 ! [V_x,V_xa,T_a] :
% 1.87/1.97 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_mult_Ominus__right,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_RealVector_Oreal__normed__algebra(T_a)
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__add__cancel,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__minus__cancel,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__add,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__add__distrib,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oab__group__add(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__divide__left,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__divide__right,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__divide__divide,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.97 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_divide_Ominus,axiom,
% 1.87/1.97 ! [V_y,V_x,T_a] :
% 1.87/1.97 ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.97 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_inverse__minus__eq,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.87/1.97 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_double__compl,axiom,
% 1.87/1.97 ! [V_x,T_a] :
% 1.87/1.97 ( class_Lattices_Oboolean__algebra(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_uminus__apply,axiom,
% 1.87/1.97 ! [V_x_2,V_A_2,T_b,T_a] :
% 1.87/1.97 ( class_Groups_Ouminus(T_a)
% 1.87/1.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_compl__eq__compl__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( class_Lattices_Oboolean__algebra(T_a)
% 1.87/1.97 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
% 1.87/1.97 <=> V_x_2 = V_y_2 ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__minus,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_equation__minus__iff,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.87/1.97 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__equation__iff,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
% 1.87/1.97 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2 ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__equal__iff__equal,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.87/1.97 <=> V_a_2 = V_b_2 ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__less__cancel__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__less__cancel,axiom,
% 1.87/1.97 ! [V_y,V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y))
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zle__antisym,axiom,
% 1.87/1.97 ! [V_w,V_z] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 1.87/1.97 => V_z = V_w ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zle__trans,axiom,
% 1.87/1.97 ! [V_k,V_j,V_i] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zle__linear,axiom,
% 1.87/1.97 ! [V_w,V_z] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 1.87/1.97 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zle__refl,axiom,
% 1.87/1.97 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zmult__1,axiom,
% 1.87/1.97 ! [V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zmult__1__right,axiom,
% 1.87/1.97 ! [V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zmult__assoc,axiom,
% 1.87/1.97 ! [V_z3,V_z2,V_z1] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_z2)),V_z3) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_z3)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zmult__commute,axiom,
% 1.87/1.97 ! [V_w,V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zless__linear,axiom,
% 1.87/1.97 ! [V_y,V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 1.87/1.97 | V_x = V_y
% 1.87/1.97 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zmult__zless__mono2,axiom,
% 1.87/1.97 ! [V_k,V_j,V_i] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_j)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_pos__zmult__eq__1__iff,axiom,
% 1.87/1.97 ! [V_n_2,V_ma_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)
% 1.87/1.97 => ( hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.87/1.97 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 1.87/1.97 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_int__0__less__1,axiom,
% 1.87/1.97 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_odd__nonzero,axiom,
% 1.87/1.97 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_succ__def,axiom,
% 1.87/1.97 ! [V_k] : c_Int_Osucc(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__0,axiom,
% 1.87/1.97 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__0__right,axiom,
% 1.87/1.97 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zless__add1__eq,axiom,
% 1.87/1.97 ! [V_za_2,V_wa_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.87/1.97 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
% 1.87/1.97 | V_wa_2 = V_za_2 ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_odd__less__0,axiom,
% 1.87/1.97 ! [V_za_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__strict__right__mono,axiom,
% 1.87/1.97 ! [V_k,V_j,V_i] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__commute,axiom,
% 1.87/1.97 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__left__commute,axiom,
% 1.87/1.97 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__assoc,axiom,
% 1.87/1.97 ! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__zmult__distrib,axiom,
% 1.87/1.97 ! [V_w,V_z2,V_z1] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_w)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__zmult__distrib2,axiom,
% 1.87/1.97 ! [V_z2,V_z1,V_w] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z2)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_int__one__le__iff__zero__less,axiom,
% 1.87/1.97 ! [V_za_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zle__add1__eq__le,axiom,
% 1.87/1.97 ! [V_za_2,V_wa_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add1__zle__eq,axiom,
% 1.87/1.97 ! [V_za_2,V_wa_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__imp__0__less,axiom,
% 1.87/1.97 ! [V_z] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zless__imp__add1__zle,axiom,
% 1.87/1.97 ! [V_z,V_w] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__zless__mono,axiom,
% 1.87/1.97 ! [V_z,V_z_H,V_w,V_w_H] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zless__le,axiom,
% 1.87/1.97 ! [V_wa_2,V_za_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
% 1.87/1.97 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2)
% 1.87/1.97 & V_za_2 != V_wa_2 ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_zadd__left__mono,axiom,
% 1.87/1.97 ! [V_k,V_j,V_i] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 1.87/1.97 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__exp,axiom,
% 1.87/1.97 ! [V_x] : hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) = V_x ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__ln__eq,axiom,
% 1.87/1.97 ! [V_x,V_u] :
% 1.87/1.97 ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_u) = V_x
% 1.87/1.97 => hAPP(c_Transcendental_Oln,V_x) = V_u ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ln__unique,axiom,
% 1.87/1.97 ! [V_x,V_y] :
% 1.87/1.97 ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y) = V_x
% 1.87/1.97 => hAPP(c_Transcendental_Oln,V_x) = V_y ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__not__eq__zero,axiom,
% 1.87/1.97 ! [V_x,T_a] :
% 1.87/1.97 ( ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.97 & class_SEQ_Obanach(T_a) )
% 1.87/1.97 => hAPP(c_Transcendental_Oexp(T_a),V_x) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_DERIV__exp,axiom,
% 1.87/1.97 ! [V_x_2,T_a] :
% 1.87/1.97 ( ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.97 & class_SEQ_Obanach(T_a) )
% 1.87/1.97 => c_Deriv_Oderiv(T_a,c_Transcendental_Oexp(T_a),V_x_2,hAPP(c_Transcendental_Oexp(T_a),V_x_2)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__le__self__iff,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__le__0__iff__le,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_le__minus__self__iff,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__0__le__iff__le,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__less__nonneg,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Olinordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__less__0__iff__less,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_neg__0__less__iff__less,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Oordered__ab__group__add(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_less__minus__self__iff,axiom,
% 1.87/1.97 ! [V_a_2,T_a] :
% 1.87/1.97 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.97 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_add__eq__0__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_right__minus,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 1.87/1.97 ! [V_b_2,V_a_2,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 1.87/1.97 <=> c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_left__minus,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_ab__left__minus,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Groups_Oab__group__add(T_a)
% 1.87/1.97 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_minus__unique,axiom,
% 1.87/1.97 ! [V_b,V_a,T_a] :
% 1.87/1.97 ( class_Groups_Ogroup__add(T_a)
% 1.87/1.97 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 1.87/1.97 ! [V_x,T_a] :
% 1.87/1.97 ( class_Rings_Ocomm__ring__1(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_square__eq__1__iff,axiom,
% 1.87/1.97 ! [V_x_2,T_a] :
% 1.87/1.97 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.87/1.97 => ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.97 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.97 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_nonzero__minus__divide__divide,axiom,
% 1.87/1.97 ! [V_a,V_b,T_a] :
% 1.87/1.97 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.97 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_nonzero__minus__divide__right,axiom,
% 1.87/1.97 ! [V_a,V_b,T_a] :
% 1.87/1.97 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.97 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_nonzero__inverse__minus__eq,axiom,
% 1.87/1.97 ! [V_a,T_a] :
% 1.87/1.97 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.97 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.97 => c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__minus__mult__self__le,axiom,
% 1.87/1.97 ! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),V_u)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__add__eq__0__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__add__minus__iff,axiom,
% 1.87/1.97 ! [V_a_2,V_x_2] :
% 1.87/1.97 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.97 <=> V_x_2 = V_a_2 ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__ge__zero,axiom,
% 1.87/1.97 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_not__exp__le__zero,axiom,
% 1.87/1.97 ! [V_x] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__gt__zero,axiom,
% 1.87/1.97 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_not__exp__less__zero,axiom,
% 1.87/1.97 ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__eq__one__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 1.87/1.97 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__zero,axiom,
% 1.87/1.97 ! [T_a] :
% 1.87/1.97 ( ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.97 & class_SEQ_Obanach(T_a) )
% 1.87/1.97 => hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__add,axiom,
% 1.87/1.97 ! [V_y,V_x,T_a] :
% 1.87/1.97 ( ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.97 & class_SEQ_Obanach(T_a) )
% 1.87/1.97 => hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_mult__exp__exp,axiom,
% 1.87/1.97 ! [V_y,V_x,T_a] :
% 1.87/1.97 ( ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.97 & class_SEQ_Obanach(T_a) )
% 1.87/1.97 => hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y)) = hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__add__le__0__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__0__le__add__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__add__less__0__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_real__0__less__add__iff,axiom,
% 1.87/1.97 ! [V_y_2,V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__le__one__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_one__le__exp__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__gt__one,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__less__one__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_one__less__exp__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__ln,axiom,
% 1.87/1.97 ! [V_x] :
% 1.87/1.97 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.97 => hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) = V_x ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_exp__ln__iff,axiom,
% 1.87/1.97 ! [V_x_2] :
% 1.87/1.97 ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2)) = V_x_2
% 1.87/1.97 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ) ).
% 1.87/1.97
% 1.87/1.97 fof(fact_DERIV__unique,axiom,
% 1.87/1.98 ! [V_E_2,V_D_2,V_x_2,V_f_2,T_a] :
% 1.87/1.98 ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.98 => ( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)
% 1.87/1.98 => ( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2)
% 1.87/1.98 => V_D_2 = V_E_2 ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_DERIV__cong,axiom,
% 1.87/1.98 ! [V_Y_2,V_X_2,V_x_2,V_f_2,T_a] :
% 1.87/1.98 ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.98 => ( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_X_2)
% 1.87/1.98 => ( V_X_2 = V_Y_2
% 1.87/1.98 => c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_Y_2) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Deriv_Olemma__DERIV__subst,axiom,
% 1.87/1.98 ! [V_E_2,V_D_2,V_x_2,V_f_2,T_a] :
% 1.87/1.98 ( class_RealVector_Oreal__normed__field(T_a)
% 1.87/1.98 => ( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)
% 1.87/1.98 => ( V_D_2 = V_E_2
% 1.87/1.98 => c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_sgn__if,axiom,
% 1.87/1.98 ! [V_x,T_a] :
% 1.87/1.98 ( class_Groups_Osgn__if(T_a)
% 1.87/1.98 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 1.87/1.98 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.98 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 1.87/1.98 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_sgn__neg,axiom,
% 1.87/1.98 ! [V_a,T_a] :
% 1.87/1.98 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.98 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_sgn__1__neg,axiom,
% 1.87/1.98 ! [V_a_2,T_a] :
% 1.87/1.98 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.98 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_ln__inverse,axiom,
% 1.87/1.98 ! [V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.98 => hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 1.87/1.98 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.87/1.98 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_unique__quotient__lemma__neg,axiom,
% 1.87/1.98 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zdiv__mono2__lemma,axiom,
% 1.87/1.98 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 1.87/1.98 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_unique__quotient__lemma,axiom,
% 1.87/1.98 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_minus__numeral__code_I5_J,axiom,
% 1.87/1.98 ! [V_w] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zminus__0,axiom,
% 1.87/1.98 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zminus__zminus,axiom,
% 1.87/1.98 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zmult__zminus,axiom,
% 1.87/1.98 ! [V_w,V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zsgn__def,axiom,
% 1.87/1.98 ! [V_i] :
% 1.87/1.98 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.87/1.98 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 1.87/1.98 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.87/1.98 => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)
% 1.87/1.98 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 1.87/1.98 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)
% 1.87/1.98 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zadd__zminus__inverse2,axiom,
% 1.87/1.98 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zminus__zadd__distrib,axiom,
% 1.87/1.98 ! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_int__0__neq__1,axiom,
% 1.87/1.98 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_number__of__is__id,axiom,
% 1.87/1.98 ! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k ).
% 1.87/1.98
% 1.87/1.98 fof(fact_self__quotient__aux2,axiom,
% 1.87/1.98 ! [V_q,V_r,V_a] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.87/1.98 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a),V_q))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_self__quotient__aux1,axiom,
% 1.87/1.98 ! [V_q,V_r,V_a] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 1.87/1.98 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_a),V_q))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_q__pos__lemma,axiom,
% 1.87/1.98 ! [V_r_H,V_q_H,V_b_H] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_q__neg__lemma,axiom,
% 1.87/1.98 ! [V_r_H,V_q_H,V_b_H] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 1.87/1.98 ! [V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_x),V_y)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 1.87/1.98 ! [V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 1.87/1.98 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 1.87/1.98 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__number__of__eq,axiom,
% 1.87/1.98 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
% 1.87/1.98 <=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_DERIV__pos__inc__right,axiom,
% 1.87/1.98 ! [V_l_2,V_x_2,V_f_2] :
% 1.87/1.98 ( c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_l_2)
% 1.87/1.98 => ? [B_d] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 1.87/1.98 & ! [B_h] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,V_x_2),hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h))) ) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_DERIV__neg__dec__right,axiom,
% 1.87/1.98 ! [V_l_2,V_x_2,V_f_2] :
% 1.87/1.98 ( c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_l_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.98 => ? [B_d] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
% 1.87/1.98 & ! [B_h] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h)),hAPP(V_f_2,V_x_2)) ) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_iszero__def,axiom,
% 1.87/1.98 ! [V_za_2,T_a] :
% 1.87/1.98 ( class_Rings_Osemiring__1(T_a)
% 1.87/1.98 => ( c_Int_Oiszero(T_a,V_za_2)
% 1.87/1.98 <=> V_za_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_iszero__0,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Rings_Osemiring__1(T_a)
% 1.87/1.98 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_not__iszero__1,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Rings_Osemiring__1(T_a)
% 1.87/1.98 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__special_I3_J,axiom,
% 1.87/1.98 ! [V_x_2,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.98 <=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__special_I1_J,axiom,
% 1.87/1.98 ! [V_y_2,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
% 1.87/1.98 <=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_number__of__pred,axiom,
% 1.87/1.98 ! [V_w,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_Opred(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__nat__number__of,axiom,
% 1.87/1.98 ! [V_v_H_2,V_v_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
% 1.87/1.98 <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) )
% 1.87/1.98 & c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__0__number__of,axiom,
% 1.87/1.98 ! [V_v_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__0__number__of,axiom,
% 1.87/1.98 ! [V_v_2] :
% 1.87/1.98 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__number__of__0,axiom,
% 1.87/1.98 ! [V_v_2] :
% 1.87/1.98 ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__nat__number__of,axiom,
% 1.87/1.98 ! [V_v_H_2,V_v_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
% 1.87/1.98 <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_minus__Pls,axiom,
% 1.87/1.98 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Pls__def,axiom,
% 1.87/1.98 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_semiring__norm_I113_J,axiom,
% 1.87/1.98 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__number__of__Pls,axiom,
% 1.87/1.98 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__Pls__right,axiom,
% 1.87/1.98 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__Pls,axiom,
% 1.87/1.98 ! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I2_J,axiom,
% 1.87/1.98 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__Pls,axiom,
% 1.87/1.98 ! [V_w] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),V_w) = c_Int_OPls ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I19_J,axiom,
% 1.87/1.98 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_succ__pred,axiom,
% 1.87/1.98 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 1.87/1.98
% 1.87/1.98 fof(fact_semiring__norm_I112_J,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_number__of__Pls,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__numeral__0__right,axiom,
% 1.87/1.98 ! [V_a,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__numeral__0,axiom,
% 1.87/1.98 ! [V_a,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_bin__less__0__simps_I1_J,axiom,
% 1.87/1.98 ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zero__is__num__zero,axiom,
% 1.87/1.98 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__nat__number__of,axiom,
% 1.87/1.98 ! [V_v_H,V_v] :
% 1.87/1.98 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H) )
% 1.87/1.98 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) )
% 1.87/1.98 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__number__of__mult__left,axiom,
% 1.87/1.98 ! [V_k,V_v_H,V_v] :
% 1.87/1.98 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.87/1.98 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H))),V_k) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__nat__number__of,axiom,
% 1.87/1.98 ! [V_v_H,V_v] :
% 1.87/1.98 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 1.87/1.98 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_iszero__Numeral0,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__1__add__number__of,axiom,
% 1.87/1.98 ! [V_v] :
% 1.87/1.98 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 1.87/1.98 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__number__of__add__1,axiom,
% 1.87/1.98 ! [V_v] :
% 1.87/1.98 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 1.87/1.98 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__iff__pred__less,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_divide__Numeral0,axiom,
% 1.87/1.98 ! [V_x,T_a] :
% 1.87/1.98 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.98 & class_Int_Onumber__ring(T_a) )
% 1.87/1.98 => c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__special_I1_J,axiom,
% 1.87/1.98 ! [V_y_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__special_I3_J,axiom,
% 1.87/1.98 ! [V_x_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__special_I1_J,axiom,
% 1.87/1.98 ! [V_y_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__special_I3_J,axiom,
% 1.87/1.98 ! [V_x_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_number__of2,axiom,
% 1.87/1.98 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__special_I4_J,axiom,
% 1.87/1.98 ! [V_x_2,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.98 <=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__special_I2_J,axiom,
% 1.87/1.98 ! [V_y_2,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => ( c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
% 1.87/1.98 <=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Numeral1__eq1__nat,axiom,
% 1.87/1.98 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__numeral__1__eq__1,axiom,
% 1.87/1.98 c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I39_J,axiom,
% 1.87/1.98 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I46_J,axiom,
% 1.87/1.98 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__eq__int__code_I16_J,axiom,
% 1.87/1.98 ! [V_k2_2,V_k1_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I34_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I17_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__int__code_I16_J,axiom,
% 1.87/1.98 ! [V_k2_2,V_k1_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I51_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 1.87/1.98 <=> V_k_2 = V_l_2 ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I22_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_bin__less__0__simps_I4_J,axiom,
% 1.87/1.98 ! [V_wa_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I12_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Bit1__def,axiom,
% 1.87/1.98 ! [V_k] : c_Int_OBit1(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_minus__Bit1,axiom,
% 1.87/1.98 ! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k))) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_iszero__number__of__Bit1,axiom,
% 1.87/1.98 ! [V_w,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Int_Oring__char__0(T_a) )
% 1.87/1.98 => ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w))) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_succ__Pls,axiom,
% 1.87/1.98 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_number__of__Bit1,axiom,
% 1.87/1.98 ! [V_w,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__numeral__1,axiom,
% 1.87/1.98 ! [V_a,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => 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 ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__numeral__1__right,axiom,
% 1.87/1.98 ! [V_a,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => 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 ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_numeral__1__eq__1,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_semiring__norm_I110_J,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_divide__Numeral1,axiom,
% 1.87/1.98 ! [V_x,T_a] :
% 1.87/1.98 ( ( class_Fields_Ofield(T_a)
% 1.87/1.98 & class_Int_Onumber__ring(T_a) )
% 1.87/1.98 => c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_divide__numeral__1,axiom,
% 1.87/1.98 ! [V_a,T_a] :
% 1.87/1.98 ( ( class_Fields_Ofield(T_a)
% 1.87/1.98 & class_Int_Onumber__ring(T_a) )
% 1.87/1.98 => c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_inverse__numeral__1,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( ( class_Fields_Ofield(T_a)
% 1.87/1.98 & class_Int_Onumber__ring(T_a) )
% 1.87/1.98 => c_Rings_Oinverse__class_Oinverse(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I29_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I5_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_one__is__num__one,axiom,
% 1.87/1.98 c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_not__iszero__Numeral1,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 1.87/1.98 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__special_I2_J,axiom,
% 1.87/1.98 ! [V_y_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__special_I4_J,axiom,
% 1.87/1.98 ! [V_x_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__special_I2_J,axiom,
% 1.87/1.98 ! [V_y_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__special_I4_J,axiom,
% 1.87/1.98 ! [V_x_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Rings_Olinordered__idom(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__special_I3_J,axiom,
% 1.87/1.98 ! [V_v,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls))) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__special_I2_J,axiom,
% 1.87/1.98 ! [V_w,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le0,axiom,
% 1.87/1.98 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__zeroE,axiom,
% 1.87/1.98 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__le__cancel1,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__not__refl,axiom,
% 1.87/1.98 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__neq__iff,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( V_ma_2 != V_n_2
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.87/1.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_linorder__neqE__nat,axiom,
% 1.87/1.98 ! [V_y,V_x] :
% 1.87/1.98 ( V_x != V_y
% 1.87/1.98 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__irrefl__nat,axiom,
% 1.87/1.98 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__not__refl2,axiom,
% 1.87/1.98 ! [V_m,V_n] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 1.87/1.98 => V_m != V_n ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__not__refl3,axiom,
% 1.87/1.98 ! [V_t,V_s] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 1.87/1.98 => V_s != V_t ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__less__cases,axiom,
% 1.87/1.98 ! [V_P_2,V_n_2,V_ma_2] :
% 1.87/1.98 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.87/1.98 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.87/1.98 => ( ( V_ma_2 = V_n_2
% 1.87/1.98 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.87/1.98 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 1.87/1.98 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 1.87/1.98 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__add__commute,axiom,
% 1.87/1.98 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__add__left__commute,axiom,
% 1.87/1.98 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__add__assoc,axiom,
% 1.87/1.98 ! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__add__left__cancel,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
% 1.87/1.98 <=> V_ma_2 = V_n_2 ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__add__right__cancel,axiom,
% 1.87/1.98 ! [V_n_2,V_k_2,V_ma_2] :
% 1.87/1.98 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
% 1.87/1.98 <=> V_ma_2 = V_n_2 ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__antisym,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 1.87/1.98 => V_m = V_n ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__trans,axiom,
% 1.87/1.98 ! [V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__imp__le,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( V_m = V_n
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__le__linear,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.87/1.98 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__refl,axiom,
% 1.87/1.98 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__assoc,axiom,
% 1.87/1.98 ! [V_k,V_n,V_m] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)),V_k) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__commute,axiom,
% 1.87/1.98 ! [V_n,V_m] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_m) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_not__less0,axiom,
% 1.87/1.98 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_neq0__conv,axiom,
% 1.87/1.98 ! [V_n_2] :
% 1.87/1.98 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__nat__zero__code,axiom,
% 1.87/1.98 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_gr__implies__not0,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.87/1.98 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_gr0I,axiom,
% 1.87/1.98 ! [V_n] :
% 1.87/1.98 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__eq__self__zero,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 1.87/1.98 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__is__0,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.98 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.98 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Nat_Oadd__0__right,axiom,
% 1.87/1.98 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 1.87/1.98
% 1.87/1.98 fof(fact_plus__nat_Oadd__0,axiom,
% 1.87/1.98 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 1.87/1.98 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__0__eq,axiom,
% 1.87/1.98 ! [V_n_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 1.87/1.98 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__cancel2,axiom,
% 1.87/1.98 ! [V_n_2,V_k_2,V_ma_2] :
% 1.87/1.98 ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2)
% 1.87/1.98 <=> ( V_ma_2 = V_n_2
% 1.87/1.98 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__cancel1,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)
% 1.87/1.98 <=> ( V_ma_2 = V_n_2
% 1.87/1.98 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__is__0,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.98 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.98 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__0__right,axiom,
% 1.87/1.98 ! [V_m] : 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) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__0,axiom,
% 1.87/1.98 ! [V_n] : 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) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__lessD1,axiom,
% 1.87/1.98 ! [V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__add__eq__less,axiom,
% 1.87/1.98 ! [V_n,V_m,V_l,V_k] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.87/1.98 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__less__mono,axiom,
% 1.87/1.98 ! [V_l,V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__less__mono1,axiom,
% 1.87/1.98 ! [V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_trans__less__add2,axiom,
% 1.87/1.98 ! [V_m,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_trans__less__add1,axiom,
% 1.87/1.98 ! [V_m,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__add__left__cancel__less,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_not__add__less2,axiom,
% 1.87/1.98 ! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_not__add__less1,axiom,
% 1.87/1.98 ! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__or__eq__imp__le,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.87/1.98 | V_m = V_n )
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__neq__implies__less,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.87/1.98 => ( V_m != V_n
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__imp__le__nat,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__eq__less__or__eq,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.87/1.98 | V_ma_2 = V_n_2 ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__less__le,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.87/1.98 & V_ma_2 != V_n_2 ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__add2,axiom,
% 1.87/1.98 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__add1,axiom,
% 1.87/1.98 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__iff__add,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 1.87/1.98 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__add__left__cancel__le,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_trans__le__add1,axiom,
% 1.87/1.98 ! [V_m,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_trans__le__add2,axiom,
% 1.87/1.98 ! [V_m,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__le__mono1,axiom,
% 1.87/1.98 ! [V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__le__mono,axiom,
% 1.87/1.98 ! [V_l,V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__leD2,axiom,
% 1.87/1.98 ! [V_n,V_k,V_m] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__leD1,axiom,
% 1.87/1.98 ! [V_n,V_k,V_m] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__leE,axiom,
% 1.87/1.98 ! [V_n,V_k,V_m] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 1.87/1.98 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 1.87/1.98 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__mult__distrib,axiom,
% 1.87/1.98 ! [V_k,V_n,V_m] : 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__mult__distrib2,axiom,
% 1.87/1.98 ! [V_n,V_m,V_k] : 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_n)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__square,axiom,
% 1.87/1.98 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__cube,axiom,
% 1.87/1.98 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m))) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__le__mono1,axiom,
% 1.87/1.98 ! [V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_k)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__le__mono2,axiom,
% 1.87/1.98 ! [V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__le__mono,axiom,
% 1.87/1.98 ! [V_l,V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_l)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__eq__1__iff,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.87/1.98 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.87/1.98 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__1__right,axiom,
% 1.87/1.98 ! [V_n] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__1__eq__mult__iff,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2)
% 1.87/1.98 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.87/1.98 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__1,axiom,
% 1.87/1.98 ! [V_n] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__gr__0,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( 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_ma_2,V_n_2))
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 1.87/1.98 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__0__less__mult__iff,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_n_2))
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 1.87/1.98 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__less__cancel1,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.87/1.98 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__less__cancel2,axiom,
% 1.87/1.98 ! [V_n_2,V_k_2,V_ma_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.87/1.98 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__less__mono1,axiom,
% 1.87/1.98 ! [V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_k)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__less__mono2,axiom,
% 1.87/1.98 ! [V_k,V_j,V_i] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__eq__self__implies__10,axiom,
% 1.87/1.98 ! [V_n,V_m] :
% 1.87/1.98 ( V_m = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)
% 1.87/1.98 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 1.87/1.98 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__le__cancel2,axiom,
% 1.87/1.98 ! [V_n_2,V_k_2,V_ma_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2),V_k_2))
% 1.87/1.98 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__le__cancel1,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__eq__cancel1,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.87/1.98 => ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)
% 1.87/1.98 <=> V_ma_2 = V_n_2 ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__less__cancel1,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 1.87/1.98 ! [V_n_2,V_ma_2,V_k_2] :
% 1.87/1.98 ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_n_2)
% 1.87/1.98 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.98 | V_ma_2 = V_n_2 ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_left__add__mult__distrib,axiom,
% 1.87/1.98 ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_termination__basic__simps_I4_J,axiom,
% 1.87/1.98 ! [V_y,V_z,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_termination__basic__simps_I3_J,axiom,
% 1.87/1.98 ! [V_z,V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_termination__basic__simps_I2_J,axiom,
% 1.87/1.98 ! [V_y,V_z,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_termination__basic__simps_I1_J,axiom,
% 1.87/1.98 ! [V_z,V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_termination__basic__simps_I5_J,axiom,
% 1.87/1.98 ! [V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__Suc__ex__iff,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 1.87/1.98 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_one__code__numeral__code,axiom,
% 1.87/1.98 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_zero__code__numeral__code,axiom,
% 1.87/1.98 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_half,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.98 & class_Int_Onumber__ring(T_a) )
% 1.87/1.98 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_incr__mult__lemma,axiom,
% 1.87/1.98 ! [V_k_2,V_P_2,V_db_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_db_2)
% 1.87/1.98 => ( ! [B_x] :
% 1.87/1.98 ( hBOOL(hAPP(V_P_2,B_x))
% 1.87/1.98 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_db_2))) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 1.87/1.98 => ! [B_x] :
% 1.87/1.98 ( hBOOL(hAPP(V_P_2,B_x))
% 1.87/1.98 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2),V_db_2)))) ) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_iszero__number__of__Bit0,axiom,
% 1.87/1.98 ! [V_wa_2,T_a] :
% 1.87/1.98 ( ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 & class_Int_Oring__char__0(T_a) )
% 1.87/1.98 => ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2)))
% 1.87/1.98 <=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_pred__Bit1,axiom,
% 1.87/1.98 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_pred__Bit0,axiom,
% 1.87/1.98 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_succ__Bit0,axiom,
% 1.87/1.98 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_succ__Bit1,axiom,
% 1.87/1.98 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__eq__int__code_I13_J,axiom,
% 1.87/1.98 ! [V_k2_2,V_k1_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I31_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__Bit0,axiom,
% 1.87/1.98 ! [V_l,V_k] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I14_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__int__code_I13_J,axiom,
% 1.87/1.98 ! [V_k2_2,V_k1_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Bit0__def,axiom,
% 1.87/1.98 ! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__Bit0__Bit0,axiom,
% 1.87/1.98 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I50_J,axiom,
% 1.87/1.98 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I49_J,axiom,
% 1.87/1.98 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_minus__Bit0,axiom,
% 1.87/1.98 ! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I48_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 1.87/1.98 <=> V_k_2 = V_l_2 ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I44_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 1.87/1.98 <=> V_k_2 = c_Int_OPls ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I38_J,axiom,
% 1.87/1.98 ! [V_l_2] :
% 1.87/1.98 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 1.87/1.98 <=> c_Int_OPls = V_l_2 ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Bit0__Pls,axiom,
% 1.87/1.98 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__Bit0__Bit1,axiom,
% 1.87/1.98 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__Bit1__Bit0,axiom,
% 1.87/1.98 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I4_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I10_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_bin__less__0__simps_I3_J,axiom,
% 1.87/1.98 ! [V_wa_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I16_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__int__code_I15_J,axiom,
% 1.87/1.98 ! [V_k2_2,V_k1_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I27_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I21_J,axiom,
% 1.87/1.98 ! [V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__eq__int__code_I14_J,axiom,
% 1.87/1.98 ! [V_k2_2,V_k1_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I32_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_number__of__Bit0,axiom,
% 1.87/1.98 ! [V_w,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I15_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__int__code_I14_J,axiom,
% 1.87/1.98 ! [V_k2_2,V_k1_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_rel__simps_I33_J,axiom,
% 1.87/1.98 ! [V_l_2,V_k_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_less__eq__int__code_I15_J,axiom,
% 1.87/1.98 ! [V_k2_2,V_k1_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__Bit1,axiom,
% 1.87/1.98 ! [V_l,V_k] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)),V_l) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_add__Bit1__Bit1,axiom,
% 1.87/1.98 ! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_Osucc(V_l))) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_double__number__of__Bit0,axiom,
% 1.87/1.98 ! [V_w,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => 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)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_number__of1,axiom,
% 1.87/1.98 ! [V_n] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_n)))
% 1.87/1.98 & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_n))) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_eq__divide__2__times__iff,axiom,
% 1.87/1.98 ! [V_za_2,V_y_2,V_x_2] :
% 1.87/1.98 ( V_x_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,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))
% 1.87/1.98 <=> 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_2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__2__right,axiom,
% 1.87/1.98 ! [V_z,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => 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) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_mult__2,axiom,
% 1.87/1.98 ! [V_z,T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => 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) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_one__add__one__is__two,axiom,
% 1.87/1.98 ! [T_a] :
% 1.87/1.98 ( class_Int_Onumber__ring(T_a)
% 1.87/1.98 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_pos2,axiom,
% 1.87/1.98 c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 1.87/1.98 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__2__right,axiom,
% 1.87/1.98 ! [V_z] : 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) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__mult__2,axiom,
% 1.87/1.98 ! [V_z] : 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) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_nat__1__add__1,axiom,
% 1.87/1.98 c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__less__half__sum,axiom,
% 1.87/1.98 ! [V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__gt__half__sum,axiom,
% 1.87/1.98 ! [V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_half__gt__zero,axiom,
% 1.87/1.98 ! [V_r,T_a] :
% 1.87/1.98 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.98 & class_Int_Onumber__ring(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_half__gt__zero__iff,axiom,
% 1.87/1.98 ! [V_r_2,T_a] :
% 1.87/1.98 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.98 & class_Int_Onumber__ring(T_a) )
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r_2) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
% 1.87/1.98 ! [V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.87/1.98 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 1.87/1.98 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 1.87/1.98 | V_x = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sum__of__halves,axiom,
% 1.87/1.98 ! [V_x] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x ).
% 1.87/1.98
% 1.87/1.98 fof(fact_DERIV__real__sqrt__generic,axiom,
% 1.87/1.98 ! [V_D_2,V_x_2] :
% 1.87/1.98 ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.98 => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.98 => V_D_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
% 1.87/1.98 => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.98 => V_D_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
% 1.87/1.98 => c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2) ) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_DERIV__const__average,axiom,
% 1.87/1.98 ! [V_k_2,V_v_2,V_b_2,V_a_2] :
% 1.87/1.98 ( V_a_2 != V_b_2
% 1.87/1.98 => ( ! [B_x] : c_Deriv_Oderiv(tc_RealDef_Oreal,V_v_2,B_x,V_k_2)
% 1.87/1.98 => hAPP(V_v_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a_2,V_b_2),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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(V_v_2,V_a_2),hAPP(V_v_2,V_b_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__lt__1__iff,axiom,
% 1.87/1.98 ! [V_x_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__gt__1__iff,axiom,
% 1.87/1.98 ! [V_y_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__ge__1__iff,axiom,
% 1.87/1.98 ! [V_y_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__le__1__iff,axiom,
% 1.87/1.98 ! [V_x_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__ge__one,axiom,
% 1.87/1.98 ! [V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__eq__1__iff,axiom,
% 1.87/1.98 ! [V_x_2] :
% 1.87/1.98 ( hAPP(c_NthRoot_Osqrt,V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 1.87/1.98 <=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__one,axiom,
% 1.87/1.98 hAPP(c_NthRoot_Osqrt,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__le__mono,axiom,
% 1.87/1.98 ! [V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__le__iff,axiom,
% 1.87/1.98 ! [V_y_2,V_x_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__less__mono,axiom,
% 1.87/1.98 ! [V_y,V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__less__iff,axiom,
% 1.87/1.98 ! [V_y_2,V_x_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__mult,axiom,
% 1.87/1.98 ! [V_y,V_x] : hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),hAPP(c_NthRoot_Osqrt,V_y)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__minus,axiom,
% 1.87/1.98 ! [V_x] : hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__inverse,axiom,
% 1.87/1.98 ! [V_x] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__divide,axiom,
% 1.87/1.98 ! [V_y,V_x] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__eq__iff,axiom,
% 1.87/1.98 ! [V_y_2,V_x_2] :
% 1.87/1.98 ( hAPP(c_NthRoot_Osqrt,V_x_2) = hAPP(c_NthRoot_Osqrt,V_y_2)
% 1.87/1.98 <=> V_x_2 = V_y_2 ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__gt__zero,axiom,
% 1.87/1.98 ! [V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.98 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__not__eq__zero,axiom,
% 1.87/1.98 ! [V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.98 => hAPP(c_NthRoot_Osqrt,V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__lt__0__iff,axiom,
% 1.87/1.98 ! [V_x_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__gt__0__iff,axiom,
% 1.87/1.98 ! [V_y_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__ge__0__iff,axiom,
% 1.87/1.98 ! [V_y_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__le__0__iff,axiom,
% 1.87/1.98 ! [V_x_2] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.98 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__ge__zero,axiom,
% 1.87/1.98 ! [V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.98 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x)) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__eq__zero__cancel,axiom,
% 1.87/1.98 ! [V_x] :
% 1.87/1.98 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.98 => ( hAPP(c_NthRoot_Osqrt,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.98 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__eq__0__iff,axiom,
% 1.87/1.98 ! [V_x_2] :
% 1.87/1.98 ( hAPP(c_NthRoot_Osqrt,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.98 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__zero,axiom,
% 1.87/1.98 hAPP(c_NthRoot_Osqrt,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_le__real__sqrt__sumsq,axiom,
% 1.87/1.98 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))) ).
% 1.87/1.98
% 1.87/1.98 fof(fact_real__sqrt__mult__self__sum__ge__zero,axiom,
% 1.87/1.99 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_sqrt__divide__self__eq,axiom,
% 1.87/1.99 ! [V_x] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.99 => c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_x) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__two__ge__zero,axiom,
% 1.87/1.99 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__two__gt__zero,axiom,
% 1.87/1.99 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__two__gt__one,axiom,
% 1.87/1.99 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_lemma__real__divide__sqrt__less,axiom,
% 1.87/1.99 ! [V_u] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_DERIV__real__sqrt,axiom,
% 1.87/1.99 ! [V_x_2] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 1.87/1.99 => c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_lemma__sqrt__hcomplex__capprox,axiom,
% 1.87/1.99 ! [V_y,V_x,V_u] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 1.87/1.99 ! [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),hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__power,axiom,
% 1.87/1.99 ! [V_k,V_x] : hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_k) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 1.87/1.99 ! [V_x,T_a] :
% 1.87/1.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 1.87/1.99 ! [V_q,V_p,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.99 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p)),c_Power_Opower__class_Opower(T_a,V_x,V_q)) = c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 1.87/1.99 ! [V_q,V_p,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q) = c_Power_Opower__class_Opower(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_p),V_q)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 1.87/1.99 ! [V_q,V_y,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_q) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q)),c_Power_Opower__class_Opower(T_a,V_y,V_q)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 1.87/1.99 ! [V_x,T_a] :
% 1.87/1.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__eq__0__iff__number__of,axiom,
% 1.87/1.99 ! [V_wa_2,V_a_2,T_a] :
% 1.87/1.99 ( ( class_Power_Opower(T_a)
% 1.87/1.99 & class_Rings_Omult__zero(T_a)
% 1.87/1.99 & class_Rings_Ono__zero__divisors(T_a)
% 1.87/1.99 & class_Rings_Ozero__neq__one(T_a) )
% 1.87/1.99 => ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__0__left__number__of,axiom,
% 1.87/1.99 ! [V_w,T_a] :
% 1.87/1.99 ( ( class_Power_Opower(T_a)
% 1.87/1.99 & class_Rings_Osemiring__0(T_a) )
% 1.87/1.99 => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a) )
% 1.87/1.99 & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power3__eq__cube,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.99 => 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(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)),V_a) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__power2,axiom,
% 1.87/1.99 ! [T_a] :
% 1.87/1.99 ( class_Rings_Osemiring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__eq__power2,axiom,
% 1.87/1.99 ! [V_a_2,T_a] :
% 1.87/1.99 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.87/1.99 => ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 1.87/1.99 ! [V_x,T_a] :
% 1.87/1.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.99 => hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__eq__square,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.99 => 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_one__power2,axiom,
% 1.87/1.99 ! [T_a] :
% 1.87/1.99 ( class_Rings_Osemiring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__minus,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Rings_Oring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__even__eq,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_a,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_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__le__power2,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__le__imp__le,axiom,
% 1.87/1.99 ! [V_y,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__eq__imp__eq,axiom,
% 1.87/1.99 ! [V_y,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.99 => V_x = V_y ) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__less__power2,axiom,
% 1.87/1.99 ! [V_a_2,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.87/1.99 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__less__0,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_sum__power2__eq__zero__iff,axiom,
% 1.87/1.99 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ( c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__eq__square__number__of,axiom,
% 1.87/1.99 ! [V_w,T_b] :
% 1.87/1.99 ( ( class_Groups_Omonoid__mult(T_b)
% 1.87/1.99 & class_Int_Onumber(T_b) )
% 1.87/1.99 => 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(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__eq__1__iff,axiom,
% 1.87/1.99 ! [V_a_2,T_a] :
% 1.87/1.99 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.87/1.99 => ( 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_Oone__class_Oone(T_a)
% 1.87/1.99 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a)
% 1.87/1.99 | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 1.87/1.99 ! [V_n,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Ocomm__semiring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_x,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(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(T_a,V_x,V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_ring__1__class_Opower__minus__even,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Oring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),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_Power_Opower__class_Opower(T_a,V_a,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)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_realpow__two__sum__zero__iff,axiom,
% 1.87/1.99 ! [V_y_2,V_x_2] :
% 1.87/1.99 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.99 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 1.87/1.99 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_four__x__squared,axiom,
% 1.87/1.99 ! [V_x] : 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_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,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)))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_two__realpow__ge__one,axiom,
% 1.87/1.99 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_realpow__square__minus__le,axiom,
% 1.87/1.99 ! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__less__imp__less,axiom,
% 1.87/1.99 ! [V_y,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_sum__power2__ge__zero,axiom,
% 1.87/1.99 ! [V_y,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_sum__power2__le__zero__iff,axiom,
% 1.87/1.99 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.99 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_not__sum__power2__lt__zero,axiom,
% 1.87/1.99 ! [V_y,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_sum__power2__gt__zero__iff,axiom,
% 1.87/1.99 ! [V_y_2,V_x_2,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 1.87/1.99 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power2__sum,axiom,
% 1.87/1.99 ! [V_y,V_x,T_a] :
% 1.87/1.99 ( class_Int_Onumber__ring(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(T_a,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)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_even__power__le__0__imp__0,axiom,
% 1.87/1.99 ! [V_k,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,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))
% 1.87/1.99 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__le__even__power_H,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,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))) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__minus1__even,axiom,
% 1.87/1.99 ! [V_n,T_a] :
% 1.87/1.99 ( class_Rings_Oring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),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) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__unique,axiom,
% 1.87/1.99 ! [V_x,V_y] :
% 1.87/1.99 ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 1.87/1.99 => hAPP(c_NthRoot_Osqrt,V_x) = V_y ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__pow2,axiom,
% 1.87/1.99 ! [V_x] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.99 => c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__pow2__iff,axiom,
% 1.87/1.99 ! [V_x_2] :
% 1.87/1.99 ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x_2
% 1.87/1.99 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__pow2__gt__zero,axiom,
% 1.87/1.99 ! [V_x] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__ge1,axiom,
% 1.87/1.99 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__ge2,axiom,
% 1.87/1.99 ! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__triangle__ineq,axiom,
% 1.87/1.99 ! [V_d,V_b,V_c,V_a] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__eq__cancel,axiom,
% 1.87/1.99 ! [V_y,V_x] :
% 1.87/1.99 ( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_x
% 1.87/1.99 => V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__eq__cancel2,axiom,
% 1.87/1.99 ! [V_y,V_x] :
% 1.87/1.99 ( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_y
% 1.87/1.99 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 1.87/1.99 ! [V_ya,V_xa,V_y,V_x] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__ge__zero,axiom,
% 1.87/1.99 ! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__inv__sqrt__pow2,axiom,
% 1.87/1.99 ! [V_x] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 1.87/1.99 => c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sum__squared__expand,axiom,
% 1.87/1.99 ! [V_y,V_x] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,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)) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__strict__mono,axiom,
% 1.87/1.99 ! [V_n,V_b,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_nat__power__less__imp__less,axiom,
% 1.87/1.99 ! [V_n,V_m,V_i] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))
% 1.87/1.99 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_nat__zero__less__power__iff,axiom,
% 1.87/1.99 ! [V_n_2,V_x_2] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
% 1.87/1.99 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 1.87/1.99 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 1.87/1.99 ! [V_n,V_x] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zpower__zadd__distrib,axiom,
% 1.87/1.99 ! [V_z,V_y,V_x] : c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y)),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_z)) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zpower__zpower,axiom,
% 1.87/1.99 ! [V_z,V_y,V_x] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),V_z) = c_Power_Opower__class_Opower(tc_Int_Oint,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_y),V_z)) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__less__power__nat__eq,axiom,
% 1.87/1.99 ! [V_n_2,V_x_2] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
% 1.87/1.99 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__less__power__nat__eq__number__of,axiom,
% 1.87/1.99 ! [V_wa_2,V_x_2] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))
% 1.87/1.99 <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.99 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_field__power__not__zero,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 1.87/1.99 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__mult__distrib,axiom,
% 1.87/1.99 ! [V_n,V_b,V_a,T_a] :
% 1.87/1.99 ( class_Groups_Ocomm__monoid__mult(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_n) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__commutes,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.99 => hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),V_a) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__one,axiom,
% 1.87/1.99 ! [V_n,T_a] :
% 1.87/1.99 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__divide,axiom,
% 1.87/1.99 ! [V_n,V_b,V_a,T_a] :
% 1.87/1.99 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__mult,axiom,
% 1.87/1.99 ! [V_n,V_m,V_a,T_a] :
% 1.87/1.99 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)) = c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),V_n) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__inverse,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 1.87/1.99 => c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__one__right,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__le__power,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__mono,axiom,
% 1.87/1.99 ! [V_n,V_b,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__less__power,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_one__le__power,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__eq__0__iff,axiom,
% 1.87/1.99 ! [V_n_2,V_a_2,T_a] :
% 1.87/1.99 ( ( class_Power_Opower(T_a)
% 1.87/1.99 & class_Rings_Omult__zero(T_a)
% 1.87/1.99 & class_Rings_Ono__zero__divisors(T_a)
% 1.87/1.99 & class_Rings_Ozero__neq__one(T_a) )
% 1.87/1.99 => ( c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__inject__exp,axiom,
% 1.87/1.99 ! [V_n_2,V_ma_2,V_a_2,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
% 1.87/1.99 => ( c_Power_Opower__class_Opower(T_a,V_a_2,V_ma_2) = c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2)
% 1.87/1.99 <=> V_ma_2 = V_n_2 ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_nonzero__power__divide,axiom,
% 1.87/1.99 ! [V_n,V_a,V_b,T_a] :
% 1.87/1.99 ( class_Fields_Ofield(T_a)
% 1.87/1.99 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__0,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Power_Opower(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__add,axiom,
% 1.87/1.99 ! [V_n,V_m,V_a,T_a] :
% 1.87/1.99 ( class_Groups_Omonoid__mult(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m)),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__one__over,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Fields_Ofield__inverse__zero(T_a)
% 1.87/1.99 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_nonzero__power__inverse,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Odivision__ring(T_a)
% 1.87/1.99 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 1.87/1.99 => c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__less__imp__less__base,axiom,
% 1.87/1.99 ! [V_b,V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__gt1__lemma,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__less__power__Suc,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__0__left,axiom,
% 1.87/1.99 ! [V_n,T_a] :
% 1.87/1.99 ( ( class_Power_Opower(T_a)
% 1.87/1.99 & class_Rings_Osemiring__0(T_a) )
% 1.87/1.99 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 1.87/1.99 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__minus,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Oring__1(T_a)
% 1.87/1.99 => c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__strict__increasing__iff,axiom,
% 1.87/1.99 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
% 1.87/1.99 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__less__imp__less__exp,axiom,
% 1.87/1.99 ! [V_n,V_m,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
% 1.87/1.99 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__strict__increasing,axiom,
% 1.87/1.99 ! [V_a,V_N,V_n,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__increasing,axiom,
% 1.87/1.99 ! [V_a,V_N,V_n,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__Suc__less,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__strict__decreasing,axiom,
% 1.87/1.99 ! [V_a,V_N,V_n,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__eq__imp__eq__base,axiom,
% 1.87/1.99 ! [V_b,V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Power_Opower__class_Opower(T_a,V_a,V_n) = c_Power_Opower__class_Opower(T_a,V_b,V_n)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.87/1.99 => V_a = V_b ) ) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__decreasing,axiom,
% 1.87/1.99 ! [V_a,V_N,V_n,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__increasing__iff,axiom,
% 1.87/1.99 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
% 1.87/1.99 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__le__imp__le__exp,axiom,
% 1.87/1.99 ! [V_n,V_m,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_one__less__power,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__semidom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_csqrt,axiom,
% 1.87/1.99 ! [V_z] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z ).
% 1.87/1.99
% 1.87/1.99 fof(fact_arctan__half,axiom,
% 1.87/1.99 ! [V_x] : hAPP(c_Transcendental_Oarctan,V_x) = 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)))),hAPP(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),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_arctan__zero__zero,axiom,
% 1.87/1.99 hAPP(c_Transcendental_Oarctan,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_arctan__minus,axiom,
% 1.87/1.99 ! [V_x] : hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x)) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_arctan__monotone_H,axiom,
% 1.87/1.99 ! [V_y,V_x] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_arctan__monotone,axiom,
% 1.87/1.99 ! [V_y,V_x] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_DERIV__arctan,axiom,
% 1.87/1.99 ! [V_x_2] : c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_cos__x__y__le__one,axiom,
% 1.87/1.99 ! [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,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sqrt__sum__squares__less,axiom,
% 1.87/1.99 ! [V_y,V_u,V_x] :
% 1.87/1.99 ( 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,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 1.87/1.99 => ( 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,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 1.87/1.99 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_zero__le__power__abs,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_power__abs,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__power__minus,axiom,
% 1.87/1.99 ! [V_n,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)) = c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_rabs__ratiotest__lemma,axiom,
% 1.87/1.99 ! [V_y,V_x,V_c] :
% 1.87/1.99 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
% 1.87/1.99 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__mult__pos,axiom,
% 1.87/1.99 ! [V_y,V_x,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 1.87/1.99 => 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(c_Groups_Otimes__class_Otimes(T_a,V_y),V_x)) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__eq__mult,axiom,
% 1.87/1.99 ! [V_b,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Oordered__ring__abs(T_a)
% 1.87/1.99 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 1.87/1.99 | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
% 1.87/1.99 & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 1.87/1.99 | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 1.87/1.99 => c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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)) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__of__nonpos,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.99 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__minus__le__zero,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.87/1.99 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__of__neg,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.99 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__if,axiom,
% 1.87/1.99 ! [V_a,T_a] :
% 1.87/1.99 ( class_Groups_Oabs__if(T_a)
% 1.87/1.99 => ( ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.99 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) )
% 1.87/1.99 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 1.87/1.99 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__div__pos,axiom,
% 1.87/1.99 ! [V_x,V_y,T_a] :
% 1.87/1.99 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 1.87/1.99 => c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__one,axiom,
% 1.87/1.99 ! [T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_real__sgn__eq,axiom,
% 1.87/1.99 ! [V_x] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)) ).
% 1.87/1.99
% 1.87/1.99 fof(fact_abs__mult__less,axiom,
% 1.87/1.99 ! [V_d,V_b,V_c,V_a,T_a] :
% 1.87/1.99 ( class_Rings_Olinordered__idom(T_a)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 1.87/1.99 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 1.87/1.99 => c_Orderings_Oord__class_Oless(T_a,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(c_Groups_Otimes__class_Otimes(T_a,V_c),V_d)) ) ) ) ).
% 1.87/1.99
% 1.87/1.99 %----Arity declarations (253)
% 1.87/1.99 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 1.87/1.99 ! [T_2,T_1] :
% 1.87/1.99 ( class_Lattices_Oboolean__algebra(T_1)
% 1.87/1.99 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_fun__Orderings_Opreorder,axiom,
% 1.87/1.99 ! [T_2,T_1] :
% 1.87/1.99 ( class_Orderings_Opreorder(T_1)
% 1.87/1.99 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_fun__Orderings_Oorder,axiom,
% 1.87/1.99 ! [T_2,T_1] :
% 1.87/1.99 ( class_Orderings_Oorder(T_1)
% 1.87/1.99 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_fun__Orderings_Oord,axiom,
% 1.87/1.99 ! [T_2,T_1] :
% 1.87/1.99 ( class_Orderings_Oord(T_1)
% 1.87/1.99 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_fun__Groups_Ouminus,axiom,
% 1.87/1.99 ! [T_2,T_1] :
% 1.87/1.99 ( class_Groups_Ouminus(T_1)
% 1.87/1.99 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.87/1.99 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 1.87/1.99 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 1.87/1.99 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 1.87/1.99 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 1.87/1.99 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 1.87/1.99 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 1.87/1.99 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 1.87/1.99 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 1.87/1.99 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 1.87/1.99 class_Orderings_Opreorder(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 1.87/1.99 class_Orderings_Olinorder(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 1.87/1.99 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 1.87/1.99 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 1.87/1.99 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 1.87/1.99 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 1.87/1.99 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 1.87/1.99 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 1.87/1.99 class_Rings_Omult__zero(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 1.87/1.99 class_Orderings_Oorder(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 1.87/1.99 class_Int_Oring__char__0(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 1.87/1.99 class_Int_Onumber__ring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 1.87/1.99 class_Rings_Osemiring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 1.87/1.99 class_Orderings_Oord(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 1.87/1.99 class_Groups_Ouminus(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 1.87/1.99 class_Groups_Osgn__if(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 1.87/1.99 class_Groups_Oabs__if(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 1.87/1.99 class_Rings_Oring__1(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Power_Opower,axiom,
% 1.87/1.99 class_Power_Opower(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 1.87/1.99 class_Groups_Ozero(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oring,axiom,
% 1.87/1.99 class_Rings_Oring(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 1.87/1.99 class_Rings_Oidom(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Int_Onumber,axiom,
% 1.87/1.99 class_Int_Onumber(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Int__Oint__Groups_Oone,axiom,
% 1.87/1.99 class_Groups_Oone(tc_Int_Oint) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.87/1.99 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 1.87/1.99 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 1.87/1.99 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 1.87/1.99 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 1.87/1.99 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 1.87/1.99 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 1.87/1.99 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 1.87/1.99 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 1.87/1.99 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 1.87/1.99 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 1.87/1.99 class_Orderings_Oorder(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 1.87/1.99 class_Rings_Osemiring(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 1.87/1.99 class_Orderings_Oord(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Power_Opower,axiom,
% 1.87/1.99 class_Power_Opower(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 1.87/1.99 class_Groups_Ozero(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 1.87/1.99 class_Int_Onumber(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 1.87/1.99 class_Groups_Oone(tc_Nat_Onat) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 1.87/1.99 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 1.87/1.99 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 1.87/1.99 class_Orderings_Oorder(tc_HOL_Obool) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 1.87/1.99 class_Orderings_Oord(tc_HOL_Obool) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 1.87/1.99 class_Groups_Ouminus(tc_HOL_Obool) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.87/1.99 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
% 1.87/1.99 class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
% 1.87/1.99 class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 1.87/1.99 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 1.87/1.99 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 1.87/1.99 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
% 1.87/1.99 class_Fields_Olinordered__field(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 1.87/1.99 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 1.87/1.99 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 1.87/1.99 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 1.87/1.99 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 1.87/1.99 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 1.87/1.99 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 1.87/1.99 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 1.87/1.99 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 1.87/1.99 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 1.87/1.99 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 1.87/1.99 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 1.87/1.99 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
% 1.87/1.99 class_Rings_Osemiring__1(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 1.87/1.99 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 1.87/1.99 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 1.87/1.99 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 1.87/1.99 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 1.87/1.99 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
% 1.87/1.99 class_Int_Onumber__ring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 1.87/1.99 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 1.87/1.99 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
% 1.87/1.99 class_Groups_Ouminus(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
% 1.87/1.99 class_Groups_Osgn__if(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
% 1.87/1.99 class_Groups_Oabs__if(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 1.87/1.99 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 1.87/1.99 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 1.87/1.99 class_Power_Opower(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 1.87/1.99 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__SEQ_Obanach,axiom,
% 1.87/1.99 class_SEQ_Obanach(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 1.87/1.99 class_Rings_Oring(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 1.87/1.99 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Int_Onumber,axiom,
% 1.87/1.99 class_Int_Onumber(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 1.87/1.99 class_Groups_Oone(tc_RealDef_Oreal) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 1.87/1.99 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
% 1.87/1.99 class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
% 1.87/1.99 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 1.87/1.99 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 1.87/1.99 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 1.87/1.99 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 1.87/1.99 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 1.87/1.99 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 1.87/1.99 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 1.87/1.99 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
% 1.87/1.99 class_Rings_Osemiring__1(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 1.87/1.99 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 1.87/1.99 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 1.87/1.99 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 1.87/1.99 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
% 1.87/1.99 class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 1.87/1.99 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
% 1.87/1.99 class_Groups_Ouminus(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 1.87/1.99 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 1.87/1.99 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 1.87/1.99 class_Power_Opower(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 1.87/1.99 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__SEQ_Obanach,axiom,
% 1.87/1.99 class_SEQ_Obanach(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 1.87/1.99 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 1.87/1.99 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
% 1.87/1.99 class_Int_Onumber(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 1.87/1.99 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 1.87/1.99 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 1.87/1.99 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 1.87/1.99 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 1.87/1.99 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 1.87/1.99 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 1.87/1.99 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 1.87/1.99 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 1.87/1.99 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 1.87/1.99 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 1.87/1.99 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 1.87/1.99 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 1.87/1.99 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/1.99
% 1.87/1.99 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 1.87/2.00 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 1.87/2.00 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 1.87/2.00 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 1.87/2.00 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 1.87/2.00 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 1.87/2.00 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 1.87/2.00 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 1.87/2.00 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 1.87/2.00 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 1.87/2.00 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 1.87/2.00
% 1.87/2.00 %----Conjectures (1)
% 1.87/2.00 fof(conj_0,conjecture,
% 1.87/2.00 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e) ).
% 1.87/2.00
% 1.87/2.00 %------------------------------------------------------------------------------
% 1.87/2.00 %-------------------------------------------
% 1.87/2.00 % Proof found
% 1.87/2.00 % SZS status Theorem for theBenchmark
% 1.87/2.00 % SZS output start Proof
% 1.87/2.00 %ClaNum:1875(EqnAxiom:148)
% 1.87/2.00 %VarNum:8927(SingletonVarNum:2865)
% 1.87/2.00 %MaxLitNum:7
% 1.87/2.00 %MaxfuncDepth:11
% 1.87/2.00 %SharedTerms:367
% 1.87/2.00 %goalClause: 554
% 1.87/2.00 %singleGoalClaCount:1
% 1.87/2.00 [150]P1(a36)
% 1.87/2.00 [151]P1(a1)
% 1.87/2.00 [152]P1(a37)
% 1.87/2.00 [153]P1(a11)
% 1.87/2.00 [154]P1(a34)
% 1.87/2.00 [155]P2(a36)
% 1.87/2.00 [156]P9(a36)
% 1.87/2.00 [157]P3(a36)
% 1.87/2.00 [158]P3(a34)
% 1.87/2.00 [159]P4(a36)
% 1.87/2.00 [160]P4(a34)
% 1.87/2.00 [161]P49(a36)
% 1.87/2.00 [162]P49(a34)
% 1.87/2.00 [163]P50(a36)
% 1.87/2.00 [164]P50(a34)
% 1.87/2.00 [165]P51(a36)
% 1.87/2.00 [166]P51(a1)
% 1.87/2.00 [167]P51(a37)
% 1.87/2.00 [168]P51(a11)
% 1.87/2.00 [169]P52(a36)
% 1.87/2.00 [170]P52(a1)
% 1.87/2.00 [171]P57(a36)
% 1.87/2.00 [172]P57(a1)
% 1.87/2.00 [173]P57(a37)
% 1.87/2.00 [174]P57(a11)
% 1.87/2.00 [175]P57(a34)
% 1.87/2.00 [176]P63(a36)
% 1.87/2.00 [177]P63(a1)
% 1.87/2.00 [178]P63(a34)
% 1.87/2.00 [179]P58(a36)
% 1.87/2.00 [180]P58(a1)
% 1.87/2.00 [181]P58(a37)
% 1.87/2.00 [182]P58(a11)
% 1.87/2.00 [183]P58(a34)
% 1.87/2.00 [184]P72(a36)
% 1.87/2.00 [185]P72(a1)
% 1.87/2.00 [186]P72(a37)
% 1.87/2.00 [187]P72(a11)
% 1.87/2.00 [188]P72(a34)
% 1.87/2.00 [189]P55(a36)
% 1.87/2.00 [190]P55(a1)
% 1.87/2.00 [191]P53(a36)
% 1.87/2.00 [192]P53(a1)
% 1.87/2.00 [193]P53(a37)
% 1.87/2.00 [194]P53(a11)
% 1.87/2.00 [195]P59(a36)
% 1.87/2.00 [196]P59(a1)
% 1.87/2.00 [197]P59(a37)
% 1.87/2.00 [198]P59(a11)
% 1.87/2.00 [199]P56(a36)
% 1.87/2.00 [200]P56(a1)
% 1.87/2.00 [201]P10(a36)
% 1.87/2.00 [202]P10(a34)
% 1.87/2.00 [203]P11(a36)
% 1.87/2.00 [204]P11(a1)
% 1.87/2.00 [205]P11(a37)
% 1.87/2.00 [206]P11(a11)
% 1.87/2.00 [207]P11(a34)
% 1.87/2.00 [208]P19(a36)
% 1.87/2.00 [209]P19(a1)
% 1.87/2.00 [210]P19(a37)
% 1.87/2.00 [211]P19(a11)
% 1.87/2.00 [212]P19(a34)
% 1.87/2.00 [213]P23(a36)
% 1.87/2.00 [214]P23(a34)
% 1.87/2.00 [215]P64(a36)
% 1.87/2.00 [216]P64(a1)
% 1.87/2.00 [217]P64(a37)
% 1.87/2.00 [218]P64(a11)
% 1.87/2.00 [219]P65(a36)
% 1.87/2.00 [220]P65(a1)
% 1.87/2.00 [221]P67(a36)
% 1.87/2.00 [222]P67(a1)
% 1.87/2.00 [223]P67(a37)
% 1.87/2.00 [224]P67(a11)
% 1.87/2.00 [225]P66(a36)
% 1.87/2.00 [226]P66(a1)
% 1.87/2.00 [227]P66(a37)
% 1.87/2.00 [228]P66(a11)
% 1.87/2.00 [229]P60(a36)
% 1.87/2.00 [230]P60(a1)
% 1.87/2.00 [231]P60(a37)
% 1.87/2.00 [232]P60(a11)
% 1.87/2.00 [233]P24(a36)
% 1.87/2.00 [234]P24(a1)
% 1.87/2.00 [235]P24(a37)
% 1.87/2.00 [236]P24(a11)
% 1.87/2.00 [237]P24(a34)
% 1.87/2.00 [238]P12(a36)
% 1.87/2.00 [239]P12(a1)
% 1.87/2.00 [240]P12(a37)
% 1.87/2.00 [241]P12(a11)
% 1.87/2.00 [242]P12(a34)
% 1.87/2.00 [243]P25(a36)
% 1.87/2.00 [244]P25(a1)
% 1.87/2.00 [245]P25(a37)
% 1.87/2.00 [246]P25(a11)
% 1.87/2.00 [247]P25(a34)
% 1.87/2.00 [248]P34(a36)
% 1.87/2.00 [249]P34(a1)
% 1.87/2.00 [250]P34(a37)
% 1.87/2.00 [251]P34(a11)
% 1.87/2.00 [252]P34(a35)
% 1.87/2.00 [253]P35(a36)
% 1.87/2.00 [254]P35(a1)
% 1.87/2.00 [255]P35(a37)
% 1.87/2.00 [256]P35(a11)
% 1.87/2.00 [257]P41(a36)
% 1.87/2.00 [258]P41(a1)
% 1.87/2.00 [259]P41(a37)
% 1.87/2.00 [260]P41(a11)
% 1.87/2.00 [261]P41(a35)
% 1.87/2.00 [262]P42(a36)
% 1.87/2.00 [263]P42(a1)
% 1.87/2.00 [264]P42(a37)
% 1.87/2.00 [265]P42(a11)
% 1.87/2.00 [266]P42(a35)
% 1.87/2.00 [267]P61(a36)
% 1.87/2.00 [268]P61(a1)
% 1.87/2.00 [269]P62(a36)
% 1.87/2.00 [270]P62(a1)
% 1.87/2.00 [271]P13(a36)
% 1.87/2.00 [272]P13(a1)
% 1.87/2.00 [273]P13(a37)
% 1.87/2.00 [274]P13(a11)
% 1.87/2.00 [275]P13(a34)
% 1.87/2.00 [276]P15(a36)
% 1.87/2.00 [277]P15(a1)
% 1.87/2.00 [278]P15(a37)
% 1.87/2.00 [279]P15(a11)
% 1.87/2.00 [280]P15(a34)
% 1.87/2.00 [281]P16(a36)
% 1.87/2.00 [282]P16(a1)
% 1.87/2.00 [283]P16(a37)
% 1.87/2.00 [284]P16(a11)
% 1.87/2.00 [285]P16(a34)
% 1.87/2.00 [286]P18(a36)
% 1.87/2.00 [287]P18(a1)
% 1.87/2.00 [288]P18(a37)
% 1.87/2.00 [289]P18(a11)
% 1.87/2.00 [290]P18(a34)
% 1.87/2.00 [291]P20(a36)
% 1.87/2.00 [292]P20(a1)
% 1.87/2.00 [293]P20(a37)
% 1.87/2.00 [294]P20(a11)
% 1.87/2.00 [295]P20(a34)
% 1.87/2.00 [296]P21(a36)
% 1.87/2.00 [297]P21(a1)
% 1.87/2.00 [298]P76(a36)
% 1.87/2.00 [299]P76(a1)
% 1.87/2.00 [300]P76(a37)
% 1.87/2.00 [301]P76(a34)
% 1.87/2.00 [302]P26(a36)
% 1.87/2.00 [303]P26(a1)
% 1.87/2.00 [304]P26(a37)
% 1.87/2.00 [305]P26(a11)
% 1.87/2.00 [306]P27(a36)
% 1.87/2.00 [307]P27(a1)
% 1.87/2.00 [308]P27(a37)
% 1.87/2.00 [309]P27(a11)
% 1.87/2.00 [310]P30(a36)
% 1.87/2.00 [311]P30(a1)
% 1.87/2.00 [312]P30(a37)
% 1.87/2.00 [313]P30(a11)
% 1.87/2.00 [314]P46(a36)
% 1.87/2.00 [315]P46(a1)
% 1.87/2.00 [316]P46(a37)
% 1.87/2.00 [317]P46(a11)
% 1.87/2.00 [318]P46(a34)
% 1.87/2.00 [319]P73(a36)
% 1.87/2.00 [320]P73(a1)
% 1.87/2.00 [321]P73(a37)
% 1.87/2.00 [322]P73(a11)
% 1.87/2.00 [323]P73(a34)
% 1.87/2.00 [324]P47(a36)
% 1.87/2.00 [325]P47(a34)
% 1.87/2.00 [326]P31(a36)
% 1.87/2.00 [327]P31(a1)
% 1.87/2.00 [328]P44(a36)
% 1.87/2.00 [329]P44(a34)
% 1.87/2.00 [330]P45(a36)
% 1.87/2.00 [331]P45(a34)
% 1.87/2.00 [332]P32(a36)
% 1.87/2.00 [333]P32(a1)
% 1.87/2.00 [334]P32(a37)
% 1.87/2.00 [335]P32(a11)
% 1.87/2.00 [336]P36(a36)
% 1.87/2.00 [337]P36(a1)
% 1.87/2.00 [338]P36(a37)
% 1.87/2.00 [339]P36(a11)
% 1.87/2.00 [340]P36(a34)
% 1.87/2.00 [341]P37(a36)
% 1.87/2.00 [342]P37(a1)
% 1.87/2.00 [343]P37(a34)
% 1.87/2.00 [344]P38(a36)
% 1.87/2.00 [345]P38(a1)
% 1.87/2.00 [346]P38(a34)
% 1.87/2.00 [347]P77(a36)
% 1.87/2.00 [348]P77(a34)
% 1.87/2.00 [349]P22(a36)
% 1.87/2.00 [350]P22(a1)
% 1.87/2.00 [351]P22(a34)
% 1.87/2.00 [352]P28(a36)
% 1.87/2.00 [353]P28(a1)
% 1.87/2.00 [354]P39(a35)
% 1.87/2.00 [355]P54(a36)
% 1.87/2.00 [356]P54(a1)
% 1.87/2.00 [357]P54(a34)
% 1.87/2.00 [358]P69(a36)
% 1.87/2.00 [359]P69(a1)
% 1.87/2.00 [360]P69(a34)
% 1.87/2.00 [361]P14(a36)
% 1.87/2.00 [362]P14(a1)
% 1.87/2.00 [363]P14(a34)
% 1.87/2.00 [364]P33(a36)
% 1.87/2.00 [365]P33(a1)
% 1.87/2.00 [366]P33(a34)
% 1.87/2.00 [367]P33(a35)
% 1.87/2.00 [368]P48(a36)
% 1.87/2.00 [369]P48(a1)
% 1.87/2.00 [370]P48(a34)
% 1.87/2.00 [371]P70(a36)
% 1.87/2.00 [372]P70(a1)
% 1.87/2.00 [373]P70(a34)
% 1.87/2.00 [374]P74(a36)
% 1.87/2.00 [375]P74(a1)
% 1.87/2.00 [376]P74(a37)
% 1.87/2.00 [377]P74(a11)
% 1.87/2.00 [378]P74(a34)
% 1.87/2.00 [379]P43(a36)
% 1.87/2.00 [380]P43(a1)
% 1.87/2.00 [381]P43(a37)
% 1.87/2.00 [382]P43(a11)
% 1.87/2.00 [383]P43(a34)
% 1.87/2.00 [384]P75(a36)
% 1.87/2.00 [385]P75(a1)
% 1.87/2.00 [386]P75(a37)
% 1.87/2.00 [387]P75(a11)
% 1.87/2.00 [388]P75(a34)
% 1.87/2.00 [389]P71(a36)
% 1.87/2.00 [390]P71(a1)
% 1.87/2.00 [391]P71(a34)
% 1.87/2.00 [392]P68(a36)
% 1.87/2.00 [393]P68(a1)
% 1.87/2.00 [394]P29(a36)
% 1.87/2.00 [395]P29(a1)
% 1.87/2.00 [396]P17(a36)
% 1.87/2.00 [397]P17(a1)
% 1.87/2.00 [545]~P6(a1,a10,a10)
% 1.87/2.00 [149]E(f2(a1),a10)
% 1.87/2.00 [398]E(f3(a1,a10),a10)
% 1.87/2.00 [400]E(f12(a1,a10),f2(a1))
% 1.87/2.00 [402]E(f12(a11,a10),f2(a11))
% 1.87/2.00 [403]E(f12(a37,a10),f2(a37))
% 1.87/2.00 [427]P6(a36,a38,f4(a36))
% 1.87/2.00 [428]P6(a36,a39,f4(a36))
% 1.87/2.00 [429]P6(a36,a22,f4(a36))
% 1.87/2.00 [430]P6(a36,a27,f4(a36))
% 1.87/2.00 [431]P6(a36,f2(a36),a41)
% 1.87/2.00 [432]P6(a36,f2(a36),a38)
% 1.87/2.00 [433]P6(a36,f2(a36),a42)
% 1.87/2.00 [434]P6(a36,f2(a36),a39)
% 1.87/2.00 [435]P6(a36,f2(a36),a22)
% 1.87/2.00 [436]P6(a36,f2(a36),a27)
% 1.87/2.00 [437]P5(a36,f2(a36),a38)
% 1.87/2.00 [444]P6(a36,f2(a36),f4(a36))
% 1.87/2.00 [445]P6(a1,f2(a1),f4(a1))
% 1.87/2.00 [447]P5(a1,f2(a1),f4(a1))
% 1.87/2.00 [456]P5(a1,f2(a1),f12(a1,a10))
% 1.87/2.00 [468]P6(a36,a38,f18(a36,a42,a41))
% 1.87/2.00 [469]P6(a36,a39,f18(a36,a42,a41))
% 1.87/2.00 [470]P6(a36,a22,f18(a36,a42,a41))
% 1.87/2.00 [471]P6(a36,a27,f18(a36,a42,a41))
% 1.87/2.00 [472]P6(a36,f2(a36),f18(a36,a42,a41))
% 1.87/2.00 [543]~E(f4(a36),f2(a36))
% 1.87/2.00 [544]~E(f4(a1),f2(a1))
% 1.87/2.00 [548]~P6(a1,a10,f2(a1))
% 1.87/2.00 [404]E(f21(a13,f4(a36)),f2(a36))
% 1.87/2.00 [405]E(f21(a14,f2(a36)),f2(a36))
% 1.87/2.00 [406]E(f21(a14,f4(a36)),f4(a36))
% 1.87/2.00 [407]E(f21(a16,f2(a36)),f2(a36))
% 1.87/2.00 [408]E(f17(a36,f2(a36)),f2(a36))
% 1.87/2.00 [409]E(f3(a1,f2(a1)),f2(a1))
% 1.87/2.00 [465]P6(a36,f21(f7(a36,a39),a41),a42)
% 1.87/2.00 [466]P6(a36,f2(a36),f21(f7(a36,a39),a41))
% 1.87/2.00 [479]E(f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,a10,f4(a1)))
% 1.87/2.00 [554]~P6(a36,f21(f7(a36,a38),a41),a42)
% 1.87/2.00 [496]E(f12(a1,f8(a1,f8(a1,a10,a10),f4(a1))),f4(a1))
% 1.87/2.00 [498]E(f12(a11,f8(a1,f8(a1,a10,a10),f4(a1))),f4(a11))
% 1.87/2.00 [499]E(f12(a37,f8(a1,f8(a1,a10,a10),f4(a1))),f4(a37))
% 1.87/2.00 [529]P5(a1,f2(a1),f12(a1,f8(a1,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))),f4(a1))))
% 1.87/2.00 [519]E(f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))),f8(a37,f4(a37),f4(a37)))
% 1.87/2.00 [520]P6(a37,f2(a37),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))
% 1.87/2.00 [521]P5(a1,f2(a1),f12(a1,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))
% 1.87/2.00 [524]P6(a36,f2(a36),f21(a14,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.00 [525]P6(a36,f4(a36),f21(a14,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.00 [526]P5(a36,f2(a36),f21(a14,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.00 [424]P5(a36,x4241,x4241)
% 1.87/2.00 [425]P5(a1,x4251,x4251)
% 1.87/2.00 [426]P5(a37,x4261,x4261)
% 1.87/2.00 [547]~P6(a37,x5471,x5471)
% 1.87/2.00 [399]E(f12(a1,x3991),x3991)
% 1.87/2.00 [422]E(f8(a1,x4221,a10),x4221)
% 1.87/2.00 [423]E(f8(a1,a10,x4231),x4231)
% 1.87/2.00 [439]P5(a37,f2(a37),x4391)
% 1.87/2.00 [551]~P6(a37,x5511,f2(a37))
% 1.87/2.00 [410]E(f21(f7(a1,a10),x4101),a10)
% 1.87/2.00 [411]E(f3(a1,f3(a1,x4111)),x4111)
% 1.87/2.00 [412]E(f21(f7(a1,x4121),f4(a1)),x4121)
% 1.87/2.00 [413]E(f21(f7(a37,x4131),f4(a37)),x4131)
% 1.87/2.00 [414]E(f21(f7(a37,x4141),f2(a37)),f2(a37))
% 1.87/2.00 [440]E(f8(a1,x4401,f2(a1)),x4401)
% 1.87/2.00 [441]E(f8(a37,x4411,f2(a37)),x4411)
% 1.87/2.00 [442]E(f8(a1,f2(a1),x4421),x4421)
% 1.87/2.00 [443]E(f8(a37,f2(a37),x4431),x4431)
% 1.87/2.00 [448]E(f8(a1,f15(x4481),f4(a1)),x4481)
% 1.87/2.00 [449]E(f17(a36,f21(a14,x4491)),f21(a14,f17(a36,x4491)))
% 1.87/2.00 [450]E(f21(a14,f3(a36,x4501)),f3(a36,f21(a14,x4501)))
% 1.87/2.00 [451]E(f21(a16,f3(a36,x4511)),f3(a36,f21(a16,x4511)))
% 1.87/2.00 [452]E(f3(a1,f12(a1,x4521)),f12(a1,f3(a1,x4521)))
% 1.87/2.00 [457]E(f8(a1,f3(a1,x4571),x4571),f2(a1))
% 1.87/2.00 [458]E(f18(a36,x4581,f5(a36,x4581)),f9(a36,x4581))
% 1.87/2.00 [459]P6(a36,f2(a36),f21(f20(a36),x4591))
% 1.87/2.00 [460]P5(a36,f2(a36),f21(f20(a36),x4601))
% 1.87/2.00 [467]P5(a37,x4671,f21(f7(a37,x4671),x4671))
% 1.87/2.00 [491]E(f8(a1,f8(a1,f15(x4911),f15(x4911)),f4(a1)),f15(f8(a1,x4911,x4911)))
% 1.87/2.00 [552]~P6(a36,f21(f20(a36),x5521),f2(a36))
% 1.87/2.00 [553]~P5(a36,f21(f20(a36),x5531),f2(a36))
% 1.87/2.00 [558]~E(f8(a1,f8(a1,x5581,x5581),f4(a1)),a10)
% 1.87/2.00 [415]E(f21(f7(a36,f4(a36)),x4151),x4151)
% 1.87/2.00 [416]E(f21(f7(a1,f4(a1)),x4161),x4161)
% 1.87/2.00 [417]E(f21(f7(a37,f4(a37)),x4171),x4171)
% 1.87/2.00 [418]E(f21(a13,f21(f20(a36),x4181)),x4181)
% 1.87/2.00 [419]E(f21(f7(a37,f2(a37)),x4191),f2(a37))
% 1.87/2.00 [485]P5(a37,x4851,f21(f7(a37,x4851),f21(f7(a37,x4851),x4851)))
% 1.87/2.00 [500]E(f8(a1,f8(a1,x5001,x5001),f4(a1)),f8(a1,f8(a1,f4(a1),x5001),x5001))
% 1.87/2.00 [503]E(f15(f8(a1,f8(a1,x5031,x5031),f4(a1))),f8(a1,x5031,x5031))
% 1.87/2.00 [510]E(f8(a1,f8(a1,f8(a1,x5101,x5101),f4(a1)),f4(a1)),f8(a1,f8(a1,x5101,f4(a1)),f8(a1,x5101,f4(a1))))
% 1.87/2.00 [511]E(f8(a1,f8(a1,f15(f3(a1,x5111)),f15(f3(a1,x5111))),f4(a1)),f3(a1,f8(a1,f8(a1,x5111,x5111),f4(a1))))
% 1.87/2.00 [559]~E(f8(a1,f8(a1,f4(a1),x5591),x5591),f2(a1))
% 1.87/2.00 [522]E(f19(a34,f6(x5221),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x5221)
% 1.87/2.00 [523]E(f21(f7(a37,x5231),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f8(a37,x5231,x5231))
% 1.87/2.00 [528]P5(a36,f4(a36),f19(a36,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))),x5281))
% 1.87/2.00 [527]E(f21(f7(a37,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x5271),f8(a37,x5271,x5271))
% 1.87/2.00 [530]E(f8(a36,f18(a36,x5301,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f18(a36,x5301,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),x5301)
% 1.87/2.00 [533]E(f21(f7(a36,f12(a36,f8(a1,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))),f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f19(a36,x5331,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f19(a36,f21(f7(a36,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x5331),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.00 [532]P7(a36,a16,x5321,f17(a36,f8(a36,f4(a36),f19(a36,x5321,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))))
% 1.87/2.00 [539]E(f21(f7(a36,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f21(a16,f18(a36,x5391,f8(a36,f4(a36),f21(a14,f8(a36,f4(a36),f19(a36,x5391,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))))))),f21(a16,x5391))
% 1.87/2.00 [461]E(f8(a1,x4611,x4612),f8(a1,x4612,x4611))
% 1.87/2.00 [462]E(f8(a37,x4621,x4622),f8(a37,x4622,x4621))
% 1.87/2.00 [473]P5(a37,x4731,f8(a37,x4732,x4731))
% 1.87/2.00 [474]P5(a37,x4741,f8(a37,x4741,x4742))
% 1.87/2.00 [555]~P6(a37,f8(a37,x5551,x5552),x5552)
% 1.87/2.00 [556]~P6(a37,f8(a37,x5561,x5562),x5561)
% 1.87/2.00 [453]E(f21(f7(a36,x4531),x4532),f21(f7(a36,x4532),x4531))
% 1.87/2.00 [454]E(f21(f7(a1,x4541),x4542),f21(f7(a1,x4542),x4541))
% 1.87/2.00 [455]E(f21(f7(a37,x4551),x4552),f21(f7(a37,x4552),x4551))
% 1.87/2.00 [464]E(f21(f7(a36,x4641),f17(a36,x4642)),f18(a36,x4641,x4642))
% 1.87/2.00 [478]E(f19(a36,f21(a14,x4781),x4782),f21(a14,f19(a36,x4781,x4782)))
% 1.87/2.00 [480]E(f18(a36,f21(a14,x4801),f21(a14,x4802)),f21(a14,f18(a36,x4801,x4802)))
% 1.87/2.00 [481]E(f8(a1,f3(a1,x4811),f3(a1,x4812)),f3(a1,f8(a1,x4811,x4812)))
% 1.87/2.00 [483]E(f8(a1,f12(a1,x4831),f12(a1,x4832)),f12(a1,f8(a1,x4831,x4832)))
% 1.87/2.00 [509]E(f8(a1,f8(a1,x5091,x5091),f8(a1,x5092,x5092)),f8(a1,f8(a1,x5091,x5092),f8(a1,x5091,x5092)))
% 1.87/2.00 [516]E(f8(a1,f8(a1,f8(a1,x5161,x5162),f8(a1,x5161,x5162)),f4(a1)),f8(a1,f8(a1,f8(a1,x5161,x5161),f4(a1)),f8(a1,x5162,x5162)))
% 1.87/2.00 [561]~E(f8(a1,x5611,x5611),f8(a1,f8(a1,x5612,x5612),f4(a1)))
% 1.87/2.00 [475]E(f21(f7(a1,f3(a1,x4751)),x4752),f3(a1,f21(f7(a1,x4751),x4752)))
% 1.87/2.00 [476]E(f21(f7(a36,f21(a14,x4761)),f21(a14,x4762)),f21(a14,f21(f7(a36,x4761),x4762)))
% 1.87/2.00 [477]E(f21(f7(a1,f12(a1,x4771)),f12(a1,x4772)),f12(a1,f21(f7(a1,x4771),x4772)))
% 1.87/2.00 [484]E(f18(a36,f21(f7(a36,x4841),x4842),f21(f7(a36,x4841),x4841)),f18(a36,x4842,x4841))
% 1.87/2.00 [490]P5(a36,f3(a36,f21(f7(a36,x4901),x4901)),f21(f7(a36,x4902),x4902))
% 1.87/2.00 [515]E(f8(a1,f8(a1,f8(a1,x5151,x5152),f8(a1,x5151,x5152)),f4(a1)),f8(a1,f8(a1,x5151,x5151),f8(a1,f8(a1,x5152,x5152),f4(a1))))
% 1.87/2.00 [512]P5(a36,x5121,f21(a14,f8(a36,f21(f7(a36,x5121),x5121),f21(f7(a36,x5122),x5122))))
% 1.87/2.00 [513]P5(a36,f2(a36),f21(a14,f8(a36,f21(f7(a36,x5131),x5131),f21(f7(a36,x5132),x5132))))
% 1.87/2.00 [517]E(f8(a1,f8(a1,f21(f7(a1,x5171),x5172),f21(f7(a1,x5171),x5172)),x5172),f21(f7(a1,f8(a1,f8(a1,x5171,x5171),f4(a1))),x5172))
% 1.87/2.00 [518]E(f8(a1,f8(a1,f8(a1,x5181,x5181),f4(a1)),f8(a1,f8(a1,x5182,x5182),f4(a1))),f8(a1,f8(a1,x5181,f8(a1,x5182,f4(a1))),f8(a1,x5181,f8(a1,x5182,f4(a1)))))
% 1.87/2.00 [531]P5(a36,f3(a36,f19(a36,x5311,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f19(a36,x5312,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.00 [534]P5(a36,x5341,f21(a14,f8(a36,f19(a36,x5342,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5341,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))))
% 1.87/2.00 [535]P5(a36,x5351,f21(a14,f8(a36,f19(a36,x5351,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5352,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))))
% 1.87/2.00 [536]P5(a36,f2(a36),f21(a14,f8(a36,f19(a36,x5361,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5362,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))))
% 1.87/2.00 [537]E(f8(a36,f8(a36,f19(a36,x5371,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5372,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f21(f7(a36,f21(f7(a36,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x5371)),x5372)),f19(a36,f8(a36,x5371,x5372),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.00 [538]P5(a36,f5(a36,f18(a36,x5381,f21(a14,f8(a36,f19(a36,x5381,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5382,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))))),f4(a36))
% 1.87/2.00 [492]E(f8(a1,x4921,f8(a1,x4922,x4923)),f8(a1,x4922,f8(a1,x4921,x4923)))
% 1.87/2.00 [493]E(f8(a37,x4931,f8(a37,x4932,x4933)),f8(a37,x4932,f8(a37,x4931,x4933)))
% 1.87/2.00 [494]E(f8(a1,f8(a1,x4941,x4942),x4943),f8(a1,x4941,f8(a1,x4942,x4943)))
% 1.87/2.00 [495]E(f8(a37,f8(a37,x4951,x4952),x4953),f8(a37,x4951,f8(a37,x4952,x4953)))
% 1.87/2.00 [508]E(f21(f7(a1,f19(a1,x5081,x5082)),f19(a1,x5081,x5083)),f19(a1,x5081,f8(a37,x5082,x5083)))
% 1.87/2.00 [486]E(f19(a1,x4861,f21(f7(a37,x4862),x4863)),f19(a1,f19(a1,x4861,x4862),x4863))
% 1.87/2.00 [501]E(f8(a1,f21(f7(a1,x5011),x5012),f21(f7(a1,x5011),x5013)),f21(f7(a1,x5011),f8(a1,x5012,x5013)))
% 1.87/2.00 [502]E(f8(a37,f21(f7(a37,x5021),x5022),f21(f7(a37,x5021),x5023)),f21(f7(a37,x5021),f8(a37,x5022,x5023)))
% 1.87/2.00 [504]E(f8(a36,f21(f7(a36,x5041),x5042),f21(f7(a36,x5043),x5042)),f21(f7(a36,f8(a36,x5041,x5043)),x5042))
% 1.87/2.00 [505]E(f8(a1,f21(f7(a1,x5051),x5052),f21(f7(a1,x5053),x5052)),f21(f7(a1,f8(a1,x5051,x5053)),x5052))
% 1.87/2.00 [507]E(f8(a37,f21(f7(a37,x5071),x5072),f21(f7(a37,x5073),x5072)),f21(f7(a37,f8(a37,x5071,x5073)),x5072))
% 1.87/2.00 [487]E(f21(f7(a36,f21(f7(a36,x4871),x4872)),x4873),f21(f7(a36,x4871),f21(f7(a36,x4872),x4873)))
% 1.87/2.00 [488]E(f21(f7(a1,f21(f7(a1,x4881),x4882)),x4883),f21(f7(a1,x4881),f21(f7(a1,x4882),x4883)))
% 1.87/2.00 [489]E(f21(f7(a37,f21(f7(a37,x4891),x4892)),x4893),f21(f7(a37,x4891),f21(f7(a37,x4892),x4893)))
% 1.87/2.00 [514]E(f8(a37,f21(f7(a37,x5141),x5142),f8(a37,f21(f7(a37,x5143),x5142),x5144)),f8(a37,f21(f7(a37,f8(a37,x5141,x5143)),x5142),x5144))
% 1.87/2.00 [542]E(f19(a36,f21(a14,f21(f7(a36,f8(a36,f19(a36,x5421,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5422,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),f8(a36,f19(a36,x5423,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5424,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f21(f7(a36,f8(a36,f19(a36,x5421,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5422,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),f8(a36,f19(a36,x5423,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5424,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))))
% 1.87/2.00 [540]P5(a36,f21(a14,f8(a36,f19(a36,f8(a36,x5401,x5402),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,f8(a36,x5403,x5404),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),f8(a36,f21(a14,f8(a36,f19(a36,x5401,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5403,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),f21(a14,f8(a36,f19(a36,x5402,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5404,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))))
% 1.87/2.00 [541]P5(a36,f2(a36),f21(a14,f21(f7(a36,f8(a36,f19(a36,x5411,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5412,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),f8(a36,f19(a36,x5413,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x5414,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))))
% 1.87/2.00 [563]~P72(x5631)+~E(f4(x5631),f2(x5631))
% 1.87/2.00 [564]~E(x5641,f2(a36))+E(f21(a14,x5641),f2(a36))
% 1.87/2.00 [565]~E(x5651,f4(a36))+E(f21(a14,x5651),f4(a36))
% 1.87/2.00 [567]~E(x5671,f2(a36))+E(f9(a36,x5671),f2(a36))
% 1.87/2.00 [568]~E(x5681,f2(a1))+E(f9(a1,x5681),f2(a1))
% 1.87/2.00 [570]~P37(x5701)+E(f12(x5701,a10),f2(x5701))
% 1.87/2.00 [572]~P74(x5721)+P8(x5721,f2(x5721))
% 1.87/2.00 [573]E(x5731,f2(a36))+~E(f21(a14,x5731),f2(a36))
% 1.87/2.00 [574]E(x5741,f4(a36))+~E(f21(a14,x5741),f4(a36))
% 1.87/2.00 [602]~P74(x6021)+~P8(x6021,f4(x6021))
% 1.87/2.00 [614]~P37(x6141)+P8(x6141,f12(x6141,a10))
% 1.87/2.00 [638]~E(a10,x6381)+E(f8(a1,x6381,x6381),a10)
% 1.87/2.00 [639]~E(x6391,a10)+E(f8(a1,x6391,x6391),a10)
% 1.87/2.00 [653]E(x6531,f2(a37))+P6(a37,f2(a37),x6531)
% 1.87/2.00 [695]~P51(x6951)+P6(x6951,f2(x6951),f4(x6951))
% 1.87/2.00 [696]~P51(x6961)+P5(x6961,f2(x6961),f4(x6961))
% 1.87/2.00 [702]P5(a1,x7021,a10)+~E(f12(a37,x7021),f2(a37))
% 1.87/2.00 [719]E(x7191,a10)+~E(f8(a1,x7191,x7191),a10)
% 1.87/2.00 [720]E(a10,x7201)+~E(f8(a1,x7201,x7201),a10)
% 1.87/2.00 [751]E(x7511,f2(a37))+~P5(a37,x7511,f2(a37))
% 1.87/2.00 [757]~P5(a1,x7571,a10)+E(f12(a37,x7571),f2(a37))
% 1.87/2.00 [770]~P6(a36,f2(a36),x7701)+E(f9(a36,x7701),f4(a36))
% 1.87/2.00 [791]~P51(x7911)+~P6(x7911,f4(x7911),f2(x7911))
% 1.87/2.00 [792]~P51(x7921)+~P5(x7921,f4(x7921),f2(x7921))
% 1.87/2.00 [793]~P6(a36,f2(a36),x7931)+~E(f21(a14,x7931),f2(a36))
% 1.87/2.00 [880]~P5(a1,f4(a1),x8801)+P6(a1,f2(a1),x8801)
% 1.87/2.00 [881]~P6(a1,f2(a1),x8811)+P5(a1,f4(a1),x8811)
% 1.87/2.00 [905]~P6(a1,a10,x9051)+P6(a37,f2(a37),f12(a37,x9051))
% 1.87/2.00 [911]P6(a36,f21(a13,x9111),x9111)+~P6(a36,f2(a36),x9111)
% 1.87/2.00 [921]~P6(a36,f4(a36),x9211)+P6(a36,f2(a36),f21(a13,x9211))
% 1.87/2.00 [923]~P6(a36,f2(a36),x9231)+P6(a36,f2(a36),f21(a14,x9231))
% 1.87/2.00 [924]~P6(a36,f4(a36),x9241)+P6(a36,f4(a36),f21(a14,x9241))
% 1.87/2.00 [925]~P5(a36,f4(a36),x9251)+P5(a36,f2(a36),f21(a13,x9251))
% 1.87/2.00 [927]~P5(a36,f2(a36),x9271)+P5(a36,f2(a36),f21(a14,x9271))
% 1.87/2.00 [929]~P5(a36,f4(a36),x9291)+P5(a36,f4(a36),f21(a14,x9291))
% 1.87/2.00 [930]~P6(a36,x9301,f2(a36))+P6(a36,f21(a14,x9301),f2(a36))
% 1.87/2.00 [931]~P6(a36,x9311,f4(a36))+P6(a36,f21(a14,x9311),f4(a36))
% 1.87/2.00 [932]~P5(a36,x9321,f2(a36))+P5(a36,f21(a14,x9321),f2(a36))
% 1.87/2.00 [933]~P5(a36,x9331,f4(a36))+P5(a36,f21(a14,x9331),f4(a36))
% 1.87/2.00 [942]P6(a1,a10,x9421)+~P6(a37,f2(a37),f12(a37,x9421))
% 1.87/2.00 [968]P6(a36,x9681,f2(a36))+~P6(a36,f21(a14,x9681),f2(a36))
% 1.87/2.00 [969]P6(a36,x9691,f4(a36))+~P6(a36,f21(a14,x9691),f4(a36))
% 1.87/2.00 [970]P5(a36,x9701,f2(a36))+~P5(a36,f21(a14,x9701),f2(a36))
% 1.87/2.00 [971]P5(a36,x9711,f4(a36))+~P5(a36,f21(a14,x9711),f4(a36))
% 1.87/2.00 [972]P6(a36,f2(a36),x9721)+~P6(a36,f2(a36),f21(a14,x9721))
% 1.87/2.00 [973]P6(a36,f4(a36),x9731)+~P6(a36,f4(a36),f21(a14,x9731))
% 1.87/2.00 [974]P5(a36,f2(a36),x9741)+~P5(a36,f2(a36),f21(a14,x9741))
% 1.87/2.00 [975]P5(a36,f4(a36),x9751)+~P5(a36,f4(a36),f21(a14,x9751))
% 1.87/2.00 [1133]~P6(a1,a10,x11331)+P6(a1,a10,f8(a1,x11331,x11331))
% 1.87/2.00 [1134]~P5(a1,a10,x11341)+P5(a1,a10,f8(a1,x11341,x11341))
% 1.87/2.00 [1135]~P6(a1,x11351,a10)+P6(a1,f8(a1,x11351,x11351),a10)
% 1.87/2.00 [1136]~P5(a1,x11361,a10)+P5(a1,f8(a1,x11361,x11361),a10)
% 1.87/2.00 [1164]~P6(a1,x11641,f2(a1))+P6(a1,f8(a1,x11641,x11641),f2(a1))
% 1.87/2.00 [1229]P6(a1,x12291,a10)+~P6(a1,f8(a1,x12291,x12291),a10)
% 1.87/2.00 [1230]P5(a1,x12301,a10)+~P5(a1,f8(a1,x12301,x12301),a10)
% 1.87/2.00 [1231]P6(a1,a10,x12311)+~P6(a1,a10,f8(a1,x12311,x12311))
% 1.87/2.00 [1232]P5(a1,a10,x12321)+~P5(a1,a10,f8(a1,x12321,x12321))
% 1.87/2.00 [1247]P6(a1,x12471,f2(a1))+~P6(a1,f8(a1,x12471,x12471),f2(a1))
% 1.87/2.00 [1333]P7(a36,a13,x13331,f17(a36,x13331))+~P6(a36,f2(a36),x13331)
% 1.87/2.00 [571]~E(x5711,f2(a36))+E(f21(f20(a36),x5711),f4(a36))
% 1.87/2.00 [578]~P3(x5781)+E(f17(x5781,f2(x5781)),f2(x5781))
% 1.87/2.00 [579]~P50(x5791)+E(f17(x5791,f2(x5791)),f2(x5791))
% 1.87/2.00 [580]~P49(x5801)+E(f17(x5801,f4(x5801)),f4(x5801))
% 1.87/2.00 [581]~P47(x5811)+E(f9(x5811,f2(x5811)),f2(x5811))
% 1.87/2.00 [582]~P31(x5821)+E(f9(x5821,f2(x5821)),f2(x5821))
% 1.87/2.00 [583]~P45(x5831)+E(f9(x5831,f4(x5831)),f4(x5831))
% 1.87/2.00 [584]~P22(x5841)+E(f3(x5841,f2(x5841)),f2(x5841))
% 1.87/2.00 [585]~P52(x5851)+E(f5(x5851,f4(x5851)),f4(x5851))
% 1.87/2.00 [593]E(x5931,f2(a36))+~E(f21(f20(a36),x5931),f4(a36))
% 1.87/2.00 [819]P6(a36,f2(a36),x8191)+~E(f21(f20(a36),f21(a13,x8191)),x8191)
% 1.87/2.00 [837]~P6(a36,f2(a36),x8371)+E(f21(f20(a36),f21(a13,x8371)),x8371)
% 1.87/2.00 [841]E(x8411,f2(a36))+P6(a36,f2(a36),f21(f7(a36,x8411),x8411))
% 1.87/2.00 [904]~P6(a36,f2(a36),x9041)+E(f21(a13,f17(a36,x9041)),f3(a36,f21(a13,x9041)))
% 1.87/2.00 [907]~P6(a1,x9071,a10)+E(f8(a37,f4(a37),f12(a37,x9071)),f4(a37))
% 1.87/2.00 [908]~P6(a1,x9081,a10)+E(f8(a37,f12(a37,x9081),f4(a37)),f4(a37))
% 1.87/2.00 [946]~P6(a36,f2(a36),x9461)+P6(a36,f4(a36),f21(f20(a36),x9461))
% 1.87/2.00 [947]~P5(a36,f2(a36),x9471)+P5(a36,f4(a36),f21(f20(a36),x9471))
% 1.87/2.00 [948]~P6(a36,x9481,f2(a36))+P6(a36,f21(f20(a36),x9481),f4(a36))
% 1.87/2.00 [949]~P5(a36,x9491,f2(a36))+P5(a36,f21(f20(a36),x9491),f4(a36))
% 1.87/2.00 [1025]P6(a36,x10251,f2(a36))+~P6(a36,f21(f20(a36),x10251),f4(a36))
% 1.87/2.00 [1026]P5(a36,x10261,f2(a36))+~P5(a36,f21(f20(a36),x10261),f4(a36))
% 1.87/2.00 [1027]P6(a36,f2(a36),x10271)+~P6(a36,f4(a36),f21(f20(a36),x10271))
% 1.87/2.00 [1028]P5(a36,f2(a36),x10281)+~P5(a36,f4(a36),f21(f20(a36),x10281))
% 1.87/2.00 [1030]~P51(x10301)+P6(x10301,f2(x10301),f8(x10301,f4(x10301),f4(x10301)))
% 1.87/2.00 [1031]~P5(a36,f2(a36),x10311)+E(f18(a36,f21(a14,x10311),x10311),f17(a36,f21(a14,x10311)))
% 1.87/2.00 [1062]~E(x10621,f2(a36))+~P6(a36,f2(a36),f21(f7(a36,x10621),x10621))
% 1.87/2.00 [1170]~P5(a1,f2(a1),x11701)+P6(a1,f2(a1),f8(a1,f4(a1),x11701))
% 1.87/2.00 [1211]~P5(a36,f2(a36),x12111)+P5(a36,f8(a36,f4(a36),x12111),f21(f20(a36),x12111))
% 1.87/2.00 [1450]~P5(a1,f2(a1),f12(a1,x14501))+P5(a1,f2(a1),f12(a1,f8(a1,x14501,x14501)))
% 1.87/2.00 [1467]~P6(a36,f2(a36),x14671)+P7(a36,a13,x14671,f18(a36,f4(a36),x14671))
% 1.87/2.00 [1479]~P5(a1,a10,x14791)+P6(a1,a10,f8(a1,f8(a1,x14791,x14791),f4(a1)))
% 1.87/2.00 [1480]~P5(a1,a10,x14801)+P5(a1,a10,f8(a1,f8(a1,x14801,x14801),f4(a1)))
% 1.87/2.00 [1481]~P6(a1,x14811,a10)+P6(a1,f8(a1,f8(a1,x14811,x14811),f4(a1)),a10)
% 1.87/2.00 [1482]~P6(a1,x14821,a10)+P5(a1,f8(a1,f8(a1,x14821,x14821),f4(a1)),a10)
% 1.87/2.00 [1512]~P6(a1,x15121,f2(a1))+P6(a1,f8(a1,f8(a1,x15121,x15121),f4(a1)),f2(a1))
% 1.87/2.00 [1653]P6(a1,x16531,a10)+~P6(a1,f8(a1,f8(a1,x16531,x16531),f4(a1)),a10)
% 1.87/2.00 [1654]P6(a1,x16541,a10)+~P5(a1,f8(a1,f8(a1,x16541,x16541),f4(a1)),a10)
% 1.87/2.00 [1655]P5(a1,a10,x16551)+~P6(a1,a10,f8(a1,f8(a1,x16551,x16551),f4(a1)))
% 1.87/2.00 [1656]P5(a1,a10,x16561)+~P5(a1,a10,f8(a1,f8(a1,x16561,x16561),f4(a1)))
% 1.87/2.00 [1666]P6(a1,x16661,f2(a1))+~P6(a1,f8(a1,f8(a1,x16661,x16661),f4(a1)),f2(a1))
% 1.87/2.00 [741]E(x7411,f2(a36))+E(f21(f7(a36,f17(a36,x7411)),x7411),f4(a36))
% 1.87/2.00 [1168]P6(a1,x11681,a10)+E(f8(a37,f4(a37),f12(a37,x11681)),f12(a37,f8(a1,x11681,f4(a1))))
% 1.87/2.00 [1169]P6(a1,x11691,a10)+E(f8(a37,f12(a37,x11691),f4(a37)),f12(a37,f8(a1,x11691,f4(a1))))
% 1.87/2.00 [1275]~P37(x12751)+E(f12(x12751,f8(a1,f8(a1,a10,a10),f4(a1))),f4(x12751))
% 1.87/2.00 [1399]~P5(a36,f2(a36),x13991)+P5(a36,f21(a13,f8(a36,f4(a36),x13991)),x13991)
% 1.87/2.00 [1519]~P6(a1,x15191,f2(a1))+P6(a1,f8(a1,f8(a1,f4(a1),x15191),x15191),f2(a1))
% 1.87/2.00 [1669]P6(a1,x16691,f2(a1))+~P6(a1,f8(a1,f8(a1,f4(a1),x16691),x16691),f2(a1))
% 1.87/2.00 [1763]~P5(a1,f2(a1),f12(a1,x17631))+P5(a1,f2(a1),f12(a1,f8(a1,f8(a1,x17631,x17631),f4(a1))))
% 1.87/2.00 [1780]~P37(x17801)+~P8(x17801,f12(x17801,f8(a1,f8(a1,a10,a10),f4(a1))))
% 1.87/2.00 [1802]~P37(x18021)+E(f8(x18021,f4(x18021),f4(x18021)),f12(x18021,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))
% 1.87/2.00 [1806]~P74(x18061)+E(f19(x18061,f2(x18061),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f2(x18061))
% 1.87/2.00 [1807]~P74(x18071)+E(f19(x18071,f4(x18071),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f4(x18071))
% 1.87/2.00 [1816]~P5(a36,f2(a36),x18161)+E(f19(a36,f21(a14,x18161),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18161)
% 1.87/2.00 [1818]~P6(a36,f2(a36),x18181)+E(f19(a36,f17(a36,f21(a14,x18181)),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f17(a36,x18181))
% 1.87/2.00 [1822]P5(a36,f2(a36),x18221)+~E(f19(a36,f21(a14,x18221),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18221)
% 1.87/2.00 [1835]~P6(a36,f2(a36),x18351)+P6(a36,f2(a36),f19(a36,f21(a14,x18351),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.00 [1839]~P6(a36,f2(a36),x18391)+P7(a36,a14,x18391,f18(a36,f17(a36,f21(a14,x18391)),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.00 [1848]~P6(a36,f2(a36),x18481)+P6(a36,f18(a36,x18481,f21(a14,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),x18481)
% 1.87/2.00 [641]~E(x6411,x6412)+P5(a36,x6411,x6412)
% 1.87/2.00 [644]~E(x6441,x6442)+P5(a37,x6441,x6442)
% 1.87/2.00 [659]~P34(x6591)+P5(x6591,x6592,x6592)
% 1.87/2.00 [730]~E(x7301,x7302)+~P6(a36,x7301,x7302)
% 1.87/2.00 [731]~E(x7311,x7312)+~P6(a1,x7311,x7312)
% 1.87/2.00 [736]~E(x7361,x7362)+~P6(a37,x7361,x7362)
% 1.87/2.00 [753]~P6(x7531,x7532,x7532)+~P34(x7531)
% 1.87/2.00 [774]P5(a36,x7742,x7741)+P5(a36,x7741,x7742)
% 1.87/2.00 [775]P5(a1,x7752,x7751)+P5(a1,x7751,x7752)
% 1.87/2.00 [776]P5(a37,x7762,x7761)+P5(a37,x7761,x7762)
% 1.87/2.00 [854]~P6(a36,x8541,x8542)+P5(a36,x8541,x8542)
% 1.87/2.00 [855]~P6(a1,x8551,x8552)+P5(a1,x8551,x8552)
% 1.87/2.00 [860]~P6(a37,x8601,x8602)+P5(a37,x8601,x8602)
% 1.87/2.00 [597]~P34(x5972)+P34(f40(x5971,x5972))
% 1.87/2.00 [598]~P41(x5982)+P41(f40(x5981,x5982))
% 1.87/2.00 [599]~P42(x5992)+P42(f40(x5991,x5992))
% 1.87/2.00 [600]~P39(x6002)+P39(f40(x6001,x6002))
% 1.87/2.00 [601]~P33(x6012)+P33(f40(x6011,x6012))
% 1.87/2.00 [611]E(x6111,x6112)+~E(f21(a14,x6111),f21(a14,x6112))
% 1.87/2.00 [703]~E(x7032,f3(a36,x7031))+E(f8(a36,x7031,x7032),f2(a36))
% 1.87/2.00 [740]~E(f8(a37,x7402,x7401),x7402)+E(x7401,f2(a37))
% 1.87/2.00 [744]~P6(a37,x7442,x7441)+~E(x7441,f2(a37))
% 1.87/2.00 [745]E(x7451,f2(a37))+~E(f8(a37,x7452,x7451),f2(a37))
% 1.87/2.00 [746]E(x7461,f2(a37))+~E(f8(a37,x7461,x7462),f2(a37))
% 1.87/2.00 [768]E(x7681,f3(a36,x7682))+~E(f8(a36,x7682,x7681),f2(a36))
% 1.87/2.00 [879]~P5(a1,x8791,x8792)+P6(a1,f15(x8791),x8792)
% 1.87/2.00 [885]P5(a1,x8851,x8852)+~P6(a1,f15(x8851),x8852)
% 1.87/2.00 [919]~E(x9192,f2(a37))+P6(a37,f2(a37),f19(a37,x9191,x9192))
% 1.87/2.00 [937]E(x9371,x9372)+~E(f8(a1,x9371,x9371),f8(a1,x9372,x9372))
% 1.87/2.00 [960]~P5(a1,x9601,a10)+P5(a37,f12(a37,x9601),f12(a37,x9602))
% 1.87/2.00 [986]~P6(a36,x9861,x9862)+P6(a36,f21(a14,x9861),f21(a14,x9862))
% 1.87/2.00 [987]~P6(a36,x9871,x9872)+P6(a36,f21(a16,x9871),f21(a16,x9872))
% 1.87/2.00 [988]~P6(a1,x9881,x9882)+P6(a1,f12(a1,x9881),f12(a1,x9882))
% 1.87/2.00 [990]~P5(a36,x9901,x9902)+P5(a36,f21(a14,x9901),f21(a14,x9902))
% 1.87/2.00 [991]~P5(a36,x9911,x9912)+P5(a36,f21(a16,x9911),f21(a16,x9912))
% 1.87/2.00 [992]~P5(a1,x9921,x9922)+P5(a1,f12(a1,x9921),f12(a1,x9922))
% 1.87/2.00 [993]~P5(a1,x9931,x9932)+P5(a37,f12(a37,x9931),f12(a37,x9932))
% 1.87/2.00 [1068]P6(a36,x10681,x10682)+~P6(a36,f21(a14,x10681),f21(a14,x10682))
% 1.87/2.00 [1069]P6(a1,x10691,x10692)+~P6(a1,f12(a1,x10691),f12(a1,x10692))
% 1.87/2.00 [1070]P6(a1,x10701,x10702)+~P6(a37,f12(a37,x10701),f12(a37,x10702))
% 1.87/2.00 [1071]P5(a36,x10711,x10712)+~P5(a36,f21(a14,x10711),f21(a14,x10712))
% 1.87/2.00 [1072]P5(a1,x10721,x10722)+~P5(a1,f12(a1,x10721),f12(a1,x10722))
% 1.87/2.00 [1162]~P6(a37,f2(a37),x11621)+P6(a37,f2(a37),f19(a37,x11621,x11622))
% 1.87/2.00 [1163]~P5(a1,f2(a1),x11631)+P5(a1,f2(a1),f19(a1,x11631,x11632))
% 1.87/2.00 [1202]~P6(a36,f3(a36,x12021),x12022)+P6(a36,f2(a36),f8(a36,x12021,x12022))
% 1.87/2.00 [1203]~P5(a36,f3(a36,x12031),x12032)+P5(a36,f2(a36),f8(a36,x12031,x12032))
% 1.87/2.00 [1204]~P6(a36,x12042,f3(a36,x12041))+P6(a36,f8(a36,x12041,x12042),f2(a36))
% 1.87/2.00 [1205]~P5(a36,x12052,f3(a36,x12051))+P5(a36,f8(a36,x12051,x12052),f2(a36))
% 1.87/2.00 [1264]P6(a36,x12641,f3(a36,x12642))+~P6(a36,f8(a36,x12642,x12641),f2(a36))
% 1.87/2.00 [1265]P5(a36,x12651,f3(a36,x12652))+~P5(a36,f8(a36,x12652,x12651),f2(a36))
% 1.87/2.00 [1266]P6(a36,f3(a36,x12661),x12662)+~P6(a36,f2(a36),f8(a36,x12661,x12662))
% 1.87/2.00 [1267]P5(a36,f3(a36,x12671),x12672)+~P5(a36,f2(a36),f8(a36,x12671,x12672))
% 1.87/2.00 [1307]~P6(a1,x13071,x13072)+P6(a1,f8(a1,x13071,x13071),f8(a1,x13072,x13072))
% 1.87/2.00 [1313]~P5(a1,x13131,x13132)+P5(a1,f8(a1,x13131,x13131),f8(a1,x13132,x13132))
% 1.87/2.00 [1514]P6(a1,x15141,x15142)+~P6(a1,f8(a1,x15141,x15141),f8(a1,x15142,x15142))
% 1.87/2.00 [1517]P5(a1,x15171,x15172)+~P5(a1,f8(a1,x15171,x15171),f8(a1,x15172,x15172))
% 1.87/2.00 [613]E(f21(a13,x6131),x6132)+~E(f21(f20(a36),x6132),x6131)
% 1.87/2.00 [616]~E(x6162,f2(a37))+E(f21(f7(a37,x6161),x6162),f2(a37))
% 1.87/2.00 [617]~E(x6171,f2(a37))+E(f21(f7(a37,x6171),x6172),f2(a37))
% 1.87/2.00 [622]~P50(x6221)+E(f17(x6221,f17(x6221,x6222)),x6222)
% 1.87/2.00 [623]~P22(x6231)+E(f3(x6231,f3(x6231,x6232)),x6232)
% 1.87/2.00 [624]~P39(x6241)+E(f3(x6241,f3(x6241,x6242)),x6242)
% 1.87/2.00 [626]~P40(x6261)+E(f21(f7(x6261,x6262),x6262),x6262)
% 1.87/2.00 [635]~P1(x6351)+E(f21(f7(x6351,x6352),f4(x6351)),x6352)
% 1.87/2.00 [636]~P11(x6361)+E(f21(f7(x6361,x6362),f4(x6361)),x6362)
% 1.87/2.00 [637]~P19(x6371)+E(f21(f7(x6371,x6372),f4(x6371)),x6372)
% 1.87/2.00 [640]E(x6401,x6402)+~E(f21(f20(a36),x6401),f21(f20(a36),x6402))
% 1.87/2.00 [645]~P1(x6451)+E(f21(f7(x6451,x6452),f2(x6451)),f2(x6451))
% 1.87/2.00 [646]~P58(x6461)+E(f21(f7(x6461,x6462),f2(x6461)),f2(x6461))
% 1.87/2.00 [648]~P23(x6481)+E(f21(f7(x6481,x6482),f2(x6481)),f2(x6481))
% 1.87/2.00 [658]~P52(x6581)+E(f9(x6581,f9(x6581,x6582)),f9(x6581,x6582))
% 1.87/2.00 [670]~P1(x6701)+E(f19(x6701,x6702,f4(a37)),x6702)
% 1.87/2.00 [671]~P19(x6711)+E(f19(x6711,x6712,f4(a37)),x6712)
% 1.87/2.00 [674]E(x6741,f4(a37))+~E(f21(f7(a37,x6742),x6741),f4(a37))
% 1.87/2.00 [675]E(x6751,f4(a37))+~E(f21(f7(a37,x6751),x6752),f4(a37))
% 1.87/2.00 [678]~P49(x6781)+E(f18(x6781,x6782,f4(x6781)),x6782)
% 1.87/2.00 [679]~P1(x6791)+E(f8(x6791,x6792,f2(x6791)),x6792)
% 1.87/2.00 [680]~P18(x6801)+E(f8(x6801,x6802,f2(x6801)),x6802)
% 1.87/2.00 [681]~P20(x6811)+E(f8(x6811,x6812,f2(x6811)),x6812)
% 1.87/2.00 [682]~P1(x6821)+E(f8(x6821,f2(x6821),x6822),x6822)
% 1.87/2.00 [683]~P18(x6831)+E(f8(x6831,f2(x6831),x6832),x6832)
% 1.87/2.00 [684]~P20(x6841)+E(f8(x6841,f2(x6841),x6842),x6842)
% 1.87/2.00 [685]~P1(x6851)+E(f19(x6851,x6852,f2(a37)),f4(x6851))
% 1.87/2.00 [686]~P43(x6861)+E(f19(x6861,x6862,f2(a37)),f4(x6861))
% 1.87/2.00 [691]~P50(x6911)+E(f18(x6911,x6912,f2(x6911)),f2(x6911))
% 1.87/2.00 [692]~P49(x6921)+E(f18(x6921,f2(x6921),x6922),f2(x6921))
% 1.87/2.00 [693]~P10(x6931)+E(f18(x6931,f2(x6931),x6932),f2(x6931))
% 1.87/2.00 [694]~P19(x6941)+E(f19(x6941,f4(x6941),x6942),f4(x6941))
% 1.87/2.00 [709]~P4(x7091)+E(f18(x7091,f4(x7091),x7092),f17(x7091,x7092))
% 1.87/2.00 [710]~P49(x7101)+E(f18(x7101,f4(x7101),x7102),f17(x7101,x7102))
% 1.87/2.00 [711]~E(x7111,x7112)+E(f8(a36,x7111,f3(a36,x7112)),f2(a36))
% 1.87/2.00 [716]~P37(x7161)+E(f3(x7161,f12(x7161,x7162)),f12(x7161,f3(a1,x7162)))
% 1.87/2.00 [721]~P37(x7211)+E(f8(x7211,x7212,f12(x7211,a10)),x7212)
% 1.87/2.00 [722]~P37(x7221)+E(f8(x7221,f12(x7221,a10),x7222),x7222)
% 1.87/2.00 [723]~P50(x7231)+E(f17(x7231,f3(x7231,x7232)),f3(x7231,f17(x7231,x7232)))
% 1.87/2.00 [724]~P47(x7241)+E(f9(x7241,f3(x7241,x7242)),f3(x7241,f9(x7241,x7242)))
% 1.87/2.00 [747]~P22(x7471)+E(f8(x7471,x7472,f3(x7471,x7472)),f2(x7471))
% 1.87/2.00 [748]~P22(x7481)+E(f8(x7481,f3(x7481,x7482),x7482),f2(x7481))
% 1.87/2.00 [749]~P14(x7491)+E(f8(x7491,f3(x7491,x7492),x7492),f2(x7491))
% 1.87/2.00 [828]E(x8281,x8282)+~E(f8(a36,x8281,f3(a36,x8282)),f2(a36))
% 1.87/2.00 [835]E(x8351,x8352)+~E(f21(x8351,f23(x8352,x8351)),f21(x8352,f23(x8352,x8351)))
% 1.87/2.00 [882]~P56(x8821)+P5(x8821,f2(x8821),f21(f7(x8821,x8822),x8822))
% 1.87/2.00 [883]~P29(x8831)+P5(x8831,f3(x8831,f5(x8831,x8832)),f2(x8831))
% 1.87/2.00 [884]~P37(x8841)+E(f8(x8841,f3(x8841,f4(x8841)),f12(x8841,x8842)),f12(x8841,f15(x8842)))
% 1.87/2.00 [909]~P5(a37,x9091,x9092)+E(f8(a37,x9091,f28(x9092,x9091)),x9092)
% 1.87/2.00 [910]~P5(a37,x9101,x9102)+E(f8(a37,x9101,f24(x9102,x9101)),x9102)
% 1.87/2.00 [920]~E(x9201,x9202)+P6(a1,x9201,f8(a1,x9202,f4(a1)))
% 1.87/2.00 [967]~P51(x9671)+P6(x9671,x9672,f8(x9671,x9672,f4(x9671)))
% 1.87/2.00 [999]~P6(a1,x9991,a10)+E(f21(f7(a37,f12(a37,x9991)),f12(a37,x9992)),f2(a37))
% 1.87/2.00 [1020]~P6(a1,x10201,a10)+E(f8(a37,f12(a37,x10201),f12(a37,x10202)),f12(a37,x10202))
% 1.87/2.00 [1038]~P6(a36,x10381,x10382)+P6(a36,f21(f20(a36),x10381),f21(f20(a36),x10382))
% 1.87/2.00 [1039]~P5(a36,x10391,x10392)+P5(a36,f21(f20(a36),x10391),f21(f20(a36),x10392))
% 1.87/2.00 [1104]~P56(x11041)+~P6(x11041,f21(f7(x11041,x11042),x11042),f2(x11041))
% 1.87/2.00 [1138]P6(a36,x11381,x11382)+~P6(a36,f21(f20(a36),x11381),f21(f20(a36),x11382))
% 1.87/2.00 [1139]P5(a36,x11391,x11392)+~P5(a36,f21(f20(a36),x11391),f21(f20(a36),x11392))
% 1.87/2.00 [1155]~P6(a1,x11551,x11552)+P6(a1,x11551,f8(a1,x11552,f4(a1)))
% 1.87/2.00 [1156]~P5(a1,x11561,x11562)+P6(a1,x11561,f8(a1,x11562,f4(a1)))
% 1.87/2.00 [1158]~P6(a1,x11581,x11582)+P5(a1,f8(a1,x11581,f4(a1)),x11582)
% 1.87/2.00 [1175]P6(a37,f2(a37),x11751)+~P6(a37,f2(a37),f21(f7(a37,x11752),x11751))
% 1.87/2.00 [1176]P6(a37,f2(a37),x11761)+~P6(a37,f2(a37),f21(f7(a37,x11761),x11762))
% 1.87/2.00 [1248]P5(a1,x12481,x12482)+~P6(a1,x12481,f8(a1,x12482,f4(a1)))
% 1.87/2.00 [1249]P6(a1,x12491,x12492)+~P5(a1,f8(a1,x12491,f4(a1)),x12492)
% 1.87/2.00 [1396]~P37(x13961)+E(f8(x13961,f8(x13961,f2(x13961),f12(x13961,x13962)),f12(x13961,x13962)),f12(x13961,f8(a1,x13962,x13962)))
% 1.87/2.00 [1490]~P37(x14901)+E(f21(f7(x14901,f8(x14901,f4(x14901),f4(x14901))),f12(x14901,x14902)),f12(x14901,f8(a1,x14902,x14902)))
% 1.87/2.00 [1585]E(x15851,x15852)+~E(f8(a1,f8(a1,x15851,x15851),f4(a1)),f8(a1,f8(a1,x15852,x15852),f4(a1)))
% 1.87/2.00 [1624]~P5(a1,x16241,x16242)+P6(a1,f8(a1,x16241,x16241),f8(a1,f8(a1,x16242,x16242),f4(a1)))
% 1.87/2.00 [1626]~P5(a1,x16261,x16262)+P5(a1,f8(a1,x16261,x16261),f8(a1,f8(a1,x16262,x16262),f4(a1)))
% 1.87/2.00 [1628]~P6(a1,x16281,x16282)+P6(a1,f8(a1,f8(a1,x16281,x16281),f4(a1)),f8(a1,x16282,x16282))
% 1.87/2.00 [1630]~P6(a1,x16301,x16302)+P5(a1,f8(a1,f8(a1,x16301,x16301),f4(a1)),f8(a1,x16302,x16302))
% 1.87/2.00 [1746]~P6(a1,x17461,x17462)+P6(a1,f8(a1,f8(a1,x17461,x17461),f4(a1)),f8(a1,f8(a1,x17462,x17462),f4(a1)))
% 1.87/2.00 [1748]~P5(a1,x17481,x17482)+P5(a1,f8(a1,f8(a1,x17481,x17481),f4(a1)),f8(a1,f8(a1,x17482,x17482),f4(a1)))
% 1.87/2.00 [1753]P5(a1,x17531,x17532)+~P6(a1,f8(a1,x17531,x17531),f8(a1,f8(a1,x17532,x17532),f4(a1)))
% 1.87/2.00 [1755]P5(a1,x17551,x17552)+~P5(a1,f8(a1,x17551,x17551),f8(a1,f8(a1,x17552,x17552),f4(a1)))
% 1.87/2.00 [1757]P6(a1,x17571,x17572)+~P6(a1,f8(a1,f8(a1,x17571,x17571),f4(a1)),f8(a1,x17572,x17572))
% 1.87/2.00 [1759]P6(a1,x17591,x17592)+~P5(a1,f8(a1,f8(a1,x17591,x17591),f4(a1)),f8(a1,x17592,x17592))
% 1.87/2.00 [1793]P6(a1,x17931,x17932)+~P6(a1,f8(a1,f8(a1,x17931,x17931),f4(a1)),f8(a1,f8(a1,x17932,x17932),f4(a1)))
% 1.87/2.00 [1795]P5(a1,x17951,x17952)+~P5(a1,f8(a1,f8(a1,x17951,x17951),f4(a1)),f8(a1,f8(a1,x17952,x17952),f4(a1)))
% 1.87/2.00 [654]~P1(x6541)+E(f21(f7(x6541,f4(x6541)),x6542),x6542)
% 1.87/2.00 [655]~P11(x6551)+E(f21(f7(x6551,f4(x6551)),x6552),x6552)
% 1.87/2.00 [656]~P19(x6561)+E(f21(f7(x6561,f4(x6561)),x6562),x6562)
% 1.87/2.00 [661]~P1(x6611)+E(f21(f7(x6611,f2(x6611)),x6612),f2(x6611))
% 1.87/2.00 [662]~P58(x6621)+E(f21(f7(x6621,f2(x6621)),x6622),f2(x6621))
% 1.87/2.00 [664]~P23(x6641)+E(f21(f7(x6641,f2(x6641)),x6642),f2(x6641))
% 1.87/2.00 [1094]~P37(x10941)+E(f8(x10941,f4(x10941),f12(x10941,x10942)),f12(x10941,f8(a1,x10942,f4(a1))))
% 1.87/2.00 [1152]P6(a1,x11521,a10)+E(f21(f7(a37,f12(a37,x11521)),f12(a37,x11522)),f12(a37,f21(f7(a1,x11521),x11522)))
% 1.87/2.00 [1253]E(x12531,f2(a36))+~E(f8(a36,f21(f7(a36,x12532),x12532),f21(f7(a36,x12531),x12531)),f2(a36))
% 1.87/2.00 [1254]E(x12541,f2(a36))+~E(f8(a36,f21(f7(a36,x12541),x12541),f21(f7(a36,x12542),x12542)),f2(a36))
% 1.87/2.00 [1648]~P37(x16481)+E(f8(x16481,f8(x16481,f4(x16481),f12(x16481,x16482)),f12(x16481,x16482)),f12(x16481,f8(a1,f8(a1,x16482,x16482),f4(a1))))
% 1.87/2.00 [863]~P48(x8631)+E(f21(f7(x8631,f3(x8631,f4(x8631))),x8632),f3(x8631,x8632))
% 1.87/2.00 [1350]~P1(x13501)+E(f8(x13501,x13502,x13502),f21(f7(x13501,f8(x13501,f4(x13501),f4(x13501))),x13502))
% 1.87/2.00 [1702]~P37(x17021)+E(f21(f7(x17021,x17022),f12(x17021,f8(a1,f8(a1,a10,a10),f4(a1)))),x17022)
% 1.87/2.01 [1760]~P37(x17601)+E(f8(x17601,f4(x17601),f12(x17601,x17602)),f12(x17601,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),x17602)))
% 1.87/2.01 [1761]~P37(x17611)+E(f8(x17611,f12(x17611,x17612),f4(x17611)),f12(x17611,f8(a1,x17612,f8(a1,f8(a1,a10,a10),f4(a1)))))
% 1.87/2.01 [1838]~P19(x18381)+E(f19(x18381,x18382,f12(a37,f8(a1,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))),f4(a1)))),f21(f7(x18381,f21(f7(x18381,x18382),x18382)),x18382))
% 1.87/2.01 [1801]~P37(x18011)+E(f21(f7(x18011,f12(x18011,f8(a1,f8(a1,a10,a10),f4(a1)))),x18012),x18012)
% 1.87/2.01 [1811]~P1(x18111)+E(f21(f7(x18111,x18112),x18112),f19(x18111,x18112,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1812]~P19(x18121)+E(f19(x18121,x18122,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f21(f7(x18121,x18122),x18122))
% 1.87/2.01 [1813]~P37(x18131)+E(f21(f7(x18131,x18132),f12(x18131,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f8(x18131,x18132,x18132))
% 1.87/2.01 [1829]~P71(x18291)+E(f19(x18291,f3(x18291,x18292),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18291,x18292,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1830]~P52(x18301)+P5(x18301,f2(x18301),f19(x18301,x18302,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1836]~P6(a36,x18361,x18362)+P6(a36,x18361,f18(a36,f8(a36,x18361,x18362),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1837]~P6(a36,x18371,x18372)+P6(a36,f18(a36,f8(a36,x18371,x18372),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18372)
% 1.87/2.01 [1840]~P52(x18401)+~P6(x18401,f19(x18401,x18402,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f2(x18401))
% 1.87/2.01 [1828]~P37(x18281)+E(f21(f7(x18281,f12(x18281,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18282),f8(x18281,x18282,x18282))
% 1.87/2.01 [1852]E(x18521,f2(a36))+~E(f8(a36,f19(a36,x18522,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x18521,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(a36))
% 1.87/2.01 [1853]E(x18531,f2(a36))+~E(f8(a36,f19(a36,x18531,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x18532,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(a36))
% 1.87/2.01 [1846]~P71(x18461)+E(f19(x18461,f3(x18461,f4(x18461)),f21(f7(a37,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18462)),f4(x18461))
% 1.87/2.01 [1867]E(x18671,f2(a36))+~E(f21(a14,f8(a36,f19(a36,x18672,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x18671,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),x18672)
% 1.87/2.01 [1868]E(x18681,f2(a36))+~E(f21(a14,f8(a36,f19(a36,x18681,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x18682,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),x18682)
% 1.87/2.01 [798]~P1(x7981)+E(f8(x7981,x7982,x7983),f8(x7981,x7983,x7982))
% 1.87/2.01 [865]P5(a37,x8651,x8652)+~E(x8652,f8(a37,x8651,x8653))
% 1.87/2.01 [935]E(x9351,x9352)+~E(f8(a37,x9353,x9351),f8(a37,x9353,x9352))
% 1.87/2.01 [936]E(x9361,x9362)+~E(f8(a37,x9361,x9363),f8(a37,x9362,x9363))
% 1.87/2.01 [1142]~P6(a37,x11421,x11423)+P6(a37,x11421,f8(a37,x11422,x11423))
% 1.87/2.01 [1144]~P6(a37,x11441,x11442)+P6(a37,x11441,f8(a37,x11442,x11443))
% 1.87/2.01 [1146]~P5(a37,x11461,x11463)+P5(a37,x11461,f8(a37,x11462,x11463))
% 1.87/2.01 [1148]~P5(a37,x11481,x11482)+P5(a37,x11481,f8(a37,x11482,x11483))
% 1.87/2.01 [1210]~P10(x12101)+P7(x12101,f7(x12101,x12102),x12103,x12102)
% 1.87/2.01 [1235]P6(a37,x12351,x12352)+~P6(a37,f8(a37,x12351,x12353),x12352)
% 1.87/2.01 [1238]P5(a37,x12381,x12382)+~P5(a37,f8(a37,x12383,x12381),x12382)
% 1.87/2.01 [1239]P5(a37,x12391,x12392)+~P5(a37,f8(a37,x12391,x12393),x12392)
% 1.87/2.01 [1305]~P6(a1,x13051,x13053)+P6(a1,f8(a1,x13051,x13052),f8(a1,x13053,x13052))
% 1.87/2.01 [1308]~P6(a37,x13082,x13083)+P6(a37,f8(a37,x13081,x13082),f8(a37,x13081,x13083))
% 1.87/2.01 [1309]~P6(a37,x13091,x13093)+P6(a37,f8(a37,x13091,x13092),f8(a37,x13093,x13092))
% 1.87/2.01 [1310]~P5(a36,x13102,x13103)+P5(a36,f8(a36,x13101,x13102),f8(a36,x13101,x13103))
% 1.87/2.01 [1311]~P5(a1,x13112,x13113)+P5(a1,f8(a1,x13111,x13112),f8(a1,x13111,x13113))
% 1.87/2.01 [1314]~P5(a37,x13142,x13143)+P5(a37,f8(a37,x13141,x13142),f8(a37,x13141,x13143))
% 1.87/2.01 [1315]~P5(a37,x13151,x13153)+P5(a37,f8(a37,x13151,x13152),f8(a37,x13153,x13152))
% 1.87/2.01 [1515]P6(a37,x15151,x15152)+~P6(a37,f8(a37,x15153,x15151),f8(a37,x15153,x15152))
% 1.87/2.01 [1518]P5(a37,x15181,x15182)+~P5(a37,f8(a37,x15183,x15181),f8(a37,x15183,x15182))
% 1.87/2.01 [706]~E(x7062,f2(a37))+E(f21(f7(a37,x7061),x7062),f21(f7(a37,x7063),x7062))
% 1.87/2.01 [708]~E(x7081,f2(a37))+E(f21(f7(a37,x7081),x7082),f21(f7(a37,x7081),x7083))
% 1.87/2.01 [725]~P1(x7251)+E(f21(f7(x7251,x7252),x7253),f21(f7(x7251,x7253),x7252))
% 1.87/2.01 [833]~P4(x8331)+E(f21(f7(x8331,x8332),f17(x8331,x8333)),f18(x8331,x8332,x8333))
% 1.87/2.01 [834]~P49(x8341)+E(f21(f7(x8341,x8342),f17(x8341,x8343)),f18(x8341,x8342,x8343))
% 1.87/2.01 [917]~P69(x9171)+E(f21(f7(x9171,f3(x9171,x9172)),f3(x9171,x9173)),f21(f7(x9171,x9172),x9173))
% 1.87/2.01 [934]~P3(x9341)+E(f18(x9341,f3(x9341,x9342),f3(x9341,x9343)),f18(x9341,x9342,x9343))
% 1.87/2.01 [980]~P3(x9801)+E(f17(x9801,f18(x9801,x9802,x9803)),f18(x9801,x9803,x9802))
% 1.87/2.01 [1029]~P22(x10291)+E(f8(x10291,f3(x10291,x10292),f8(x10291,x10292,x10293)),x10293)
% 1.87/2.01 [1063]~P3(x10631)+E(f18(x10631,x10632,f3(x10631,x10633)),f3(x10631,f18(x10631,x10632,x10633)))
% 1.87/2.01 [1064]~P50(x10641)+E(f19(x10641,f17(x10641,x10642),x10643),f17(x10641,f19(x10641,x10642,x10643)))
% 1.87/2.01 [1065]~P49(x10651)+E(f18(x10651,f3(x10651,x10652),x10653),f3(x10651,f18(x10651,x10652,x10653)))
% 1.87/2.01 [1066]~P52(x10661)+E(f19(x10661,f5(x10661,x10662),x10663),f5(x10661,f19(x10661,x10662,x10663)))
% 1.87/2.01 [1067]~P10(x10671)+E(f18(x10671,f3(x10671,x10672),x10673),f3(x10671,f18(x10671,x10672,x10673)))
% 1.87/2.01 [1105]~P52(x11051)+P5(x11051,f2(x11051),f19(x11051,f5(x11051,x11052),x11053))
% 1.87/2.01 [1118]~P37(x11181)+E(f8(x11181,f12(x11181,x11182),f12(x11181,x11183)),f12(x11181,f8(a1,x11182,x11183)))
% 1.87/2.01 [1119]~P22(x11191)+E(f8(x11191,f3(x11191,x11192),f3(x11191,x11193)),f3(x11191,f8(x11191,x11193,x11192)))
% 1.87/2.01 [1120]~P14(x11201)+E(f8(x11201,f3(x11201,x11202),f3(x11201,x11203)),f3(x11201,f8(x11201,x11202,x11203)))
% 1.87/2.01 [1166]P6(a37,f2(a37),x11661)+P5(a37,f21(f7(a37,x11662),x11661),f21(f7(a37,x11663),x11661))
% 1.87/2.01 [1167]P6(a37,f2(a37),x11671)+P5(a37,f21(f7(a37,x11671),x11672),f21(f7(a37,x11671),x11673))
% 1.87/2.01 [1207]~P5(a37,x12072,x12073)+P5(a37,f21(f7(a37,x12071),x12072),f21(f7(a37,x12071),x12073))
% 1.87/2.01 [1209]~P5(a37,x12091,x12093)+P5(a37,f21(f7(a37,x12091),x12092),f21(f7(a37,x12093),x12092))
% 1.87/2.01 [1347]P6(a37,x13471,x13472)+~P6(a37,f21(f7(a37,x13473),x13471),f21(f7(a37,x13473),x13472))
% 1.87/2.01 [1348]P6(a37,x13481,x13482)+~P6(a37,f21(f7(a37,x13481),x13483),f21(f7(a37,x13482),x13483))
% 1.87/2.01 [1358]P6(a37,f2(a37),x13581)+~P6(a37,f21(f7(a37,x13582),x13581),f21(f7(a37,x13583),x13581))
% 1.87/2.01 [1359]P6(a37,f2(a37),x13591)+~P6(a37,f21(f7(a37,x13591),x13592),f21(f7(a37,x13591),x13593))
% 1.87/2.01 [1649]~P71(x16491)+E(f21(f7(x16491,f19(x16491,f3(x16491,f4(x16491)),x16492)),f19(x16491,x16493,x16492)),f19(x16491,f3(x16491,x16493),x16492))
% 1.87/2.01 [912]~P69(x9121)+E(f21(f7(x9121,x9122),f3(x9121,x9123)),f3(x9121,f21(f7(x9121,x9122),x9123)))
% 1.87/2.01 [914]~P23(x9141)+E(f21(f7(x9141,x9142),f3(x9141,x9143)),f3(x9141,f21(f7(x9141,x9142),x9143)))
% 1.87/2.01 [915]~P69(x9151)+E(f21(f7(x9151,f3(x9151,x9152)),x9153),f21(f7(x9151,x9152),f3(x9151,x9153)))
% 1.87/2.01 [916]~P40(x9161)+E(f21(f7(x9161,x9162),f21(f7(x9161,x9162),x9163)),f21(f7(x9161,x9162),x9163))
% 1.87/2.01 [1016]~P69(x10161)+E(f21(f7(x10161,f3(x10161,x10162)),x10163),f3(x10161,f21(f7(x10161,x10162),x10163)))
% 1.87/2.01 [1018]~P23(x10181)+E(f21(f7(x10181,f3(x10181,x10182)),x10183),f3(x10181,f21(f7(x10181,x10182),x10183)))
% 1.87/2.01 [1078]~P37(x10781)+E(f21(f7(x10781,f12(x10781,x10782)),f12(x10781,x10783)),f12(x10781,f21(f7(a1,x10782),x10783)))
% 1.87/2.01 [1091]~P3(x10911)+E(f21(f7(x10911,f17(x10911,x10912)),f17(x10911,x10913)),f17(x10911,f21(f7(x10911,x10912),x10913)))
% 1.87/2.01 [1092]~P52(x10921)+E(f21(f7(x10921,f9(x10921,x10922)),f9(x10921,x10923)),f9(x10921,f21(f7(x10921,x10922),x10923)))
% 1.87/2.01 [1093]~P44(x10931)+E(f21(f7(x10931,f9(x10931,x10932)),f9(x10931,x10933)),f9(x10931,f21(f7(x10931,x10932),x10933)))
% 1.87/2.01 [1103]~P22(x11031)+E(f8(x11031,x11032,f8(x11031,f3(x11031,x11032),x11033)),x11033)
% 1.87/2.01 [1240]~P52(x12401)+E(f5(x12401,f19(x12401,f3(x12401,x12402),x12403)),f5(x12401,f19(x12401,x12402,x12403)))
% 1.87/2.01 [1324]~P3(x13241)+E(f19(x13241,f18(x13241,f4(x13241),x13242),x13243),f18(x13241,f4(x13241),f19(x13241,x13242,x13243)))
% 1.87/2.01 [1445]~P19(x14451)+E(f21(f7(x14451,f19(x14451,x14452,x14453)),x14452),f21(f7(x14451,x14452),f19(x14451,x14452,x14453)))
% 1.87/2.01 [1549]~P56(x15491)+P5(x15491,f2(x15491),f8(x15491,f21(f7(x15491,x15492),x15492),f21(f7(x15491,x15493),x15493)))
% 1.87/2.01 [1734]~P56(x17341)+~P6(x17341,f8(x17341,f21(f7(x17341,x17342),x17342),f21(f7(x17341,x17343),x17343)),f2(x17341))
% 1.87/2.01 [1273]~P6(a1,x12731,a10)+E(f21(f7(a37,f12(a37,x12731)),f21(f7(a37,f12(a37,x12732)),x12733)),f2(a37))
% 1.87/2.01 [1400]~P37(x14001)+E(f21(f7(x14001,f3(x14001,f12(x14001,x14002))),x14003),f21(f7(x14001,f12(x14001,f3(a1,x14002))),x14003))
% 1.87/2.01 [1451]~P1(x14511)+E(f8(x14511,x14512,f21(f7(x14511,x14513),x14512)),f21(f7(x14511,f8(x14511,x14513,f4(x14511))),x14512))
% 1.87/2.01 [1452]~P1(x14521)+E(f8(x14521,f21(f7(x14521,x14522),x14523),x14523),f21(f7(x14521,f8(x14521,x14522,f4(x14521))),x14523))
% 1.87/2.01 [1679]P6(a1,x16791,a10)+E(f21(f7(a37,f12(a37,x16791)),f21(f7(a37,f12(a37,x16792)),x16793)),f21(f7(a37,f12(a37,f21(f7(a1,x16791),x16792))),x16793))
% 1.87/2.01 [1861]~P52(x18611)+P5(x18611,f2(x18611),f8(x18611,f19(x18611,x18612,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18611,x18613,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))
% 1.87/2.01 [1869]~P52(x18691)+~P6(x18691,f8(x18691,f19(x18691,x18692,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18691,x18693,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(x18691))
% 1.87/2.01 [1850]~P1(x18501)+E(f19(x18501,x18502,f21(f7(a37,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18503)),f21(f7(x18501,f19(x18501,x18502,x18503)),f19(x18501,x18502,x18503)))
% 1.87/2.01 [1851]~P19(x18511)+E(f19(x18511,x18512,f21(f7(a37,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18513)),f19(x18511,f19(x18511,x18512,x18513),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1858]~E(f21(f7(a36,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18581),f18(a36,x18582,x18583))+E(x18581,f18(a36,x18582,f21(f7(a36,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18583)))
% 1.87/2.01 [1859]~P71(x18591)+E(f19(x18591,f3(x18591,x18592),f21(f7(a37,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18593)),f19(x18591,x18592,f21(f7(a37,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18593)))
% 1.87/2.01 [1860]~P52(x18601)+P5(x18601,f2(x18601),f19(x18601,x18602,f21(f7(a37,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18603)))
% 1.87/2.01 [1865]E(f21(f7(a36,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18651),f18(a36,x18652,x18653))+~E(x18651,f18(a36,x18652,f21(f7(a36,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18653)))
% 1.87/2.01 [1874]~P37(x18741)+E(f8(x18741,f8(x18741,f19(x18741,x18742,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18741,x18743,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f21(f7(x18741,f21(f7(x18741,f12(x18741,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18742)),x18743)),f19(x18741,f8(x18741,x18742,x18743),f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1268]~P1(x12681)+E(f8(x12681,x12682,f8(x12681,x12683,x12684)),f8(x12681,x12683,f8(x12681,x12682,x12684)))
% 1.87/2.01 [1270]~P1(x12701)+E(f8(x12701,f8(x12701,x12702,x12703),x12704),f8(x12701,x12702,f8(x12701,x12703,x12704)))
% 1.87/2.01 [1271]~P13(x12711)+E(f8(x12711,f8(x12711,x12712,x12713),x12714),f8(x12711,x12712,f8(x12711,x12713,x12714)))
% 1.87/2.01 [1272]~P1(x12721)+E(f8(x12721,f8(x12721,x12722,x12723),x12724),f8(x12721,f8(x12721,x12722,x12724),x12723))
% 1.87/2.01 [1463]~P49(x14631)+E(f8(x14631,f18(x14631,x14632,x14633),f18(x14631,x14634,x14633)),f18(x14631,f8(x14631,x14632,x14634),x14633))
% 1.87/2.01 [1464]~P10(x14641)+E(f8(x14641,f18(x14641,x14642,x14643),f18(x14641,x14644,x14643)),f18(x14641,f8(x14641,x14642,x14644),x14643))
% 1.87/2.01 [1465]~P3(x14651)+E(f18(x14651,f19(x14651,x14652,x14653),f19(x14651,x14654,x14653)),f19(x14651,f18(x14651,x14652,x14654),x14653))
% 1.87/2.01 [1594]~P19(x15941)+E(f21(f7(x15941,f19(x15941,x15942,x15943)),f19(x15941,x15942,x15944)),f19(x15941,x15942,f8(a37,x15943,x15944)))
% 1.87/2.01 [1595]~P1(x15951)+E(f21(f7(x15951,f19(x15951,x15952,x15953)),f19(x15951,x15952,x15954)),f19(x15951,x15952,f8(a37,x15953,x15954)))
% 1.87/2.01 [866]~P33(x8662)+E(f21(f3(f40(x8661,x8662),x8663),x8664),f3(x8662,f21(x8663,x8664)))
% 1.87/2.01 [1153]~P1(x11531)+E(f21(f7(x11531,x11532),f21(f7(x11531,x11533),x11534)),f21(f7(x11531,x11533),f21(f7(x11531,x11532),x11534)))
% 1.87/2.01 [1216]~P49(x12161)+E(f18(x12161,f21(f7(x12161,x12162),x12163),x12164),f21(f7(x12161,x12162),f18(x12161,x12163,x12164)))
% 1.87/2.01 [1220]~P1(x12201)+E(f19(x12201,f19(x12201,x12202,x12203),x12204),f19(x12201,x12202,f21(f7(a37,x12203),x12204)))
% 1.87/2.01 [1221]~P19(x12211)+E(f19(x12211,x12212,f21(f7(a37,x12213),x12214)),f19(x12211,f19(x12211,x12212,x12213),x12214))
% 1.87/2.01 [1351]~P1(x13511)+E(f8(x13511,f21(f7(x13511,x13512),x13513),f21(f7(x13511,x13512),x13514)),f21(f7(x13511,x13512),f8(x13511,x13513,x13514)))
% 1.87/2.01 [1353]~P23(x13531)+E(f8(x13531,f21(f7(x13531,x13532),x13533),f21(f7(x13531,x13532),x13534)),f21(f7(x13531,x13532),f8(x13531,x13533,x13534)))
% 1.87/2.01 [1522]~P23(x15221)+E(f8(x15221,f21(f7(x15221,x15222),x15223),f21(f7(x15221,x15224),x15223)),f21(f7(x15221,f8(x15221,x15222,x15224)),x15223))
% 1.87/2.01 [1523]~P46(x15231)+E(f8(x15231,f21(f7(x15231,x15232),x15233),f21(f7(x15231,x15234),x15233)),f21(f7(x15231,f8(x15231,x15232,x15234)),x15233))
% 1.87/2.01 [1524]~P1(x15241)+E(f8(x15241,f21(f7(x15241,x15242),x15243),f21(f7(x15241,x15244),x15243)),f21(f7(x15241,f8(x15241,x15242,x15244)),x15243))
% 1.87/2.01 [1582]~P1(x15821)+E(f21(f7(x15821,f19(x15821,x15822,x15823)),f19(x15821,x15824,x15823)),f19(x15821,f21(f7(x15821,x15822),x15824),x15823))
% 1.87/2.01 [1583]~P11(x15831)+E(f21(f7(x15831,f19(x15831,x15832,x15833)),f19(x15831,x15834,x15833)),f19(x15831,f21(f7(x15831,x15832),x15834),x15833))
% 1.87/2.01 [1596]~P37(x15961)+E(f8(x15961,f12(x15961,x15962),f8(x15961,f12(x15961,x15963),x15964)),f8(x15961,f12(x15961,f8(a1,x15962,x15963)),x15964))
% 1.87/2.01 [1257]~P1(x12571)+E(f21(f7(x12571,f21(f7(x12571,x12572),x12573)),x12574),f21(f7(x12571,x12572),f21(f7(x12571,x12573),x12574)))
% 1.87/2.01 [1258]~P12(x12581)+E(f21(f7(x12581,f21(f7(x12581,x12582),x12583)),x12584),f21(f7(x12581,x12582),f21(f7(x12581,x12583),x12584)))
% 1.87/2.01 [1426]~P1(x14261)+E(f21(f7(x14261,f21(f7(x14261,x14262),x14263)),x14264),f21(f7(x14261,f21(f7(x14261,x14262),x14264)),x14263))
% 1.87/2.01 [1674]~P37(x16741)+E(f21(f7(x16741,f12(x16741,x16742)),f21(f7(x16741,f12(x16741,x16743)),x16744)),f21(f7(x16741,f12(x16741,f21(f7(a1,x16742),x16743))),x16744))
% 1.87/2.01 [1610]~P1(x16101)+E(f8(x16101,f8(x16101,x16102,x16103),f8(x16101,x16104,x16105)),f8(x16101,f8(x16101,x16102,x16104),f8(x16101,x16103,x16105)))
% 1.87/2.01 [1621]~P1(x16211)+E(f21(f7(x16211,f21(f7(x16211,x16212),x16213)),f21(f7(x16211,x16214),x16215)),f21(f7(x16211,f21(f7(x16211,x16212),x16214)),f21(f7(x16211,x16213),x16215)))
% 1.87/2.01 [1632]~P3(x16321)+E(f18(x16321,f21(f7(x16321,x16322),x16323),f21(f7(x16321,x16324),x16325)),f21(f7(x16321,f18(x16321,x16322,x16324)),f18(x16321,x16323,x16325)))
% 1.87/2.01 [1776]~P73(x17761)+E(f8(x17761,f21(f7(x17761,x17762),x17763),f8(x17761,f21(f7(x17761,x17764),x17763),x17765)),f8(x17761,f21(f7(x17761,f8(x17761,x17762,x17764)),x17763),x17765))
% 1.87/2.01 [780]E(x7801,f2(a1))+~P6(a1,f2(a1),x7801)+E(f9(a1,x7801),f4(a1))
% 1.87/2.01 [789]~E(x7891,f4(a36))+~P6(a36,f2(a36),x7891)+E(f21(a13,x7891),f2(a36))
% 1.87/2.01 [800]E(x8001,f4(a36))+~P6(a36,f2(a36),x8001)+~E(f21(a13,x8001),f2(a36))
% 1.87/2.01 [1174]~P6(a36,x11741,f4(a36))+~P6(a36,f2(a36),x11741)+P6(a36,f21(a13,x11741),f2(a36))
% 1.87/2.01 [1185]~P6(a36,f2(a36),x11851)+P6(a36,x11851,f4(a36))+~P6(a36,f21(a13,x11851),f2(a36))
% 1.87/2.01 [1187]~P6(a36,f2(a36),x11871)+P6(a36,f4(a36),x11871)+~P6(a36,f2(a36),f21(a13,x11871))
% 1.87/2.01 [1189]~P6(a36,f2(a36),x11891)+P5(a36,f4(a36),x11891)+~P5(a36,f2(a36),f21(a13,x11891))
% 1.87/2.01 [615]~P10(x6151)+~P77(x6151)+E(f21(f20(x6151),f2(x6151)),f4(x6151))
% 1.87/2.01 [738]E(x7381,f2(a36))+P6(a36,f2(a36),x7381)+E(f9(a36,x7381),f3(a36,f4(a36)))
% 1.87/2.01 [739]E(x7391,f2(a1))+P6(a1,f2(a1),x7391)+E(f9(a1,x7391),f3(a1,f4(a1)))
% 1.87/2.01 [1778]~P4(x17781)+~P37(x17781)+E(f17(x17781,f12(x17781,f8(a1,f8(a1,a10,a10),f4(a1)))),f12(x17781,f8(a1,f8(a1,a10,a10),f4(a1))))
% 1.87/2.01 [1832]~P9(x18321)+~P37(x18321)+P6(x18321,f2(x18321),f18(x18321,f4(x18321),f12(x18321,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [786]E(x7861,x7862)+P6(a1,x7862,x7861)+P6(a1,x7861,x7862)
% 1.87/2.01 [788]E(x7881,x7882)+P6(a37,x7882,x7881)+P6(a37,x7881,x7882)
% 1.87/2.01 [868]E(x8681,x8682)+P6(a36,x8681,x8682)+~P5(a36,x8681,x8682)
% 1.87/2.01 [869]E(x8691,x8692)+P6(a1,x8691,x8692)+~P5(a1,x8691,x8692)
% 1.87/2.01 [872]E(x8721,x8722)+P6(a37,x8721,x8722)+~P5(a37,x8721,x8722)
% 1.87/2.01 [938]E(x9381,x9382)+~P5(a36,x9382,x9381)+~P5(a36,x9381,x9382)
% 1.87/2.01 [939]E(x9391,x9392)+~P5(a1,x9392,x9391)+~P5(a1,x9391,x9392)
% 1.87/2.01 [940]E(x9401,x9402)+~P5(a37,x9402,x9401)+~P5(a37,x9401,x9402)
% 1.87/2.01 [575]~P74(x5751)+P8(x5751,x5752)+~E(x5752,f2(x5751))
% 1.87/2.01 [577]~P21(x5771)+~E(x5772,f2(x5771))+E(f3(x5771,x5772),x5772)
% 1.87/2.01 [586]~P22(x5861)+~E(f2(x5861),x5862)+E(f3(x5861,x5862),f2(x5861))
% 1.87/2.01 [587]~P50(x5871)+~E(x5872,f2(x5871))+E(f17(x5871,x5872),f2(x5871))
% 1.87/2.01 [588]~P3(x5881)+~E(x5882,f4(x5881))+E(f17(x5881,x5882),f4(x5881))
% 1.87/2.01 [589]~P52(x5891)+~E(x5892,f2(x5891))+E(f9(x5891,x5892),f2(x5891))
% 1.87/2.01 [590]~P47(x5901)+~E(x5902,f2(x5901))+E(f9(x5901,x5902),f2(x5901))
% 1.87/2.01 [591]~P31(x5911)+~E(x5912,f2(x5911))+E(f9(x5911,x5912),f2(x5911))
% 1.87/2.01 [592]~P22(x5921)+~E(x5922,f2(x5921))+E(f3(x5921,x5922),f2(x5921))
% 1.87/2.01 [594]~P74(x5942)+~P8(x5942,x5941)+E(x5941,f2(x5942))
% 1.87/2.01 [596]~P21(x5962)+~E(f3(x5962,x5961),x5961)+E(x5961,f2(x5962))
% 1.87/2.01 [604]~P49(x6042)+~E(f17(x6042,x6041),f2(x6042))+E(x6041,f2(x6042))
% 1.87/2.01 [605]~P50(x6052)+~E(f17(x6052,x6051),f2(x6052))+E(x6051,f2(x6052))
% 1.87/2.01 [606]~P52(x6062)+~E(f9(x6062,x6061),f2(x6062))+E(x6061,f2(x6062))
% 1.87/2.01 [607]~P47(x6072)+~E(f9(x6072,x6071),f2(x6072))+E(x6071,f2(x6072))
% 1.87/2.01 [608]~P22(x6082)+~E(f3(x6082,x6081),f2(x6082))+E(x6081,f2(x6082))
% 1.87/2.01 [609]~P3(x6092)+~E(f17(x6092,x6091),f4(x6092))+E(x6091,f4(x6092))
% 1.87/2.01 [610]~P22(x6101)+~E(f3(x6101,x6102),f2(x6101))+E(f2(x6101),x6102)
% 1.87/2.01 [677]~E(x6772,f2(a37))+~E(x6771,f2(a37))+E(f8(a37,x6771,x6772),f2(a37))
% 1.87/2.01 [688]~P49(x6882)+E(f18(x6882,x6881,x6881),f4(x6882))+E(x6881,f2(x6882))
% 1.87/2.01 [689]~P50(x6892)+E(f18(x6892,x6891,x6891),f4(x6892))+E(x6891,f2(x6892))
% 1.87/2.01 [698]~P50(x6981)+~E(x6982,f2(x6981))+E(f18(x6981,x6982,x6982),f2(x6981))
% 1.87/2.01 [699]~P21(x6991)+~E(x6992,f2(x6991))+E(f8(x6991,x6992,x6992),f2(x6991))
% 1.87/2.01 [714]~P17(x7141)+P6(x7141,x7142,f2(x7141))+E(f5(x7141,x7142),x7142)
% 1.87/2.01 [758]~P52(x7581)+P6(x7581,f2(x7581),x7582)+~E(f9(x7581,x7582),f4(x7581))
% 1.87/2.01 [772]~P21(x7722)+~E(f8(x7722,x7721,x7721),f2(x7722))+E(x7721,f2(x7722))
% 1.87/2.01 [821]~P52(x8211)+~P6(x8211,f2(x8211),x8212)+E(f9(x8211,x8212),f4(x8211))
% 1.87/2.01 [838]~P29(x8381)+~P6(x8381,x8382,f2(x8381))+E(f5(x8381,x8382),f3(x8381,x8382))
% 1.87/2.01 [839]~P29(x8391)+~P5(x8391,x8392,f2(x8391))+E(f5(x8391,x8392),f3(x8391,x8392))
% 1.87/2.01 [840]~P17(x8401)+~P6(x8401,x8402,f2(x8401))+E(f5(x8401,x8402),f3(x8401,x8402))
% 1.87/2.01 [995]~P52(x9951)+~P6(x9951,x9952,f2(x9951))+P6(x9951,x9952,f3(x9951,x9952))
% 1.87/2.01 [996]~P21(x9961)+~P5(x9961,x9962,f2(x9961))+P5(x9961,x9962,f3(x9961,x9962))
% 1.87/2.01 [997]~P21(x9971)+~P6(x9971,f2(x9971),x9972)+P6(x9971,f3(x9971,x9972),x9972)
% 1.87/2.01 [998]~P21(x9981)+~P5(x9981,f2(x9981),x9982)+P5(x9981,f3(x9981,x9982),x9982)
% 1.87/2.01 [1000]~P28(x10001)+~P6(x10001,x10002,f2(x10001))+P6(x10001,f2(x10001),f3(x10001,x10002))
% 1.87/2.01 [1001]~P28(x10011)+~P5(x10011,x10012,f2(x10011))+P5(x10011,f2(x10011),f3(x10011,x10012))
% 1.87/2.01 [1002]~P2(x10021)+~P6(x10021,f2(x10021),x10022)+P6(x10021,f2(x10021),f17(x10021,x10022))
% 1.87/2.01 [1003]~P9(x10031)+~P6(x10031,f2(x10031),x10032)+P6(x10031,f2(x10031),f17(x10031,x10032))
% 1.87/2.01 [1004]~P52(x10041)+~P6(x10041,f2(x10041),x10042)+P6(x10041,f2(x10041),f9(x10041,x10042))
% 1.87/2.01 [1005]~P9(x10051)+~P5(x10051,f2(x10051),x10052)+P5(x10051,f2(x10051),f17(x10051,x10052))
% 1.87/2.01 [1006]~P2(x10061)+~P6(x10061,x10062,f2(x10061))+P6(x10061,f17(x10061,x10062),f2(x10061))
% 1.87/2.01 [1007]~P9(x10071)+~P6(x10071,x10072,f2(x10071))+P6(x10071,f17(x10071,x10072),f2(x10071))
% 1.87/2.01 [1008]~P9(x10081)+~P5(x10081,x10082,f2(x10081))+P6(x10081,f17(x10081,x10082),f4(x10081))
% 1.87/2.01 [1009]~P52(x10091)+~P6(x10091,x10092,f2(x10091))+P6(x10091,f9(x10091,x10092),f2(x10091))
% 1.87/2.01 [1010]~P9(x10101)+~P5(x10101,x10102,f2(x10101))+P5(x10101,f17(x10101,x10102),f2(x10101))
% 1.87/2.01 [1011]~P9(x10111)+~P5(x10111,x10112,f2(x10111))+P5(x10111,f17(x10111,x10112),f4(x10111))
% 1.87/2.01 [1012]~P9(x10121)+~P6(x10121,f4(x10121),x10122)+P6(x10121,f17(x10121,x10122),f4(x10121))
% 1.87/2.01 [1013]~P28(x10131)+~P6(x10131,f2(x10131),x10132)+P6(x10131,f3(x10131,x10132),f2(x10131))
% 1.87/2.01 [1014]~P9(x10141)+~P5(x10141,f4(x10141),x10142)+P5(x10141,f17(x10141,x10142),f4(x10141))
% 1.87/2.01 [1015]~P28(x10151)+~P5(x10151,f2(x10151),x10152)+P5(x10151,f3(x10151,x10152),f2(x10151))
% 1.87/2.01 [1021]~P52(x10211)+~P6(x10211,x10212,f3(x10211,x10212))+P6(x10211,x10212,f2(x10211))
% 1.87/2.01 [1022]~P21(x10221)+~P5(x10221,x10222,f3(x10221,x10222))+P5(x10221,x10222,f2(x10221))
% 1.87/2.01 [1023]~P21(x10231)+~P6(x10231,f3(x10231,x10232),x10232)+P6(x10231,f2(x10231),x10232)
% 1.87/2.01 [1024]~P21(x10241)+~P5(x10241,f3(x10241,x10242),x10242)+P5(x10241,f2(x10241),x10242)
% 1.87/2.01 [1045]~P28(x10451)+~P6(x10451,f2(x10451),f3(x10451,x10452))+P6(x10451,x10452,f2(x10451))
% 1.87/2.01 [1046]~P9(x10461)+~P6(x10461,f4(x10461),f17(x10461,x10462))+P6(x10461,x10462,f4(x10461))
% 1.87/2.01 [1047]~P28(x10471)+~P5(x10471,f2(x10471),f3(x10471,x10472))+P5(x10471,x10472,f2(x10471))
% 1.87/2.01 [1048]~P9(x10481)+~P5(x10481,f4(x10481),f17(x10481,x10482))+P5(x10481,x10482,f4(x10481))
% 1.87/2.01 [1049]~P9(x10491)+~P6(x10491,f17(x10491,x10492),f2(x10491))+P6(x10491,x10492,f2(x10491))
% 1.87/2.01 [1050]~P52(x10501)+~P6(x10501,f9(x10501,x10502),f2(x10501))+P6(x10501,x10502,f2(x10501))
% 1.87/2.01 [1051]~P9(x10511)+~P5(x10511,f17(x10511,x10512),f2(x10511))+P5(x10511,x10512,f2(x10511))
% 1.87/2.01 [1052]~P9(x10521)+~P6(x10521,f2(x10521),f17(x10521,x10522))+P6(x10521,f2(x10521),x10522)
% 1.87/2.01 [1053]~P9(x10531)+~P6(x10531,f4(x10531),f17(x10531,x10532))+P6(x10531,f2(x10531),x10532)
% 1.87/2.01 [1054]~P9(x10541)+~P5(x10541,f4(x10541),f17(x10541,x10542))+P6(x10541,f2(x10541),x10542)
% 1.87/2.01 [1055]~P52(x10551)+~P6(x10551,f2(x10551),f9(x10551,x10552))+P6(x10551,f2(x10551),x10552)
% 1.87/2.01 [1056]~P9(x10561)+~P5(x10561,f2(x10561),f17(x10561,x10562))+P5(x10561,f2(x10561),x10562)
% 1.87/2.01 [1057]~P28(x10571)+~P6(x10571,f3(x10571,x10572),f2(x10571))+P6(x10571,f2(x10571),x10572)
% 1.87/2.01 [1058]~P28(x10581)+~P5(x10581,f3(x10581,x10582),f2(x10581))+P5(x10581,f2(x10581),x10582)
% 1.87/2.01 [1179]P5(a1,x11791,x11792)+P5(a1,x11791,a10)+~P5(a37,f12(a37,x11791),f12(a37,x11792))
% 1.87/2.01 [1181]~P6(a1,x11811,x11812)+~P6(a1,a10,x11812)+P6(a37,f12(a37,x11811),f12(a37,x11812))
% 1.87/2.01 [1190]~P21(x11901)+~P6(x11901,f2(x11901),x11902)+P6(x11901,f2(x11901),f8(x11901,x11902,x11902))
% 1.87/2.01 [1192]~P21(x11921)+~P5(x11921,f2(x11921),x11922)+P5(x11921,f2(x11921),f8(x11921,x11922,x11922))
% 1.87/2.01 [1195]~P52(x11951)+~P6(x11951,x11952,f2(x11951))+P6(x11951,f8(x11951,x11952,x11952),f2(x11951))
% 1.87/2.01 [1196]~P21(x11961)+~P6(x11961,x11962,f2(x11961))+P6(x11961,f8(x11961,x11962,x11962),f2(x11961))
% 1.87/2.01 [1197]~P21(x11971)+~P5(x11971,x11972,f2(x11971))+P5(x11971,f8(x11971,x11972,x11972),f2(x11971))
% 1.87/2.01 [1218]~P6(a1,x12182,x12181)+P6(a1,a10,x12181)+~P6(a37,f12(a37,x12182),f12(a37,x12181))
% 1.87/2.01 [1251]E(x12511,f2(a37))+P6(a37,f2(a37),x12512)+~P6(a37,f2(a37),f19(a37,x12512,x12511))
% 1.87/2.01 [1276]~P52(x12761)+~P6(x12761,f8(x12761,x12762,x12762),f2(x12761))+P6(x12761,x12762,f2(x12761))
% 1.87/2.01 [1277]~P21(x12771)+~P6(x12771,f8(x12771,x12772,x12772),f2(x12771))+P6(x12771,x12772,f2(x12771))
% 1.87/2.01 [1278]~P21(x12781)+~P5(x12781,f8(x12781,x12782,x12782),f2(x12781))+P5(x12781,x12782,f2(x12781))
% 1.87/2.01 [1279]~P21(x12791)+~P6(x12791,f2(x12791),f8(x12791,x12792,x12792))+P6(x12791,f2(x12791),x12792)
% 1.87/2.01 [1280]~P21(x12801)+~P5(x12801,f2(x12801),f8(x12801,x12802,x12802))+P5(x12801,f2(x12801),x12802)
% 1.87/2.01 [1281]~P5(a36,x12811,f2(a36))+~P5(a36,x12812,f2(a36))+P5(a36,f2(a36),f18(a36,x12811,x12812))
% 1.87/2.01 [1282]~P5(a36,x12822,f2(a36))+~P5(a36,f2(a36),x12822)+P5(a36,f2(a36),f18(a36,x12821,x12822))
% 1.87/2.01 [1283]~P5(a36,x12831,f2(a36))+~P5(a36,f2(a36),x12831)+P5(a36,f2(a36),f18(a36,x12831,x12832))
% 1.87/2.01 [1284]~P5(a36,f2(a36),x12842)+~P5(a36,f2(a36),x12841)+P5(a36,f2(a36),f18(a36,x12841,x12842))
% 1.87/2.01 [1285]~P5(a1,f2(a1),x12852)+~P5(a1,f2(a1),x12851)+P5(a1,f2(a1),f8(a1,x12851,x12852))
% 1.87/2.01 [1354]P5(a36,x13541,f2(a36))+P5(a36,f2(a36),x13542)+~P5(a36,f2(a36),f18(a36,x13542,x13541))
% 1.87/2.01 [1355]P5(a36,x13551,f2(a36))+P5(a36,f2(a36),x13552)+~P5(a36,f2(a36),f18(a36,x13551,x13552))
% 1.87/2.01 [1356]P6(a37,f2(a37),x13561)+P6(a37,f2(a37),x13562)+~P6(a37,f2(a37),f8(a37,x13562,x13561))
% 1.87/2.01 [628]~E(x6282,f4(a37))+~E(x6281,f4(a37))+E(f21(f7(a37,x6281),x6282),f4(a37))
% 1.87/2.01 [629]~P10(x6291)+~P77(x6291)+~E(f21(f20(x6291),x6292),f2(x6291))
% 1.87/2.01 [630]~P49(x6302)+E(x6301,f2(x6302))+E(f17(x6302,f17(x6302,x6301)),x6301)
% 1.87/2.01 [651]~P70(x6511)+~E(x6512,f4(x6511))+E(f21(f7(x6511,x6512),x6512),f4(x6511))
% 1.87/2.01 [676]E(x6761,f4(a37))+E(x6762,f2(a37))+~E(f21(f7(a37,x6762),x6761),x6762)
% 1.87/2.01 [687]E(x6871,f2(a37))+E(x6872,f2(a37))+~E(f21(f7(a37,x6872),x6871),f2(a37))
% 1.87/2.01 [712]~P49(x7122)+E(x7121,f2(x7122))+E(f21(f7(x7122,x7121),f17(x7122,x7121)),f4(x7122))
% 1.87/2.01 [717]~P70(x7171)+~E(x7172,f3(x7171,f4(x7171)))+E(f21(f7(x7171,x7172),x7172),f4(x7171))
% 1.87/2.01 [752]~P49(x7522)+E(x7521,f2(x7522))+E(f17(x7522,f3(x7522,x7521)),f3(x7522,f17(x7522,x7521)))
% 1.87/2.01 [755]~P3(x7551)+~P37(x7551)+E(f18(x7551,x7552,f12(x7551,a10)),f2(x7551))
% 1.87/2.01 [822]~P52(x8221)+P6(x8221,x8222,f2(x8221))+~E(f9(x8221,x8222),f3(x8221,f4(x8221)))
% 1.87/2.01 [862]~P52(x8621)+~P6(x8621,x8622,f2(x8621))+E(f9(x8621,x8622),f3(x8621,f4(x8621)))
% 1.87/2.01 [902]E(x9021,f4(a1))+~P6(a1,f2(a1),x9022)+~E(f21(f7(a1,x9022),x9021),f4(a1))
% 1.87/2.01 [903]E(x9031,f4(a1))+~P6(a1,f2(a1),x9031)+~E(f21(f7(a1,x9031),x9032),f4(a1))
% 1.87/2.01 [1154]P6(a1,x11541,a10)+~P6(a1,x11542,a10)+E(f8(a37,f12(a37,x11541),f12(a37,x11542)),f12(a37,x11541))
% 1.87/2.01 [1243]~P6(a36,f2(a36),x12432)+~P6(a36,f2(a36),x12431)+P6(a36,f2(a36),f21(f7(a36,x12431),x12432))
% 1.87/2.01 [1244]~P6(a37,f2(a37),x12442)+~P6(a37,f2(a37),x12441)+P6(a37,f2(a37),f21(f7(a37,x12441),x12442))
% 1.87/2.01 [1245]~P5(a1,f2(a1),x12452)+~P5(a1,f2(a1),x12451)+P5(a1,f2(a1),f21(f7(a1,x12451),x12452))
% 1.87/2.01 [1246]~P10(x12461)+~P77(x12461)+P7(x12461,f20(x12461),x12462,f21(f20(x12461),x12462))
% 1.87/2.01 [1252]E(x12521,x12522)+P6(a1,x12521,x12522)+~P6(a1,x12521,f8(a1,x12522,f4(a1)))
% 1.87/2.01 [1255]P6(a1,x12551,a10)+P6(a1,x12552,a10)+E(f8(a37,f12(a37,x12551),f12(a37,x12552)),f12(a37,f8(a1,x12551,x12552)))
% 1.87/2.01 [784]~P4(x7842)+E(x7841,f2(x7842))+E(f21(f7(x7842,f17(x7842,x7841)),x7841),f4(x7842))
% 1.87/2.01 [785]~P49(x7852)+E(x7851,f2(x7852))+E(f21(f7(x7852,f17(x7852,x7851)),x7851),f4(x7852))
% 1.87/2.01 [794]~P10(x7941)+~P77(x7941)+E(f17(x7941,f21(f20(x7941),x7942)),f21(f20(x7941),f3(x7941,x7942)))
% 1.87/2.01 [1079]~E(x10792,f2(a36))+~E(x10791,f2(a36))+E(f8(a36,f21(f7(a36,x10791),x10791),f21(f7(a36,x10792),x10792)),f2(a36))
% 1.87/2.01 [1335]~P6(a36,f2(a36),x13352)+~P6(a36,f2(a36),x13351)+E(f8(a36,f21(a13,x13351),f21(a13,x13352)),f21(a13,f21(f7(a36,x13351),x13352)))
% 1.87/2.01 [1349]~P37(x13491)+~E(f12(x13491,x13492),f2(x13491))+P8(x13491,f12(x13491,f8(a1,x13492,f3(a1,a10))))
% 1.87/2.01 [1384]~P37(x13841)+~E(f12(x13841,x13842),f2(x13841))+P8(x13841,f12(x13841,f8(a1,a10,f3(a1,x13842))))
% 1.87/2.01 [1609]~P37(x16091)+E(f12(x16091,x16092),f2(x16091))+~P8(x16091,f12(x16091,f8(a1,x16092,f3(a1,a10))))
% 1.87/2.01 [1612]~P37(x16121)+E(f12(x16121,x16122),f2(x16121))+~P8(x16121,f12(x16121,f8(a1,a10,f3(a1,x16122))))
% 1.87/2.01 [1785]~P38(x17851)+~P37(x17851)+~P8(x17851,f12(x17851,f8(a1,f8(a1,x17852,x17852),f4(a1))))
% 1.87/2.01 [1803]~P37(x18031)+~E(f12(x18031,x18032),f4(x18031))+P8(x18031,f12(x18031,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f3(a1,x18032))))
% 1.87/2.01 [1805]~P37(x18051)+E(f12(x18051,x18052),f4(x18051))+~P8(x18051,f12(x18051,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f3(a1,x18052))))
% 1.87/2.01 [1717]~P4(x17171)+~P37(x17171)+E(f18(x17171,x17172,f12(x17171,f8(a1,f8(a1,a10,a10),f4(a1)))),x17172)
% 1.87/2.01 [1808]~P70(x18081)+~E(x18082,f2(x18081))+E(f19(x18081,x18082,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f2(x18081))
% 1.87/2.01 [1809]~P70(x18091)+~E(x18092,f4(x18091))+E(f19(x18091,x18092,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f4(x18091))
% 1.87/2.01 [1810]~P70(x18101)+~E(x18102,f3(x18101,f4(x18101)))+E(f19(x18101,x18102,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f4(x18101))
% 1.87/2.01 [1814]~P37(x18141)+~E(f12(x18141,x18142),f4(x18141))+P8(x18141,f12(x18141,f8(a1,x18142,f3(a1,f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1824]E(f21(a14,x18241),x18242)+~P5(a36,f2(a36),x18242)+~E(f19(a36,x18242,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18241)
% 1.87/2.01 [1825]~P37(x18251)+E(f12(x18251,x18252),f4(x18251))+~P8(x18251,f12(x18251,f8(a1,x18252,f3(a1,f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1831]~P52(x18312)+E(x18311,f2(x18312))+P6(x18312,f2(x18312),f19(x18312,x18311,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1841]~P52(x18412)+~E(x18411,f2(x18412))+~P6(x18412,f2(x18412),f19(x18412,x18411,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1847]~E(x18472,f2(a36))+~E(x18471,f2(a36))+E(f8(a36,f19(a36,x18471,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x18472,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(a36))
% 1.87/2.01 [667]~E(x6672,x6673)+~P34(x6671)+P5(x6671,x6672,x6673)
% 1.87/2.01 [669]~E(x6692,x6693)+~P41(x6691)+P5(x6691,x6692,x6693)
% 1.87/2.01 [764]~P6(x7643,x7641,x7642)+~E(x7641,x7642)+~P35(x7643)
% 1.87/2.01 [765]~P6(x7653,x7651,x7652)+~E(x7651,x7652)+~P41(x7653)
% 1.87/2.01 [805]P5(x8051,x8053,x8052)+~P35(x8051)+P6(x8051,x8052,x8053)
% 1.87/2.01 [807]P5(x8071,x8073,x8072)+~P35(x8071)+P5(x8071,x8072,x8073)
% 1.87/2.01 [887]~P34(x8871)+~P6(x8871,x8872,x8873)+P5(x8871,x8872,x8873)
% 1.87/2.01 [889]~P41(x8891)+~P6(x8891,x8892,x8893)+P5(x8891,x8892,x8893)
% 1.87/2.01 [953]~P6(x9531,x9533,x9532)+~P34(x9531)+~P6(x9531,x9532,x9533)
% 1.87/2.01 [954]~P5(x9541,x9543,x9542)+~P34(x9541)+~P6(x9541,x9542,x9543)
% 1.87/2.01 [955]~P6(x9551,x9553,x9552)+~P35(x9551)+~P6(x9551,x9552,x9553)
% 1.87/2.01 [958]~P5(x9581,x9583,x9582)+~P35(x9581)+~P6(x9581,x9582,x9583)
% 1.87/2.01 [959]~P6(x9591,x9593,x9592)+~P41(x9591)+~P6(x9591,x9592,x9593)
% 1.87/2.01 [1100]~P5(a36,x11001,x11003)+P5(a36,x11001,x11002)+~P5(a36,x11003,x11002)
% 1.87/2.01 [1101]~P5(a1,x11011,x11013)+P5(a1,x11011,x11012)+~P5(a1,x11013,x11012)
% 1.87/2.01 [1102]~P5(a37,x11021,x11023)+P5(a37,x11021,x11022)+~P5(a37,x11023,x11022)
% 1.87/2.01 [619]~P22(x6192)+~E(x6193,f3(x6192,x6191))+E(x6191,f3(x6192,x6193))
% 1.87/2.01 [621]~P22(x6211)+~E(f3(x6211,x6213),x6212)+E(f3(x6211,x6212),x6213)
% 1.87/2.01 [632]~P50(x6323)+E(x6321,x6322)+~E(f17(x6323,x6321),f17(x6323,x6322))
% 1.87/2.01 [633]~P22(x6333)+E(x6331,x6332)+~E(f3(x6333,x6331),f3(x6333,x6332))
% 1.87/2.01 [634]~P39(x6343)+E(x6341,x6342)+~E(f3(x6343,x6341),f3(x6343,x6342))
% 1.87/2.01 [690]~P76(x6901)+~E(x6903,f2(x6901))+E(f8(x6901,x6902,x6903),x6902)
% 1.87/2.01 [742]~P22(x7421)+~E(x7423,f3(x7421,x7422))+E(f8(x7421,x7422,x7423),f2(x7421))
% 1.87/2.01 [743]~P22(x7431)+~E(x7432,f3(x7431,x7433))+E(f8(x7431,x7432,x7433),f2(x7431))
% 1.87/2.01 [767]~P76(x7672)+~E(f8(x7672,x7673,x7671),x7673)+E(x7671,f2(x7672))
% 1.87/2.01 [773]~P70(x7732)+~E(f19(x7732,x7731,x7733),f2(x7732))+E(x7731,f2(x7732))
% 1.87/2.01 [795]~P22(x7952)+~E(f8(x7952,x7953,x7951),f2(x7952))+E(x7951,f3(x7952,x7953))
% 1.87/2.01 [796]~P22(x7962)+~E(f8(x7962,x7961,x7963),f2(x7962))+E(x7961,f3(x7962,x7963))
% 1.87/2.01 [797]~P22(x7971)+~E(f8(x7971,x7972,x7973),f2(x7971))+E(f3(x7971,x7972),x7973)
% 1.87/2.01 [1032]~P28(x10321)+~P6(x10321,x10323,x10322)+P6(x10321,f3(x10321,x10322),f3(x10321,x10323))
% 1.87/2.01 [1034]~P28(x10341)+~P5(x10341,x10343,x10342)+P5(x10341,f3(x10341,x10342),f3(x10341,x10343))
% 1.87/2.01 [1036]~P39(x10361)+~P5(x10361,x10363,x10362)+P5(x10361,f3(x10361,x10362),f3(x10361,x10363))
% 1.87/2.01 [1083]~P28(x10831)+~P6(x10831,x10833,f3(x10831,x10832))+P6(x10831,x10832,f3(x10831,x10833))
% 1.87/2.01 [1085]~P28(x10851)+~P5(x10851,x10853,f3(x10851,x10852))+P5(x10851,x10852,f3(x10851,x10853))
% 1.87/2.01 [1087]~P28(x10871)+~P6(x10871,f3(x10871,x10873),x10872)+P6(x10871,f3(x10871,x10872),x10873)
% 1.87/2.01 [1089]~P28(x10891)+~P5(x10891,f3(x10891,x10893),x10892)+P5(x10891,f3(x10891,x10892),x10893)
% 1.87/2.01 [1111]~P9(x11111)+P5(x11111,x11112,x11113)+P6(x11111,f2(x11111),f29(x11113,x11112,x11111))
% 1.87/2.01 [1112]~P2(x11121)+P5(x11121,x11122,x11123)+P6(x11121,f2(x11121),f31(x11123,x11122,x11121))
% 1.87/2.01 [1113]~P9(x11131)+P5(x11131,x11132,x11133)+P6(x11131,f29(x11133,x11132,x11131),f4(x11131))
% 1.87/2.01 [1114]~P28(x11141)+P6(x11141,x11142,x11143)+~P6(x11141,f3(x11141,x11143),f3(x11141,x11142))
% 1.87/2.01 [1115]~P28(x11151)+P5(x11151,x11152,x11153)+~P5(x11151,f3(x11151,x11153),f3(x11151,x11152))
% 1.87/2.01 [1116]~P39(x11161)+P5(x11161,x11162,x11163)+~P5(x11161,f3(x11161,x11163),f3(x11161,x11162))
% 1.87/2.01 [1191]~P51(x11911)+~P6(x11911,f2(x11911),x11912)+P6(x11911,f2(x11911),f19(x11911,x11912,x11913))
% 1.87/2.01 [1193]~P51(x11931)+~P5(x11931,f2(x11931),x11932)+P5(x11931,f2(x11931),f19(x11931,x11932,x11933))
% 1.87/2.01 [1194]~P51(x11941)+~P5(x11941,f4(x11941),x11942)+P5(x11941,f4(x11941),f19(x11941,x11942,x11943))
% 1.87/2.01 [1619]P6(a37,x16191,x16192)+~P6(a37,f19(a37,x16193,x16191),f19(a37,x16193,x16192))+~P6(a37,f2(a37),x16193)
% 1.87/2.01 [1657]~P7(a36,x16573,x16572,x16571)+~P6(a36,x16571,f2(a36))+P6(a36,f2(a36),f32(x16571,x16572,x16573))
% 1.87/2.01 [1658]~P7(a36,x16583,x16582,x16581)+~P6(a36,f2(a36),x16581)+P6(a36,f2(a36),f33(x16581,x16582,x16583))
% 1.87/2.01 [649]~P63(x6491)+~E(x6493,f2(x6491))+E(f21(f7(x6491,x6492),x6493),f2(x6491))
% 1.87/2.01 [650]~P63(x6501)+~E(x6502,f2(x6501))+E(f21(f7(x6501,x6502),x6503),f2(x6501))
% 1.87/2.01 [750]~P49(x7501)+E(f17(x7501,x7502),x7503)+~E(f21(f7(x7501,x7502),x7503),f4(x7501))
% 1.87/2.01 [790]~P54(x7901)+~E(x7902,f3(x7901,x7903))+E(f21(f7(x7901,x7902),x7902),f21(f7(x7901,x7903),x7903))
% 1.87/2.01 [823]E(x8231,x8232)+E(x8233,f2(a36))+~E(f21(f7(a36,x8233),x8231),f21(f7(a36,x8233),x8232))
% 1.87/2.01 [825]E(x8251,x8252)+E(x8253,f2(a37))+~E(f21(f7(a37,x8253),x8251),f21(f7(a37,x8253),x8252))
% 1.87/2.01 [826]E(x8261,x8262)+E(x8263,f2(a36))+~E(f21(f7(a36,x8261),x8263),f21(f7(a36,x8262),x8263))
% 1.87/2.01 [827]E(x8271,x8272)+E(x8273,f2(a37))+~E(f21(f7(a37,x8271),x8273),f21(f7(a37,x8272),x8273))
% 1.87/2.01 [941]~P49(x9412)+E(x9411,f2(x9412))+E(f18(x9412,f3(x9412,x9413),f3(x9412,x9411)),f18(x9412,x9413,x9411))
% 1.87/2.01 [1061]E(x10611,x10612)+~P6(a37,f2(a37),x10613)+~E(f21(f7(a37,x10613),x10611),f21(f7(a37,x10613),x10612))
% 1.87/2.01 [1080]~P49(x10802)+E(x10801,f2(x10802))+E(f18(x10802,x10803,f3(x10802,x10801)),f3(x10802,f18(x10802,x10803,x10801)))
% 1.87/2.01 [1081]~P49(x10812)+E(x10811,f2(x10812))+E(f19(x10812,f17(x10812,x10811),x10813),f17(x10812,f19(x10812,x10811,x10813)))
% 1.87/2.01 [1242]~P9(x12421)+~P6(x12421,f2(x12421),x12423)+E(f18(x12421,f5(x12421,x12422),x12423),f5(x12421,f18(x12421,x12422,x12423)))
% 1.87/2.01 [1385]~P6(a36,x13851,x13853)+~P6(a36,f2(a36),x13852)+P6(a36,f21(f7(a36,x13851),x13852),f21(f7(a36,x13853),x13852))
% 1.87/2.01 [1386]~P6(a36,x13862,x13863)+~P6(a36,f2(a36),x13861)+P6(a36,f21(f7(a36,x13861),x13862),f21(f7(a36,x13861),x13863))
% 1.87/2.01 [1387]~P6(a1,x13872,x13873)+~P6(a1,f2(a1),x13871)+P6(a1,f21(f7(a1,x13871),x13872),f21(f7(a1,x13871),x13873))
% 1.87/2.01 [1391]~P6(a37,x13911,x13913)+~P6(a37,f2(a37),x13912)+P6(a37,f21(f7(a37,x13911),x13912),f21(f7(a37,x13913),x13912))
% 1.87/2.01 [1392]~P6(a37,x13922,x13923)+~P6(a37,f2(a37),x13921)+P6(a37,f21(f7(a37,x13921),x13922),f21(f7(a37,x13921),x13923))
% 1.87/2.01 [1393]~P5(a36,x13932,x13933)+~P6(a36,f2(a36),x13931)+P5(a36,f21(f7(a36,x13931),x13932),f21(f7(a36,x13931),x13933))
% 1.87/2.01 [1394]~P5(a36,x13941,x13943)+~P6(a36,f2(a36),x13942)+P5(a36,f21(f7(a36,x13941),x13942),f21(f7(a36,x13943),x13942))
% 1.87/2.01 [1425]E(x14251,f2(a36))+~P5(a36,x14252,f2(a36))+~P5(a36,f5(a36,x14251),f21(f7(a36,x14252),f5(a36,x14253)))
% 1.87/2.01 [1483]P6(a36,x14831,x14832)+~P6(a36,f2(a36),x14833)+~P6(a36,f21(f7(a36,x14831),x14833),f21(f7(a36,x14832),x14833))
% 1.87/2.01 [1485]P5(a36,x14851,x14852)+~P6(a36,f2(a36),x14853)+~P5(a36,f21(f7(a36,x14853),x14851),f21(f7(a36,x14853),x14852))
% 1.87/2.01 [1486]P5(a36,x14861,x14862)+~P6(a36,f2(a36),x14863)+~P5(a36,f21(f7(a36,x14861),x14863),f21(f7(a36,x14862),x14863))
% 1.87/2.01 [1488]P5(a37,x14881,x14882)+~P6(a37,f2(a37),x14883)+~P5(a37,f21(f7(a37,x14883),x14881),f21(f7(a37,x14883),x14882))
% 1.87/2.01 [1489]P5(a37,x14891,x14892)+~P6(a37,f2(a37),x14893)+~P5(a37,f21(f7(a37,x14891),x14893),f21(f7(a37,x14892),x14893))
% 1.87/2.01 [1495]~P51(x14951)+~P6(x14951,f4(x14951),x14952)+P6(x14951,f4(x14951),f21(f7(x14951,x14952),f19(x14951,x14952,x14953)))
% 1.87/2.01 [1622]~P51(x16221)+~P6(x16221,f4(x16221),x16222)+P6(x16221,f19(x16221,x16222,x16223),f21(f7(x16221,x16222),f19(x16221,x16222,x16223)))
% 1.87/2.01 [1667]~P2(x16671)+P5(x16671,x16672,x16673)+~P5(x16671,x16672,f8(x16671,x16673,f31(x16673,x16672,x16671)))
% 1.87/2.01 [1217]~P52(x12171)+~P5(x12171,f2(x12171),x12173)+E(f5(x12171,f21(f7(x12171,x12172),x12173)),f21(f7(x12171,f5(x12171,x12172)),x12173))
% 1.87/2.01 [1223]~P10(x12231)+~P77(x12231)+E(f21(f7(x12231,f21(f20(x12231),x12232)),f21(f20(x12231),x12233)),f21(f20(x12231),f8(x12231,x12232,x12233)))
% 1.87/2.01 [1325]~P55(x13252)+E(x13251,f2(x13252))+~E(f8(x13252,f21(f7(x13252,x13253),x13253),f21(f7(x13252,x13251),x13251)),f2(x13252))
% 1.87/2.01 [1326]~P55(x13262)+E(x13261,f2(x13262))+~E(f8(x13262,f21(f7(x13262,x13261),x13261),f21(f7(x13262,x13263),x13263)),f2(x13262))
% 1.87/2.01 [1407]~P37(x14071)+~E(f12(x14071,x14072),f12(x14071,x14073))+P8(x14071,f12(x14071,f8(a1,x14072,f3(a1,x14073))))
% 1.87/2.01 [1576]~P55(x15762)+E(x15761,f2(x15762))+P6(x15762,f2(x15762),f8(x15762,f21(f7(x15762,x15763),x15763),f21(f7(x15762,x15761),x15761)))
% 1.87/2.01 [1577]~P55(x15772)+E(x15771,f2(x15772))+P6(x15772,f2(x15772),f8(x15772,f21(f7(x15772,x15771),x15771),f21(f7(x15772,x15773),x15773)))
% 1.87/2.01 [1631]~P37(x16311)+E(f12(x16311,x16312),f12(x16311,x16313))+~P8(x16311,f12(x16311,f8(a1,x16312,f3(a1,x16313))))
% 1.87/2.01 [1724]~P2(x17241)+~P6(x17241,x17242,x17243)+P6(x17241,x17242,f18(x17241,f8(x17241,x17242,x17243),f8(x17241,f4(x17241),f4(x17241))))
% 1.87/2.01 [1725]~P2(x17251)+~P6(x17251,x17252,x17253)+P6(x17251,f18(x17251,f8(x17251,x17252,x17253),f8(x17251,f4(x17251),f4(x17251))),x17253)
% 1.87/2.01 [1735]~P55(x17352)+E(x17351,f2(x17352))+~P5(x17352,f8(x17352,f21(f7(x17352,x17353),x17353),f21(f7(x17352,x17351),x17351)),f2(x17352))
% 1.87/2.01 [1736]~P55(x17362)+E(x17361,f2(x17362))+~P5(x17362,f8(x17362,f21(f7(x17362,x17361),x17361),f21(f7(x17362,x17363),x17363)),f2(x17362))
% 1.87/2.01 [1771]~P9(x17711)+P5(x17711,x17712,x17713)+~P5(x17711,f21(f7(x17711,f29(x17713,x17712,x17711)),x17712),x17713)
% 1.87/2.01 [1854]~P52(x18542)+E(x18541,f2(x18542))+~E(f8(x18542,f19(x18542,x18543,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18542,x18541,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(x18542))
% 1.87/2.01 [1855]~P52(x18552)+E(x18551,f2(x18552))+~E(f8(x18552,f19(x18552,x18551,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18552,x18553,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(x18552))
% 1.87/2.01 [1862]~P52(x18622)+E(x18621,f2(x18622))+P6(x18622,f2(x18622),f8(x18622,f19(x18622,x18623,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18622,x18621,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))
% 1.87/2.01 [1863]~P52(x18632)+E(x18631,f2(x18632))+P6(x18632,f2(x18632),f8(x18632,f19(x18632,x18631,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18632,x18633,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))
% 1.87/2.01 [1870]~P52(x18702)+E(x18701,f2(x18702))+~P5(x18702,f8(x18702,f19(x18702,x18703,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18702,x18701,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(x18702))
% 1.87/2.01 [1871]~P52(x18712)+E(x18711,f2(x18712))+~P5(x18712,f8(x18712,f19(x18712,x18711,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18712,x18713,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(x18712))
% 1.87/2.01 [1866]~P52(x18662)+E(x18661,f2(x18662))+~P5(x18662,f19(x18662,x18661,f21(f7(a37,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),x18663)),f2(x18662))
% 1.87/2.01 [1875]~P6(a36,f5(a36,x18751),f18(a36,x18753,f21(a14,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))+~P6(a36,f5(a36,x18752),f18(a36,x18753,f21(a14,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))+P6(a36,f21(a14,f8(a36,f19(a36,x18751,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x18752,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),x18753)
% 1.87/2.01 [962]~P15(x9623)+E(x9621,x9622)+~E(f8(x9623,x9624,x9621),f8(x9623,x9624,x9622))
% 1.87/2.01 [963]~P16(x9633)+E(x9631,x9632)+~E(f8(x9633,x9634,x9631),f8(x9633,x9634,x9632))
% 1.87/2.01 [965]~P15(x9653)+E(x9651,x9652)+~E(f8(x9653,x9651,x9654),f8(x9653,x9652,x9654))
% 1.87/2.01 [1090]~P42(x10902)+~P6(f40(x10901,x10902),x10903,x10904)+P5(f40(x10901,x10902),x10903,x10904)
% 1.87/2.01 [1180]~P42(x11801)+~P5(f40(x11802,x11801),x11804,x11803)+~P6(f40(x11802,x11801),x11803,x11804)
% 1.87/2.01 [1241]~P6(a37,x12413,x12414)+P6(a37,x12411,x12412)+~E(f8(a37,x12413,x12412),f8(a37,x12411,x12414))
% 1.87/2.01 [1339]~P26(x13391)+~P6(x13391,x13393,x13394)+P6(x13391,f8(x13391,x13392,x13393),f8(x13391,x13392,x13394))
% 1.87/2.01 [1340]~P30(x13401)+~P6(x13401,x13403,x13404)+P6(x13401,f8(x13401,x13402,x13403),f8(x13401,x13402,x13404))
% 1.87/2.01 [1341]~P26(x13411)+~P6(x13411,x13412,x13414)+P6(x13411,f8(x13411,x13412,x13413),f8(x13411,x13414,x13413))
% 1.87/2.01 [1342]~P30(x13421)+~P6(x13421,x13422,x13424)+P6(x13421,f8(x13421,x13422,x13423),f8(x13421,x13424,x13423))
% 1.87/2.01 [1343]~P26(x13431)+~P5(x13431,x13433,x13434)+P5(x13431,f8(x13431,x13432,x13433),f8(x13431,x13432,x13434))
% 1.87/2.01 [1344]~P27(x13441)+~P5(x13441,x13443,x13444)+P5(x13441,f8(x13441,x13442,x13443),f8(x13441,x13442,x13444))
% 1.87/2.01 [1345]~P26(x13451)+~P5(x13451,x13452,x13454)+P5(x13451,f8(x13451,x13452,x13453),f8(x13451,x13454,x13453))
% 1.87/2.01 [1346]~P27(x13461)+~P5(x13461,x13462,x13464)+P5(x13461,f8(x13461,x13462,x13463),f8(x13461,x13464,x13463))
% 1.87/2.01 [1456]~P6(a1,x14561,x14563)+~P5(a1,x14562,x14564)+P6(a1,f8(a1,x14561,x14562),f8(a1,x14563,x14564))
% 1.87/2.01 [1457]~P6(a37,x14572,x14574)+~P6(a37,x14571,x14573)+P6(a37,f8(a37,x14571,x14572),f8(a37,x14573,x14574))
% 1.87/2.01 [1458]~P5(a37,x14582,x14584)+~P5(a37,x14581,x14583)+P5(a37,f8(a37,x14581,x14582),f8(a37,x14583,x14584))
% 1.87/2.01 [1542]~P26(x15421)+P6(x15421,x15422,x15423)+~P6(x15421,f8(x15421,x15424,x15422),f8(x15421,x15424,x15423))
% 1.87/2.01 [1544]~P26(x15441)+P6(x15441,x15442,x15443)+~P6(x15441,f8(x15441,x15442,x15444),f8(x15441,x15443,x15444))
% 1.87/2.01 [1546]~P26(x15461)+P5(x15461,x15462,x15463)+~P5(x15461,f8(x15461,x15464,x15462),f8(x15461,x15464,x15463))
% 1.87/2.01 [1548]~P26(x15481)+P5(x15481,x15482,x15483)+~P5(x15481,f8(x15481,x15482,x15484),f8(x15481,x15483,x15484))
% 1.87/2.01 [1357]~P5(a37,x13572,x13574)+~P5(a37,x13571,x13573)+P5(a37,f21(f7(a37,x13571),x13572),f21(f7(a37,x13573),x13574))
% 1.87/2.01 [1466]~P4(x14662)+E(x14661,f2(x14662))+E(f18(x14662,f19(x14662,x14663,x14664),f19(x14662,x14661,x14664)),f19(x14662,f18(x14662,x14663,x14661),x14664))
% 1.87/2.01 [1819]~P42(x18192)+P5(f40(x18191,x18192),x18193,x18194)+~P5(x18192,f21(x18193,f30(x18194,x18193,x18191,x18192)),f21(x18194,f30(x18194,x18193,x18191,x18192)))
% 1.87/2.01 [1200]~P3(x12002)+E(x12001,f2(x12002))+E(f18(x12002,f21(f7(x12002,x12003),x12001),f21(f7(x12002,x12004),x12001)),f18(x12002,x12003,x12004))
% 1.87/2.01 [1201]~P3(x12012)+E(x12011,f2(x12012))+E(f18(x12012,f21(f7(x12012,x12011),x12013),f21(f7(x12012,x12011),x12014)),f18(x12012,x12013,x12014))
% 1.87/2.01 [1650]~P73(x16501)+~P36(x16501)+E(f8(x16501,f21(f7(x16501,x16502),f12(x16501,x16503)),f21(f7(x16501,x16504),f12(x16501,x16503))),f21(f7(x16501,f8(x16501,x16502,x16504)),f12(x16501,x16503)))
% 1.87/2.01 [1572]~P3(x15722)+E(x15721,f2(x15722))+E(f18(x15722,f8(x15722,x15723,f21(f7(x15722,x15724),x15721)),x15721),f8(x15722,x15724,f18(x15722,x15723,x15721)))
% 1.87/2.01 [1573]~P4(x15732)+E(x15731,f2(x15732))+E(f18(x15732,f8(x15732,f21(f7(x15732,x15731),x15733),x15734),x15731),f8(x15732,x15733,f18(x15732,x15734,x15731)))
% 1.87/2.01 [1574]~P3(x15742)+E(x15741,f2(x15742))+E(f18(x15742,f8(x15742,x15743,f21(f7(x15742,x15744),x15741)),x15741),f8(x15742,f18(x15742,x15743,x15741),x15744))
% 1.87/2.01 [1575]~P4(x15752)+E(x15751,f2(x15752))+E(f18(x15752,f8(x15752,x15753,f21(f7(x15752,x15751),x15754)),x15751),f8(x15752,f18(x15752,x15753,x15751),x15754))
% 1.87/2.01 [1652]~P73(x16521)+~P36(x16521)+E(f8(x16521,f21(f7(x16521,f12(x16521,x16522)),x16523),f21(f7(x16521,f12(x16521,x16522)),x16524)),f21(f7(x16521,f12(x16521,x16522)),f8(x16521,x16523,x16524)))
% 1.87/2.01 [1845]E(x18451,x18452)+~P7(a36,x18453,f26(x18454,x18453,x18452,x18451),x18454)+E(f18(a36,f8(a36,f21(x18453,x18451),f21(x18453,x18452)),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f21(x18453,f18(a36,f8(a36,x18451,x18452),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))
% 1.87/2.01 [1151]~P42(x11511)+P5(x11511,f21(x11512,x11513),f21(x11514,x11513))+~P5(f40(x11515,x11511),x11512,x11514)
% 1.87/2.01 [1460]~E(x14602,x14604)+~P76(x14601)+E(f8(x14601,f21(f7(x14601,x14602),x14603),f21(f7(x14601,x14604),x14605)),f8(x14601,f21(f7(x14601,x14602),x14605),f21(f7(x14601,x14604),x14603)))
% 1.87/2.01 [1823]E(x18231,f4(a1))+E(x18231,f2(a1))+~P5(a1,f2(a1),x18231)+~P6(a1,x18231,f12(a1,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))
% 1.87/2.01 [831]~P31(x8312)+~P6(x8312,f2(x8312),x8311)+E(f9(x8312,x8311),f4(x8312))+E(x8311,f2(x8312))
% 1.87/2.01 [981]~P52(x9811)+~P37(x9811)+P6(x9811,f2(x9811),f12(x9811,x9812))+~P6(a1,a10,x9812)
% 1.87/2.01 [982]~P52(x9821)+~P37(x9821)+P5(x9821,f2(x9821),f12(x9821,x9822))+~P5(a1,a10,x9822)
% 1.87/2.01 [983]~P52(x9831)+~P37(x9831)+P6(x9831,f12(x9831,x9832),f2(x9831))+~P6(a1,x9832,a10)
% 1.87/2.01 [984]~P52(x9841)+~P37(x9841)+P5(x9841,f12(x9841,x9842),f2(x9841))+~P5(a1,x9842,a10)
% 1.87/2.01 [1040]~P37(x10402)+~P52(x10402)+~P6(x10402,f12(x10402,x10401),f2(x10402))+P6(a1,x10401,a10)
% 1.87/2.01 [1041]~P37(x10412)+~P52(x10412)+~P5(x10412,f12(x10412,x10411),f2(x10412))+P5(a1,x10411,a10)
% 1.87/2.01 [1042]~P37(x10422)+~P52(x10422)+~P6(x10422,f2(x10422),f12(x10422,x10421))+P6(a1,a10,x10421)
% 1.87/2.01 [1043]~P37(x10432)+~P52(x10432)+~P5(x10432,f2(x10432),f12(x10432,x10431))+P5(a1,a10,x10431)
% 1.87/2.01 [1075]~P2(x10752)+~P6(x10752,f17(x10752,x10751),f2(x10752))+P6(x10752,x10751,f2(x10752))+E(x10751,f2(x10752))
% 1.87/2.01 [1076]~P2(x10762)+~P6(x10762,f2(x10762),f17(x10762,x10761))+P6(x10762,f2(x10762),x10761)+E(x10761,f2(x10762))
% 1.87/2.01 [1095]E(x10951,x10952)+~E(f21(a13,x10951),f21(a13,x10952))+~P6(a36,f2(a36),x10952)+~P6(a36,f2(a36),x10951)
% 1.87/2.01 [1182]~P9(x11821)+P6(x11821,f4(x11821),x11822)+~P6(x11821,f17(x11821,x11822),f4(x11821))+P5(x11821,x11822,f2(x11821))
% 1.87/2.01 [1183]~P9(x11831)+P5(x11831,f4(x11831),x11832)+~P5(x11831,f17(x11831,x11832),f4(x11831))+P5(x11831,x11832,f2(x11831))
% 1.87/2.01 [1212]~P2(x12121)+~P6(x12121,x12122,f4(x12121))+~P6(x12121,f2(x12121),x12122)+P6(x12121,f4(x12121),f17(x12121,x12122))
% 1.87/2.01 [1213]~P9(x12131)+~P6(x12131,x12132,f4(x12131))+~P6(x12131,f2(x12131),x12132)+P6(x12131,f4(x12131),f17(x12131,x12132))
% 1.87/2.01 [1214]~P2(x12141)+~P5(x12141,x12142,f4(x12141))+~P6(x12141,f2(x12141),x12142)+P5(x12141,f4(x12141),f17(x12141,x12142))
% 1.87/2.01 [1215]~P9(x12151)+~P5(x12151,x12152,f4(x12151))+~P6(x12151,f2(x12151),x12152)+P5(x12151,f4(x12151),f17(x12151,x12152))
% 1.87/2.01 [1336]~P6(a36,x13361,x13362)+~P6(a36,f2(a36),x13362)+~P6(a36,f2(a36),x13361)+P6(a36,f21(a13,x13361),f21(a13,x13362))
% 1.87/2.01 [1337]~P5(a36,x13371,x13372)+~P6(a36,f2(a36),x13372)+~P6(a36,f2(a36),x13371)+P5(a36,f21(a13,x13371),f21(a13,x13372))
% 1.87/2.01 [1338]P7(a36,a14,x13381,x13382)+E(x13381,f2(a36))+P6(a36,x13381,f2(a36))+P6(a36,f2(a36),x13381)
% 1.87/2.01 [1401]P6(a36,x14011,x14012)+~P6(a36,f2(a36),x14012)+~P6(a36,f2(a36),x14011)+~P6(a36,f21(a13,x14011),f21(a13,x14012))
% 1.87/2.01 [1402]P5(a36,x14021,x14022)+~P6(a36,f2(a36),x14022)+~P6(a36,f2(a36),x14021)+~P5(a36,f21(a13,x14021),f21(a13,x14022))
% 1.87/2.01 [713]~P43(x7132)+~P75(x7132)+E(x7131,f2(a37))+E(f19(x7132,f2(x7132),x7131),f2(x7132))
% 1.87/2.01 [718]~P43(x7181)+~P75(x7181)+~E(x7182,f2(a37))+E(f19(x7181,f2(x7181),x7182),f4(x7181))
% 1.87/2.01 [769]~P70(x7692)+E(x7691,f4(x7692))+~E(f21(f7(x7692,x7691),x7691),f4(x7692))+E(x7691,f3(x7692,f4(x7692)))
% 1.87/2.01 [781]~P31(x7812)+P6(x7812,f2(x7812),x7811)+E(x7811,f2(x7812))+E(f9(x7812,x7811),f3(x7812,f4(x7812)))
% 1.87/2.01 [873]~E(x8732,f4(a1))+~E(x8731,f4(a1))+~P6(a1,f2(a1),x8731)+E(f21(f7(a1,x8731),x8732),f4(a1))
% 1.87/2.01 [1259]~P37(x12591)+~P38(x12591)+~P8(x12591,f12(x12591,x12592))+P8(x12591,f12(x12591,f8(a1,x12592,x12592)))
% 1.87/2.01 [1472]~P37(x14721)+~P38(x14721)+P8(x14721,f12(x14721,x14722))+~P8(x14721,f12(x14721,f8(a1,x14722,x14722)))
% 1.87/2.01 [1586]~P37(x15862)+~P52(x15862)+~P6(x15862,f12(x15862,x15861),f4(x15862))+P6(a1,x15861,f8(a1,f8(a1,a10,a10),f4(a1)))
% 1.87/2.01 [1587]~P37(x15872)+~P52(x15872)+~P5(x15872,f12(x15872,x15871),f4(x15872))+P5(a1,x15871,f8(a1,f8(a1,a10,a10),f4(a1)))
% 1.87/2.01 [1588]~P37(x15882)+~P52(x15882)+~P6(x15882,f4(x15882),f12(x15882,x15881))+P6(a1,f8(a1,f8(a1,a10,a10),f4(a1)),x15881)
% 1.87/2.01 [1589]~P37(x15892)+~P52(x15892)+~P5(x15892,f4(x15892),f12(x15892,x15891))+P5(a1,f8(a1,f8(a1,a10,a10),f4(a1)),x15891)
% 1.87/2.01 [1675]~P52(x16751)+~P37(x16751)+P6(x16751,f4(x16751),f12(x16751,x16752))+~P6(a1,f8(a1,f8(a1,a10,a10),f4(a1)),x16752)
% 1.87/2.01 [1676]~P52(x16761)+~P37(x16761)+P5(x16761,f4(x16761),f12(x16761,x16762))+~P5(a1,f8(a1,f8(a1,a10,a10),f4(a1)),x16762)
% 1.87/2.01 [1677]~P52(x16771)+~P37(x16771)+P6(x16771,f12(x16771,x16772),f4(x16771))+~P6(a1,x16772,f8(a1,f8(a1,a10,a10),f4(a1)))
% 1.87/2.01 [1678]~P52(x16781)+~P37(x16781)+P5(x16781,f12(x16781,x16782),f4(x16781))+~P5(a1,x16782,f8(a1,f8(a1,a10,a10),f4(a1)))
% 1.87/2.01 [1821]~P70(x18212)+E(x18211,f4(x18212))+E(x18211,f3(x18212,f4(x18212)))+~E(f19(x18212,x18211,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f4(x18212))
% 1.87/2.01 [1826]P7(a36,a14,x18261,x18262)+E(x18261,f2(a36))+P6(a36,x18261,f2(a36))+~E(x18262,f18(a36,f17(a36,f21(a14,x18261)),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1827]P7(a36,a14,x18271,x18272)+E(x18271,f2(a36))+P6(a36,f2(a36),x18271)+~E(x18272,f18(a36,f3(a36,f17(a36,f21(a14,x18271))),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1834]~P9(x18341)+~P37(x18341)+~P6(x18341,f2(x18341),x18342)+P6(x18341,f2(x18341),f18(x18341,x18342,f12(x18341,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1842]~P9(x18421)+~P37(x18421)+P6(x18421,f2(x18421),x18422)+~P6(x18421,f2(x18421),f18(x18421,x18422,f12(x18421,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1844]P7(a36,a14,x18441,x18442)+E(x18441,f2(a36))+~E(x18442,f18(a36,f3(a36,f17(a36,f21(a14,x18441))),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))+~E(x18442,f18(a36,f17(a36,f21(a14,x18441)),f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [809]P6(x8093,x8091,x8092)+~P52(x8093)+E(x8091,x8092)+P6(x8093,x8092,x8091)
% 1.87/2.01 [815]P6(x8153,x8151,x8152)+~P35(x8153)+E(x8151,x8152)+P6(x8153,x8152,x8151)
% 1.87/2.01 [818]P5(x8181,x8182,x8183)+~E(x8182,x8183)+~P35(x8181)+P6(x8181,x8182,x8183)
% 1.87/2.01 [893]~P41(x8933)+~P5(x8933,x8932,x8931)+E(x8931,x8932)+P6(x8933,x8932,x8931)
% 1.87/2.01 [895]~P35(x8953)+~P5(x8953,x8951,x8952)+E(x8951,x8952)+P6(x8953,x8951,x8952)
% 1.87/2.01 [901]~P41(x9013)+~P5(x9013,x9011,x9012)+E(x9011,x9012)+P6(x9013,x9011,x9012)
% 1.87/2.01 [979]~P5(x9793,x9792,x9791)+~P5(x9793,x9791,x9792)+E(x9791,x9792)+~P41(x9793)
% 1.87/2.01 [1044]P5(x10441,x10443,x10442)+~P34(x10441)+~P5(x10441,x10442,x10443)+P6(x10441,x10442,x10443)
% 1.87/2.01 [657]~P37(x6573)+~P38(x6573)+E(x6571,x6572)+~E(f12(x6573,x6571),f12(x6573,x6572))
% 1.87/2.01 [700]~E(x7003,x7001)+~P49(x7002)+E(f18(x7002,x7003,x7001),f4(x7002))+E(x7001,f2(x7002))
% 1.87/2.01 [777]~P49(x7773)+E(x7771,x7772)+~E(f18(x7773,x7771,x7772),f4(x7773))+E(x7772,f2(x7773))
% 1.87/2.01 [1059]~P52(x10591)+~P37(x10591)+~P6(a1,x10592,x10593)+P6(x10591,f12(x10591,x10592),f12(x10591,x10593))
% 1.87/2.01 [1060]~P52(x10601)+~P37(x10601)+~P5(a1,x10602,x10603)+P5(x10601,f12(x10601,x10602),f12(x10601,x10603))
% 1.87/2.01 [1131]~P37(x11313)+~P52(x11313)+~P6(x11313,f12(x11313,x11311),f12(x11313,x11312))+P6(a1,x11311,x11312)
% 1.87/2.01 [1132]~P37(x11323)+~P52(x11323)+~P5(x11323,f12(x11323,x11321),f12(x11323,x11322))+P5(a1,x11321,x11322)
% 1.87/2.01 [1225]~P2(x12251)+~P6(x12251,x12253,x12252)+~P6(x12251,x12252,f2(x12251))+P6(x12251,f17(x12251,x12252),f17(x12251,x12253))
% 1.87/2.01 [1226]~P2(x12261)+~P5(x12261,x12263,x12262)+~P6(x12261,x12262,f2(x12261))+P5(x12261,f17(x12261,x12262),f17(x12261,x12263))
% 1.87/2.01 [1227]~P2(x12271)+~P6(x12271,x12273,x12272)+~P6(x12271,f2(x12271),x12273)+P6(x12271,f17(x12271,x12272),f17(x12271,x12273))
% 1.87/2.01 [1228]~P2(x12281)+~P5(x12281,x12283,x12282)+~P6(x12281,f2(x12281),x12283)+P5(x12281,f17(x12281,x12282),f17(x12281,x12283))
% 1.87/2.01 [1260]~P2(x12601)+P6(x12601,x12602,x12603)+~P6(x12601,x12602,f2(x12601))+~P6(x12601,f17(x12601,x12603),f17(x12601,x12602))
% 1.87/2.01 [1261]~P2(x12611)+P5(x12611,x12612,x12613)+~P6(x12611,x12612,f2(x12611))+~P5(x12611,f17(x12611,x12613),f17(x12611,x12612))
% 1.87/2.01 [1262]~P2(x12621)+P6(x12621,x12622,x12623)+~P6(x12621,f2(x12621),x12623)+~P6(x12621,f17(x12621,x12623),f17(x12621,x12622))
% 1.87/2.01 [1263]~P2(x12631)+P5(x12631,x12632,x12633)+~P6(x12631,f2(x12631),x12633)+~P5(x12631,f17(x12631,x12633),f17(x12631,x12632))
% 1.87/2.01 [1334]~P51(x13341)+~P6(x13341,f4(x13341),x13342)+P6(x13341,f4(x13341),f19(x13341,x13342,x13343))+~P6(a37,f2(a37),x13343)
% 1.87/2.01 [1360]~P2(x13601)+~P6(x13601,x13603,f2(x13601))+~P6(x13601,x13602,f2(x13601))+P6(x13601,f2(x13601),f18(x13601,x13602,x13603))
% 1.87/2.01 [1361]~P9(x13611)+~P6(x13611,x13613,f2(x13611))+~P6(x13611,x13612,f2(x13611))+P6(x13611,f2(x13611),f18(x13611,x13612,x13613))
% 1.87/2.01 [1362]~P2(x13621)+~P6(x13621,x13623,f2(x13621))+~P5(x13621,x13622,f2(x13621))+P5(x13621,f2(x13621),f18(x13621,x13622,x13623))
% 1.87/2.01 [1363]~P9(x13631)+~P5(x13631,x13633,f2(x13631))+~P5(x13631,x13632,f2(x13631))+P5(x13631,f2(x13631),f18(x13631,x13632,x13633))
% 1.87/2.01 [1364]~P2(x13641)+~P6(x13641,f2(x13641),x13643)+~P6(x13641,f2(x13641),x13642)+P6(x13641,f2(x13641),f18(x13641,x13642,x13643))
% 1.87/2.01 [1365]~P9(x13651)+~P6(x13651,f2(x13651),x13653)+~P6(x13651,f2(x13651),x13652)+P6(x13651,f2(x13651),f18(x13651,x13652,x13653))
% 1.87/2.01 [1366]~P32(x13661)+~P6(x13661,f2(x13661),x13663)+~P6(x13661,f2(x13661),x13662)+P6(x13661,f2(x13661),f8(x13661,x13662,x13663))
% 1.87/2.01 [1369]~P2(x13691)+~P6(x13691,f2(x13691),x13693)+~P5(x13691,f2(x13691),x13692)+P5(x13691,f2(x13691),f18(x13691,x13692,x13693))
% 1.87/2.01 [1370]~P9(x13701)+~P5(x13701,f2(x13701),x13703)+~P5(x13701,f2(x13701),x13702)+P5(x13701,f2(x13701),f18(x13701,x13702,x13703))
% 1.87/2.01 [1372]~P32(x13721)+~P6(x13721,x13723,f2(x13721))+~P6(x13721,x13722,f2(x13721))+P6(x13721,f8(x13721,x13722,x13723),f2(x13721))
% 1.87/2.01 [1373]~P32(x13731)+~P6(x13731,x13733,f2(x13731))+~P5(x13731,x13732,f2(x13731))+P6(x13731,f8(x13731,x13732,x13733),f2(x13731))
% 1.87/2.01 [1374]~P32(x13741)+~P6(x13741,x13742,f2(x13741))+~P5(x13741,x13743,f2(x13741))+P6(x13741,f8(x13741,x13742,x13743),f2(x13741))
% 1.87/2.01 [1375]~P32(x13751)+~P5(x13751,x13753,f2(x13751))+~P5(x13751,x13752,f2(x13751))+P5(x13751,f8(x13751,x13752,x13753),f2(x13751))
% 1.87/2.01 [1376]~P2(x13761)+~P6(x13761,x13763,f2(x13761))+~P6(x13761,f2(x13761),x13762)+P6(x13761,f18(x13761,x13762,x13763),f2(x13761))
% 1.87/2.01 [1377]~P2(x13771)+~P6(x13771,x13772,f2(x13771))+~P6(x13771,f2(x13771),x13773)+P6(x13771,f18(x13771,x13772,x13773),f2(x13771))
% 1.87/2.01 [1378]~P9(x13781)+~P6(x13781,x13783,f2(x13781))+~P6(x13781,f2(x13781),x13782)+P6(x13781,f18(x13781,x13782,x13783),f2(x13781))
% 1.87/2.01 [1379]~P9(x13791)+~P6(x13791,x13792,f2(x13791))+~P6(x13791,f2(x13791),x13793)+P6(x13791,f18(x13791,x13792,x13793),f2(x13791))
% 1.87/2.01 [1380]~P2(x13801)+~P6(x13801,x13803,f2(x13801))+~P5(x13801,f2(x13801),x13802)+P5(x13801,f18(x13801,x13802,x13803),f2(x13801))
% 1.87/2.01 [1381]~P2(x13811)+~P5(x13811,x13812,f2(x13811))+~P6(x13811,f2(x13811),x13813)+P5(x13811,f18(x13811,x13812,x13813),f2(x13811))
% 1.87/2.01 [1382]~P9(x13821)+~P5(x13821,x13823,f2(x13821))+~P5(x13821,f2(x13821),x13822)+P5(x13821,f18(x13821,x13822,x13823),f2(x13821))
% 1.87/2.01 [1383]~P9(x13831)+~P5(x13831,x13832,f2(x13831))+~P5(x13831,f2(x13831),x13833)+P5(x13831,f18(x13831,x13832,x13833),f2(x13831))
% 1.87/2.01 [1408]~P9(x14081)+~P6(x14081,f18(x14081,x14083,x14082),f2(x14081))+P6(x14081,x14082,f2(x14081))+P6(x14081,x14083,f2(x14081))
% 1.87/2.01 [1409]~P9(x14091)+~P5(x14091,f18(x14091,x14093,x14092),f2(x14091))+P5(x14091,x14092,f2(x14091))+P5(x14091,x14093,f2(x14091))
% 1.87/2.01 [1410]~P9(x14101)+~P6(x14101,f2(x14101),f18(x14101,x14103,x14102))+P6(x14101,x14102,f2(x14101))+P6(x14101,f2(x14101),x14103)
% 1.87/2.01 [1411]~P9(x14111)+~P6(x14111,f2(x14111),f18(x14111,x14112,x14113))+P6(x14111,x14112,f2(x14111))+P6(x14111,f2(x14111),x14113)
% 1.87/2.01 [1412]~P9(x14121)+P6(x14121,f2(x14121),x14122)+~P6(x14121,f2(x14121),f18(x14121,x14123,x14122))+P6(x14121,x14122,f2(x14121))
% 1.87/2.01 [1413]~P9(x14131)+P6(x14131,f2(x14131),x14132)+~P6(x14131,f2(x14131),f18(x14131,x14132,x14133))+P6(x14131,x14132,f2(x14131))
% 1.87/2.01 [1414]~P9(x14141)+~P5(x14141,f2(x14141),f18(x14141,x14143,x14142))+P5(x14141,x14142,f2(x14141))+P5(x14141,f2(x14141),x14143)
% 1.87/2.01 [1415]~P9(x14151)+~P5(x14151,f2(x14151),f18(x14151,x14152,x14153))+P5(x14151,x14152,f2(x14151))+P5(x14151,f2(x14151),x14153)
% 1.87/2.01 [1416]~P9(x14161)+P5(x14161,f2(x14161),x14162)+~P5(x14161,f2(x14161),f18(x14161,x14163,x14162))+P5(x14161,x14162,f2(x14161))
% 1.87/2.01 [1417]~P9(x14171)+P5(x14171,f2(x14171),x14172)+~P5(x14171,f2(x14171),f18(x14171,x14172,x14173))+P5(x14171,x14172,f2(x14171))
% 1.87/2.01 [1418]~P9(x14181)+P6(x14181,f2(x14181),x14182)+~P6(x14181,f18(x14181,x14183,x14182),f2(x14181))+P6(x14181,x14182,f2(x14181))
% 1.87/2.01 [1419]~P9(x14191)+P6(x14191,f2(x14191),x14192)+~P6(x14191,f18(x14191,x14192,x14193),f2(x14191))+P6(x14191,x14192,f2(x14191))
% 1.87/2.01 [1420]~P9(x14201)+P5(x14201,f2(x14201),x14202)+~P5(x14201,f18(x14201,x14203,x14202),f2(x14201))+P5(x14201,x14202,f2(x14201))
% 1.87/2.01 [1421]~P9(x14211)+P5(x14211,f2(x14211),x14212)+~P5(x14211,f18(x14211,x14212,x14213),f2(x14211))+P5(x14211,x14212,f2(x14211))
% 1.87/2.01 [1422]~P9(x14221)+~P6(x14221,f18(x14221,x14222,x14223),f2(x14221))+P6(x14221,f2(x14221),x14222)+P6(x14221,f2(x14221),x14223)
% 1.87/2.01 [1423]~P9(x14231)+~P5(x14231,f18(x14231,x14232,x14233),f2(x14231))+P5(x14231,f2(x14231),x14232)+P5(x14231,f2(x14231),x14233)
% 1.87/2.01 [728]~P57(x7282)+E(x7281,f2(x7282))+E(x7283,f2(x7282))+~E(f21(f7(x7282,x7283),x7281),f2(x7282))
% 1.87/2.01 [729]~P63(x7292)+E(x7291,f2(x7292))+E(x7293,f2(x7292))+~E(f21(f7(x7292,x7293),x7291),f2(x7292))
% 1.87/2.01 [892]~P54(x8923)+E(x8921,x8922)+E(x8921,f3(x8923,x8922))+~E(f21(f7(x8923,x8921),x8921),f21(f7(x8923,x8922),x8922))
% 1.87/2.01 [1286]~P55(x12861)+~P6(x12861,x12863,f2(x12861))+~P6(x12861,x12862,f2(x12861))+P6(x12861,f2(x12861),f21(f7(x12861,x12862),x12863))
% 1.87/2.01 [1287]~P55(x12871)+~P5(x12871,x12873,f2(x12871))+~P5(x12871,x12872,f2(x12871))+P5(x12871,f2(x12871),f21(f7(x12871,x12872),x12873))
% 1.87/2.01 [1289]~P65(x12891)+~P5(x12891,x12893,f2(x12891))+~P5(x12891,x12892,f2(x12891))+P5(x12891,f2(x12891),f21(f7(x12891,x12892),x12893))
% 1.87/2.01 [1290]~P59(x12901)+~P6(x12901,f2(x12901),x12903)+~P6(x12901,f2(x12901),x12902)+P6(x12901,f2(x12901),f21(f7(x12901,x12902),x12903))
% 1.87/2.01 [1291]~P51(x12911)+~P6(x12911,f4(x12911),x12913)+~P6(x12911,f4(x12911),x12912)+P6(x12911,f4(x12911),f21(f7(x12911,x12912),x12913))
% 1.87/2.01 [1292]~P55(x12921)+~P5(x12921,f2(x12921),x12923)+~P5(x12921,f2(x12921),x12922)+P5(x12921,f2(x12921),f21(f7(x12921,x12922),x12923))
% 1.87/2.01 [1293]~P64(x12931)+~P5(x12931,f2(x12931),x12933)+~P5(x12931,f2(x12931),x12932)+P5(x12931,f2(x12931),f21(f7(x12931,x12932),x12933))
% 1.87/2.01 [1294]~P65(x12941)+~P5(x12941,f2(x12941),x12943)+~P5(x12941,f2(x12941),x12942)+P5(x12941,f2(x12941),f21(f7(x12941,x12942),x12943))
% 1.87/2.01 [1296]~P59(x12961)+~P6(x12961,x12963,f2(x12961))+~P6(x12961,f2(x12961),x12962)+P6(x12961,f21(f7(x12961,x12962),x12963),f2(x12961))
% 1.87/2.01 [1297]~P59(x12971)+~P6(x12971,x12972,f2(x12971))+~P6(x12971,f2(x12971),x12973)+P6(x12971,f21(f7(x12971,x12972),x12973),f2(x12971))
% 1.87/2.01 [1299]~P55(x12991)+~P5(x12991,x12993,f2(x12991))+~P5(x12991,f2(x12991),x12992)+P5(x12991,f21(f7(x12991,x12992),x12993),f2(x12991))
% 1.87/2.01 [1300]~P55(x13001)+~P5(x13001,x13002,f2(x13001))+~P5(x13001,f2(x13001),x13003)+P5(x13001,f21(f7(x13001,x13002),x13003),f2(x13001))
% 1.87/2.01 [1302]~P64(x13021)+~P5(x13021,x13023,f2(x13021))+~P5(x13021,f2(x13021),x13022)+P5(x13021,f21(f7(x13021,x13022),x13023),f2(x13021))
% 1.87/2.01 [1304]~P64(x13041)+~P5(x13041,x13042,f2(x13041))+~P5(x13041,f2(x13041),x13043)+P5(x13041,f21(f7(x13041,x13042),x13043),f2(x13041))
% 1.87/2.01 [1316]~P55(x13161)+P5(x13161,x13162,f2(x13161))+P5(x13161,x13163,f2(x13161))+~P5(x13161,f21(f7(x13161,x13163),x13162),f2(x13161))
% 1.87/2.01 [1317]~P55(x13171)+P5(x13171,x13172,f2(x13171))+P5(x13171,f2(x13171),x13173)+~P5(x13171,f2(x13171),f21(f7(x13171,x13173),x13172))
% 1.87/2.01 [1318]~P55(x13181)+P5(x13181,x13182,f2(x13181))+P5(x13181,f2(x13181),x13183)+~P5(x13181,f2(x13181),f21(f7(x13181,x13182),x13183))
% 1.87/2.01 [1319]~P55(x13191)+P5(x13191,f2(x13191),x13192)+P5(x13191,x13192,f2(x13191))+~P5(x13191,f2(x13191),f21(f7(x13191,x13193),x13192))
% 1.87/2.01 [1320]~P55(x13201)+P5(x13201,f2(x13201),x13202)+P5(x13201,x13202,f2(x13201))+~P5(x13201,f2(x13201),f21(f7(x13201,x13202),x13203))
% 1.87/2.01 [1321]~P55(x13211)+P5(x13211,f2(x13211),x13212)+P5(x13211,x13212,f2(x13211))+~P5(x13211,f21(f7(x13211,x13213),x13212),f2(x13211))
% 1.87/2.01 [1322]~P55(x13221)+P5(x13221,f2(x13221),x13222)+P5(x13221,x13222,f2(x13221))+~P5(x13221,f21(f7(x13221,x13222),x13223),f2(x13221))
% 1.87/2.01 [1323]~P55(x13231)+P5(x13231,f2(x13231),x13232)+P5(x13231,f2(x13231),x13233)+~P5(x13231,f21(f7(x13231,x13232),x13233),f2(x13231))
% 1.87/2.01 [1397]~P59(x13971)+P6(x13971,f2(x13971),x13972)+~P6(x13971,f2(x13971),x13973)+~P6(x13971,f2(x13971),f21(f7(x13971,x13973),x13972))
% 1.87/2.01 [1398]~P59(x13981)+P6(x13981,f2(x13981),x13982)+~P6(x13981,f2(x13981),x13983)+~P6(x13981,f2(x13981),f21(f7(x13981,x13982),x13983))
% 1.87/2.01 [1668]~P51(x16681)+~P6(x16681,x16682,f4(x16681))+~P6(x16681,f2(x16681),x16682)+P6(x16681,f21(f7(x16681,x16682),f19(x16681,x16682,x16683)),f19(x16681,x16682,x16683))
% 1.87/2.01 [1777]~P49(x17772)+E(x17771,f2(x17772))+E(x17773,f2(x17772))+E(f21(f7(x17772,f21(f7(x17772,f17(x17772,x17773)),f8(x17772,x17773,x17771))),f17(x17772,x17771)),f8(x17772,f17(x17772,x17773),f17(x17772,x17771)))
% 1.87/2.01 [1800]~P4(x18002)+E(x18001,f2(x18002))+E(x18003,f2(x18002))+E(f21(f7(x18002,f21(f7(x18002,f8(x18002,x18003,x18001)),f17(x18002,x18003))),f17(x18002,x18001)),f8(x18002,f17(x18002,x18003),f17(x18002,x18001)))
% 1.87/2.01 [1106]~P49(x11062)+E(x11061,f2(x11062))+E(x11063,f2(x11062))+E(f21(f7(x11062,f17(x11062,x11061)),f17(x11062,x11063)),f17(x11062,f21(f7(x11062,x11063),x11061)))
% 1.87/2.01 [1140]~P55(x11401)+~E(x11403,f2(x11401))+~E(x11402,f2(x11401))+E(f8(x11401,f21(f7(x11401,x11402),x11402),f21(f7(x11401,x11403),x11403)),f2(x11401))
% 1.87/2.01 [1446]~P68(x14461)+~P5(x14461,x14462,f2(x14461))+~P5(x14461,x14463,f2(x14461))+E(f21(f7(x14461,f5(x14461,x14462)),f5(x14461,x14463)),f5(x14461,f21(f7(x14461,x14462),x14463)))
% 1.87/2.01 [1447]~P68(x14471)+~P5(x14471,x14472,f2(x14471))+~P5(x14471,f2(x14471),x14473)+E(f21(f7(x14471,f5(x14471,x14472)),f5(x14471,x14473)),f5(x14471,f21(f7(x14471,x14472),x14473)))
% 1.87/2.01 [1448]~P68(x14481)+~P5(x14481,x14483,f2(x14481))+~P5(x14481,f2(x14481),x14482)+E(f21(f7(x14481,f5(x14481,x14482)),f5(x14481,x14483)),f5(x14481,f21(f7(x14481,x14482),x14483)))
% 1.87/2.01 [1449]~P68(x14491)+~P5(x14491,f2(x14491),x14492)+~P5(x14491,f2(x14491),x14493)+E(f21(f7(x14491,f5(x14491,x14492)),f5(x14491,x14493)),f5(x14491,f21(f7(x14491,x14492),x14493)))
% 1.87/2.01 [1453]~P6(a1,x14532,x14533)+~P6(a1,f2(a1),x14533)+P5(a1,f4(a1),x14531)+~E(f8(a1,x14532,f21(f7(a1,x14533),x14531)),x14533)
% 1.87/2.01 [1461]~P6(a1,f2(a1),x14613)+~P5(a1,f2(a1),x14612)+P5(a1,x14611,f4(a1))+~E(f8(a1,x14612,f21(f7(a1,x14613),x14611)),x14613)
% 1.87/2.01 [1584]~P55(x15841)+~E(x15843,f2(x15841))+~E(x15842,f2(x15841))+P5(x15841,f8(x15841,f21(f7(x15841,x15842),x15842),f21(f7(x15841,x15843),x15843)),f2(x15841))
% 1.87/2.01 [1715]~P6(a1,x17152,x17153)+~P6(a1,f2(a1),x17153)+P5(a1,f2(a1),x17151)+~P5(a1,f2(a1),f8(a1,f21(f7(a1,x17153),x17151),x17152))
% 1.87/2.01 [1719]P5(a1,x17191,f2(a1))+~P6(a1,f2(a1),x17192)+~P5(a1,f2(a1),x17193)+~P6(a1,f8(a1,f21(f7(a1,x17192),x17191),x17193),f2(a1))
% 1.87/2.01 [1750]~P55(x17502)+~E(x17501,f2(x17502))+~E(x17503,f2(x17502))+~P6(x17502,f2(x17502),f8(x17502,f21(f7(x17502,x17503),x17503),f21(f7(x17502,x17501),x17501)))
% 1.87/2.01 [1857]~P51(x18571)+P5(x18571,x18572,x18573)+~P5(x18571,f2(x18571),x18573)+~P5(x18571,f19(x18571,x18572,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18571,x18573,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1849]~P52(x18491)+~E(x18493,f2(x18491))+~E(x18492,f2(x18491))+E(f8(x18491,f19(x18491,x18492,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18491,x18493,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(x18491))
% 1.87/2.01 [1864]~P52(x18641)+~E(x18643,f2(x18641))+~E(x18642,f2(x18641))+P5(x18641,f8(x18641,f19(x18641,x18642,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18641,x18643,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))),f2(x18641))
% 1.87/2.01 [1872]~P52(x18722)+~E(x18721,f2(x18722))+~E(x18723,f2(x18722))+~P6(x18722,f2(x18722),f8(x18722,f19(x18722,x18723,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18722,x18721,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1)))))))
% 1.87/2.01 [1123]~P41(x11231)+~P6(x11231,x11234,x11233)+P6(x11231,x11232,x11233)+~P6(x11231,x11232,x11234)
% 1.87/2.01 [1124]~P41(x11241)+~P5(x11241,x11244,x11243)+P6(x11241,x11242,x11243)+~P6(x11241,x11242,x11244)
% 1.87/2.01 [1125]~P41(x11251)+~P5(x11251,x11252,x11254)+P6(x11251,x11252,x11253)+~P6(x11251,x11254,x11253)
% 1.87/2.01 [1126]~P34(x11261)+~P6(x11261,x11262,x11264)+P6(x11261,x11262,x11263)+~P6(x11261,x11264,x11263)
% 1.87/2.01 [1127]~P34(x11271)+~P5(x11271,x11272,x11274)+P6(x11271,x11272,x11273)+~P6(x11271,x11274,x11273)
% 1.87/2.01 [1128]~P34(x11281)+~P5(x11281,x11284,x11283)+P6(x11281,x11282,x11283)+~P6(x11281,x11282,x11284)
% 1.87/2.01 [1129]~P41(x11291)+~P5(x11291,x11294,x11293)+P5(x11291,x11292,x11293)+~P5(x11291,x11292,x11294)
% 1.87/2.01 [1130]~P34(x11301)+~P5(x11301,x11302,x11304)+P5(x11301,x11302,x11303)+~P5(x11301,x11304,x11303)
% 1.87/2.01 [704]~P3(x7042)+~E(x7044,f2(x7042))+~E(x7041,f2(x7042))+E(x7041,f18(x7042,x7043,x7044))
% 1.87/2.01 [705]~P3(x7051)+~E(x7053,f2(x7051))+~E(x7054,f2(x7051))+E(f18(x7051,x7052,x7053),x7054)
% 1.87/2.01 [782]~P3(x7822)+E(x7821,f2(x7822))+~E(x7821,f18(x7822,x7824,x7823))+~E(x7823,f2(x7822))
% 1.87/2.01 [783]~P3(x7832)+E(x7831,f2(x7832))+~E(f18(x7832,x7834,x7833),x7831)+~E(x7833,f2(x7832))
% 1.87/2.01 [1199]~P51(x11993)+E(x11991,x11992)+~P6(x11993,f4(x11993),x11994)+~E(f19(x11993,x11994,x11991),f19(x11993,x11994,x11992))
% 1.87/2.01 [1224]~P42(x12242)+P5(f40(x12241,x12242),x12244,x12243)+~P5(f40(x12241,x12242),x12243,x12244)+P6(f40(x12241,x12242),x12243,x12244)
% 1.87/2.01 [1328]~P51(x13281)+~P6(x13281,x13282,x13284)+~P6(x13281,f2(x13281),x13283)+P6(x13281,x13282,f8(x13281,x13283,x13284))
% 1.87/2.01 [1329]~P32(x13291)+~P6(x13291,x13292,x13294)+~P5(x13291,f2(x13291),x13293)+P6(x13291,x13292,f8(x13291,x13293,x13294))
% 1.87/2.01 [1330]~P32(x13301)+~P5(x13301,x13302,x13304)+~P6(x13301,f2(x13301),x13303)+P6(x13301,x13302,f8(x13301,x13303,x13304))
% 1.87/2.01 [1331]~P32(x13311)+~P5(x13311,x13312,x13313)+~P5(x13311,f2(x13311),x13314)+P5(x13311,x13312,f8(x13311,x13313,x13314))
% 1.87/2.01 [1332]~P32(x13321)+~P5(x13321,x13322,x13324)+~P5(x13321,f2(x13321),x13323)+P5(x13321,x13322,f8(x13321,x13323,x13324))
% 1.87/2.01 [1497]~P51(x14971)+~P6(a37,x14973,x14974)+~P6(x14971,f4(x14971),x14972)+P6(x14971,f19(x14971,x14972,x14973),f19(x14971,x14972,x14974))
% 1.87/2.01 [1498]~P51(x14981)+~P5(a37,x14983,x14984)+~P6(x14981,f4(x14981),x14982)+P5(x14981,f19(x14981,x14982,x14983),f19(x14981,x14982,x14984))
% 1.87/2.01 [1499]~P51(x14991)+~P5(a37,x14993,x14994)+~P5(x14991,f4(x14991),x14992)+P5(x14991,f19(x14991,x14992,x14993),f19(x14991,x14992,x14994))
% 1.87/2.01 [1500]~P2(x15001)+~P6(x15001,x15004,x15002)+~P6(x15001,x15003,f2(x15001))+P6(x15001,f18(x15001,x15002,x15003),f18(x15001,x15004,x15003))
% 1.87/2.01 [1501]~P9(x15011)+~P5(x15011,x15014,x15012)+~P5(x15011,x15013,f2(x15011))+P5(x15011,f18(x15011,x15012,x15013),f18(x15011,x15014,x15013))
% 1.87/2.01 [1502]~P2(x15021)+~P6(x15021,x15022,x15024)+~P6(x15021,f2(x15021),x15023)+P6(x15021,f18(x15021,x15022,x15023),f18(x15021,x15024,x15023))
% 1.87/2.01 [1503]~P9(x15031)+~P5(x15031,x15032,x15034)+~P5(x15031,f2(x15031),x15033)+P5(x15031,f18(x15031,x15032,x15033),f18(x15031,x15034,x15033))
% 1.87/2.01 [1504]~P51(x15041)+~P5(x15041,x15042,x15044)+~P5(x15041,f2(x15041),x15042)+P5(x15041,f19(x15041,x15042,x15043),f19(x15041,x15044,x15043))
% 1.87/2.01 [1634]~P51(x16343)+~P6(x16343,f19(x16343,x16344,x16341),f19(x16343,x16344,x16342))+P6(a37,x16341,x16342)+~P6(x16343,f4(x16343),x16344)
% 1.87/2.01 [1636]~P51(x16363)+~P5(x16363,f19(x16363,x16364,x16361),f19(x16363,x16364,x16362))+P5(a37,x16361,x16362)+~P6(x16363,f4(x16363),x16364)
% 1.87/2.01 [1637]~P51(x16371)+P6(x16371,x16372,x16373)+~P5(x16371,f2(x16371),x16373)+~P6(x16371,f19(x16371,x16372,x16374),f19(x16371,x16373,x16374))
% 1.87/2.01 [843]~P49(x8432)+E(x8431,f2(x8432))+E(x8433,f18(x8432,x8434,x8431))+~E(f21(f7(x8432,x8433),x8431),x8434)
% 1.87/2.01 [844]~P3(x8442)+E(x8441,f2(x8442))+E(x8443,f18(x8442,x8444,x8441))+~E(f21(f7(x8442,x8443),x8441),x8444)
% 1.87/2.01 [846]~P49(x8462)+E(x8461,f2(x8462))+E(f18(x8462,x8463,x8461),x8464)+~E(x8463,f21(f7(x8462,x8464),x8461))
% 1.87/2.01 [847]~P3(x8472)+E(x8471,f2(x8472))+E(f18(x8472,x8473,x8471),x8474)+~E(x8473,f21(f7(x8472,x8474),x8471))
% 1.87/2.01 [851]~P3(x8512)+~E(x8511,f2(x8512))+E(x8511,f18(x8512,x8513,x8514))+~E(f21(f7(x8512,x8511),x8514),x8513)
% 1.87/2.01 [852]~P3(x8521)+~E(x8524,f2(x8521))+E(f18(x8521,x8522,x8523),x8524)+~E(x8522,f21(f7(x8521,x8524),x8523))
% 1.87/2.01 [875]~P49(x8752)+~E(f18(x8752,x8753,x8751),x8754)+E(x8751,f2(x8752))+E(x8753,f21(f7(x8752,x8754),x8751))
% 1.87/2.01 [876]~P3(x8762)+~E(f18(x8762,x8763,x8761),x8764)+E(x8761,f2(x8762))+E(x8763,f21(f7(x8762,x8764),x8761))
% 1.87/2.01 [877]~P49(x8772)+~E(x8773,f18(x8772,x8774,x8771))+E(x8771,f2(x8772))+E(f21(f7(x8772,x8773),x8771),x8774)
% 1.87/2.01 [878]~P3(x8782)+~E(x8783,f18(x8782,x8784,x8781))+E(x8781,f2(x8782))+E(f21(f7(x8782,x8783),x8781),x8784)
% 1.87/2.01 [1430]~P55(x14301)+~P6(x14301,x14304,x14302)+~P6(x14301,x14303,f2(x14301))+P6(x14301,f21(f7(x14301,x14302),x14303),f21(f7(x14301,x14304),x14303))
% 1.87/2.01 [1431]~P55(x14311)+~P6(x14311,x14314,x14313)+~P6(x14311,x14312,f2(x14311))+P6(x14311,f21(f7(x14311,x14312),x14313),f21(f7(x14311,x14312),x14314))
% 1.87/2.01 [1432]~P55(x14321)+~P5(x14321,x14324,x14323)+~P6(x14321,x14322,f2(x14321))+P5(x14321,f21(f7(x14321,x14322),x14323),f21(f7(x14321,x14322),x14324))
% 1.87/2.01 [1433]~P65(x14331)+~P5(x14331,x14334,x14333)+~P5(x14331,x14332,f2(x14331))+P5(x14331,f21(f7(x14331,x14332),x14333),f21(f7(x14331,x14332),x14334))
% 1.87/2.01 [1434]~P65(x14341)+~P5(x14341,x14344,x14342)+~P5(x14341,x14343,f2(x14341))+P5(x14341,f21(f7(x14341,x14342),x14343),f21(f7(x14341,x14344),x14343))
% 1.87/2.01 [1436]~P53(x14361)+~P6(x14361,x14363,x14364)+~P6(x14361,f2(x14361),x14362)+P6(x14361,f21(f7(x14361,x14362),x14363),f21(f7(x14361,x14362),x14364))
% 1.87/2.01 [1437]~P59(x14371)+~P6(x14371,x14373,x14374)+~P6(x14371,f2(x14371),x14372)+P6(x14371,f21(f7(x14371,x14372),x14373),f21(f7(x14371,x14372),x14374))
% 1.87/2.01 [1438]~P55(x14381)+~P6(x14381,x14382,x14384)+~P6(x14381,f2(x14381),x14383)+P6(x14381,f21(f7(x14381,x14382),x14383),f21(f7(x14381,x14384),x14383))
% 1.87/2.01 [1439]~P59(x14391)+~P6(x14391,x14392,x14394)+~P6(x14391,f2(x14391),x14393)+P6(x14391,f21(f7(x14391,x14392),x14393),f21(f7(x14391,x14394),x14393))
% 1.87/2.01 [1440]~P55(x14401)+~P6(x14401,x14403,x14404)+~P6(x14401,f2(x14401),x14402)+P6(x14401,f21(f7(x14401,x14402),x14403),f21(f7(x14401,x14402),x14404))
% 1.87/2.01 [1441]~P55(x14411)+~P5(x14411,x14413,x14414)+~P6(x14411,f2(x14411),x14412)+P5(x14411,f21(f7(x14411,x14412),x14413),f21(f7(x14411,x14412),x14414))
% 1.87/2.01 [1442]~P67(x14421)+~P5(x14421,x14423,x14424)+~P5(x14421,f2(x14421),x14422)+P5(x14421,f21(f7(x14421,x14422),x14423),f21(f7(x14421,x14422),x14424))
% 1.87/2.01 [1443]~P66(x14431)+~P5(x14431,x14433,x14434)+~P5(x14431,f2(x14431),x14432)+P5(x14431,f21(f7(x14431,x14432),x14433),f21(f7(x14431,x14432),x14434))
% 1.87/2.01 [1444]~P67(x14441)+~P5(x14441,x14442,x14444)+~P5(x14441,f2(x14441),x14443)+P5(x14441,f21(f7(x14441,x14442),x14443),f21(f7(x14441,x14444),x14443))
% 1.87/2.01 [1473]P6(x14731,x14733,x14732)+~P55(x14731)+P6(x14731,x14732,x14733)+~P6(x14731,f21(f7(x14731,x14734),x14732),f21(f7(x14731,x14734),x14733))
% 1.87/2.01 [1474]P6(x14741,x14743,x14742)+~P55(x14741)+P6(x14741,x14742,x14743)+~P6(x14741,f21(f7(x14741,x14742),x14744),f21(f7(x14741,x14743),x14744))
% 1.87/2.01 [1491]~P55(x14911)+P6(x14911,x14912,x14913)+P6(x14911,x14914,f2(x14911))+~P6(x14911,f21(f7(x14911,x14912),x14914),f21(f7(x14911,x14913),x14914))
% 1.87/2.01 [1492]~P55(x14921)+P6(x14921,x14922,x14923)+P6(x14921,x14924,f2(x14921))+~P6(x14921,f21(f7(x14921,x14924),x14922),f21(f7(x14921,x14924),x14923))
% 1.87/2.01 [1493]~P55(x14931)+P6(x14931,x14932,x14933)+P6(x14931,f2(x14931),x14934)+~P6(x14931,f21(f7(x14931,x14934),x14933),f21(f7(x14931,x14934),x14932))
% 1.87/2.01 [1494]~P55(x14941)+P6(x14941,x14942,x14943)+P6(x14941,f2(x14941),x14944)+~P6(x14941,f21(f7(x14941,x14943),x14944),f21(f7(x14941,x14942),x14944))
% 1.87/2.01 [1505]~P55(x15051)+P6(x15051,f2(x15051),x15052)+P6(x15051,x15052,f2(x15051))+~P6(x15051,f21(f7(x15051,x15053),x15052),f21(f7(x15051,x15054),x15052))
% 1.87/2.01 [1506]~P55(x15061)+P6(x15061,f2(x15061),x15062)+P6(x15061,x15062,f2(x15061))+~P6(x15061,f21(f7(x15061,x15062),x15063),f21(f7(x15061,x15062),x15064))
% 1.87/2.01 [1525]~P2(x15251)+~P6(x15251,x15254,f2(x15251))+P6(x15251,x15252,f18(x15251,x15253,x15254))+~P6(x15251,x15253,f21(f7(x15251,x15252),x15254))
% 1.87/2.01 [1526]~P2(x15261)+~P6(x15261,x15264,f2(x15261))+P5(x15261,x15262,f18(x15261,x15263,x15264))+~P5(x15261,x15263,f21(f7(x15261,x15262),x15264))
% 1.87/2.01 [1528]~P9(x15281)+~P6(x15281,f2(x15281),x15284)+P6(x15281,x15282,f18(x15281,x15283,x15284))+~P6(x15281,f21(f7(x15281,x15282),x15284),x15283)
% 1.87/2.01 [1529]~P2(x15291)+~P6(x15291,f2(x15291),x15294)+P6(x15291,x15292,f18(x15291,x15293,x15294))+~P6(x15291,f21(f7(x15291,x15292),x15294),x15293)
% 1.87/2.01 [1531]~P9(x15311)+~P6(x15311,f2(x15311),x15314)+P5(x15311,x15312,f18(x15311,x15313,x15314))+~P5(x15311,f21(f7(x15311,x15312),x15314),x15313)
% 1.87/2.01 [1532]~P2(x15321)+~P6(x15321,f2(x15321),x15324)+P5(x15321,x15322,f18(x15321,x15323,x15324))+~P5(x15321,f21(f7(x15321,x15322),x15324),x15323)
% 1.87/2.01 [1533]~P2(x15331)+~P6(x15331,x15333,f2(x15331))+P6(x15331,f18(x15331,x15332,x15333),x15334)+~P6(x15331,f21(f7(x15331,x15334),x15333),x15332)
% 1.87/2.01 [1534]~P2(x15341)+~P6(x15341,x15343,f2(x15341))+P5(x15341,f18(x15341,x15342,x15343),x15344)+~P5(x15341,f21(f7(x15341,x15344),x15343),x15342)
% 1.87/2.01 [1536]~P9(x15361)+~P6(x15361,f2(x15361),x15363)+P6(x15361,f18(x15361,x15362,x15363),x15364)+~P6(x15361,x15362,f21(f7(x15361,x15364),x15363))
% 1.87/2.01 [1537]~P2(x15371)+~P6(x15371,f2(x15371),x15373)+P6(x15371,f18(x15371,x15372,x15373),x15374)+~P6(x15371,x15372,f21(f7(x15371,x15374),x15373))
% 1.87/2.01 [1539]~P9(x15391)+~P6(x15391,f2(x15391),x15393)+P5(x15391,f18(x15391,x15392,x15393),x15394)+~P5(x15391,x15392,f21(f7(x15391,x15394),x15393))
% 1.87/2.01 [1540]~P2(x15401)+~P6(x15401,f2(x15401),x15403)+P5(x15401,f18(x15401,x15402,x15403),x15404)+~P5(x15401,x15402,f21(f7(x15401,x15404),x15403))
% 1.87/2.01 [1550]~P55(x15501)+P6(x15501,x15502,x15503)+~P6(x15501,x15504,f2(x15501))+~P6(x15501,f21(f7(x15501,x15504),x15503),f21(f7(x15501,x15504),x15502))
% 1.87/2.01 [1551]~P55(x15511)+P5(x15511,x15512,x15513)+~P6(x15511,x15514,f2(x15511))+~P5(x15511,f21(f7(x15511,x15514),x15513),f21(f7(x15511,x15514),x15512))
% 1.87/2.01 [1552]~P55(x15521)+P6(x15521,x15522,x15523)+~P6(x15521,f2(x15521),x15524)+~P6(x15521,f21(f7(x15521,x15524),x15522),f21(f7(x15521,x15524),x15523))
% 1.87/2.01 [1553]~P59(x15531)+P6(x15531,x15532,x15533)+~P5(x15531,f2(x15531),x15534)+~P6(x15531,f21(f7(x15531,x15534),x15532),f21(f7(x15531,x15534),x15533))
% 1.87/2.01 [1554]~P60(x15541)+P6(x15541,x15542,x15543)+~P5(x15541,f2(x15541),x15544)+~P6(x15541,f21(f7(x15541,x15544),x15542),f21(f7(x15541,x15544),x15543))
% 1.87/2.01 [1555]~P59(x15551)+P6(x15551,x15552,x15553)+~P5(x15551,f2(x15551),x15554)+~P6(x15551,f21(f7(x15551,x15552),x15554),f21(f7(x15551,x15553),x15554))
% 1.87/2.01 [1556]~P60(x15561)+P6(x15561,x15562,x15563)+~P5(x15561,f2(x15561),x15564)+~P6(x15561,f21(f7(x15561,x15562),x15564),f21(f7(x15561,x15563),x15564))
% 1.87/2.01 [1557]~P55(x15571)+P5(x15571,x15572,x15573)+~P6(x15571,f2(x15571),x15574)+~P5(x15571,f21(f7(x15571,x15574),x15572),f21(f7(x15571,x15574),x15573))
% 1.87/2.01 [1558]~P59(x15581)+P5(x15581,x15582,x15583)+~P6(x15581,f2(x15581),x15584)+~P5(x15581,f21(f7(x15581,x15584),x15582),f21(f7(x15581,x15584),x15583))
% 1.87/2.01 [1559]~P59(x15591)+P5(x15591,x15592,x15593)+~P6(x15591,f2(x15591),x15594)+~P5(x15591,f21(f7(x15591,x15592),x15594),f21(f7(x15591,x15593),x15594))
% 1.87/2.01 [1560]~P2(x15601)+~P6(x15601,x15604,f2(x15601))+~P6(x15601,x15603,f18(x15601,x15602,x15604))+P6(x15601,x15602,f21(f7(x15601,x15603),x15604))
% 1.87/2.01 [1561]~P2(x15611)+~P6(x15611,x15614,f2(x15611))+~P5(x15611,x15613,f18(x15611,x15612,x15614))+P5(x15611,x15612,f21(f7(x15611,x15613),x15614))
% 1.87/2.01 [1562]~P9(x15621)+~P6(x15621,f2(x15621),x15624)+~P6(x15621,f18(x15621,x15622,x15624),x15623)+P6(x15621,x15622,f21(f7(x15621,x15623),x15624))
% 1.87/2.01 [1563]~P2(x15631)+~P6(x15631,f2(x15631),x15634)+~P6(x15631,f18(x15631,x15632,x15634),x15633)+P6(x15631,x15632,f21(f7(x15631,x15633),x15634))
% 1.87/2.01 [1564]~P9(x15641)+~P6(x15641,f2(x15641),x15644)+~P5(x15641,f18(x15641,x15642,x15644),x15643)+P5(x15641,x15642,f21(f7(x15641,x15643),x15644))
% 1.87/2.01 [1565]~P2(x15651)+~P6(x15651,f2(x15651),x15654)+~P5(x15651,f18(x15651,x15652,x15654),x15653)+P5(x15651,x15652,f21(f7(x15651,x15653),x15654))
% 1.87/2.01 [1566]~P2(x15661)+~P6(x15661,x15663,f2(x15661))+~P6(x15661,f18(x15661,x15664,x15663),x15662)+P6(x15661,f21(f7(x15661,x15662),x15663),x15664)
% 1.87/2.01 [1567]~P2(x15671)+~P6(x15671,x15673,f2(x15671))+~P5(x15671,f18(x15671,x15674,x15673),x15672)+P5(x15671,f21(f7(x15671,x15672),x15673),x15674)
% 1.87/2.01 [1568]~P9(x15681)+~P6(x15681,f2(x15681),x15683)+~P6(x15681,x15682,f18(x15681,x15684,x15683))+P6(x15681,f21(f7(x15681,x15682),x15683),x15684)
% 1.87/2.01 [1569]~P2(x15691)+~P6(x15691,f2(x15691),x15693)+~P6(x15691,x15692,f18(x15691,x15694,x15693))+P6(x15691,f21(f7(x15691,x15692),x15693),x15694)
% 1.87/2.01 [1570]~P9(x15701)+~P6(x15701,f2(x15701),x15703)+~P5(x15701,x15702,f18(x15701,x15704,x15703))+P5(x15701,f21(f7(x15701,x15702),x15703),x15704)
% 1.87/2.01 [1571]~P2(x15711)+~P6(x15711,f2(x15711),x15713)+~P5(x15711,x15712,f18(x15711,x15714,x15713))+P5(x15711,f21(f7(x15711,x15712),x15713),x15714)
% 1.87/2.01 [1749]~P6(a36,f2(a36),x17494)+~P6(a36,f2(a36),x17492)+~P6(a36,f21(f7(a36,x17494),x17491),f21(f7(a36,x17492),x17493))+P6(a36,f21(f7(a36,x17491),f17(a36,x17492)),f21(f7(a36,x17493),f17(a36,x17494)))
% 1.87/2.01 [1764]~P6(a36,f2(a36),x17643)+~P6(a36,f2(a36),x17641)+~P6(a36,f21(f7(a36,x17643),x17642),f21(f7(a36,x17641),x17644))+P6(a36,f21(f7(a36,f17(a36,x17641)),x17642),f21(f7(a36,f17(a36,x17643)),x17644))
% 1.87/2.01 [1751]~P7(x17513,x17514,x17515,x17511)+E(x17511,x17512)+~P7(x17513,x17514,x17515,x17512)+~P10(x17513)
% 1.87/2.01 [1475]~P30(x14751)+~P6(x14751,x14753,x14755)+~P6(x14751,x14752,x14754)+P6(x14751,f8(x14751,x14752,x14753),f8(x14751,x14754,x14755))
% 1.87/2.01 [1476]~P30(x14761)+~P6(x14761,x14763,x14765)+~P5(x14761,x14762,x14764)+P6(x14761,f8(x14761,x14762,x14763),f8(x14761,x14764,x14765))
% 1.87/2.01 [1477]~P30(x14771)+~P6(x14771,x14772,x14774)+~P5(x14771,x14773,x14775)+P6(x14771,f8(x14771,x14772,x14773),f8(x14771,x14774,x14775))
% 1.87/2.01 [1478]~P27(x14781)+~P5(x14781,x14783,x14785)+~P5(x14781,x14782,x14784)+P5(x14781,f8(x14781,x14782,x14783),f8(x14781,x14784,x14785))
% 1.87/2.01 [1651]~P52(x16511)+~P6(x16511,f5(x16511,x16512),x16514)+~P6(x16511,f5(x16511,x16513),x16515)+P6(x16511,f21(f7(x16511,f5(x16511,x16512)),f5(x16511,x16513)),f21(f7(x16511,x16514),x16515))
% 1.87/2.01 [1689]~P76(x16895)+E(x16891,x16892)+E(x16893,x16894)+~E(f8(x16895,f21(f7(x16895,x16893),x16891),f21(f7(x16895,x16894),x16892)),f8(x16895,f21(f7(x16895,x16893),x16892),f21(f7(x16895,x16894),x16891)))
% 1.87/2.01 [1762]~P4(x17622)+E(x17621,f2(x17622))+E(x17623,f2(x17622))+E(f18(x17622,f8(x17622,f21(f7(x17622,x17624),x17621),f21(f7(x17622,x17625),x17623)),f21(f7(x17622,x17623),x17621)),f8(x17622,f18(x17622,x17624,x17623),f18(x17622,x17625,x17621)))
% 1.87/2.01 [665]~P49(x6653)+E(x6651,x6652)+~E(f17(x6653,x6651),f17(x6653,x6652))+E(x6652,f2(x6653))+E(x6651,f2(x6653))
% 1.87/2.01 [1233]~P32(x12332)+~P5(x12332,f2(x12332),x12333)+~P5(x12332,f2(x12332),x12331)+~E(f8(x12332,x12333,x12331),f2(x12332))+E(x12331,f2(x12332))
% 1.87/2.01 [1234]~P32(x12342)+~P5(x12342,f2(x12342),x12343)+~P5(x12342,f2(x12342),x12341)+~E(f8(x12342,x12341,x12343),f2(x12342))+E(x12341,f2(x12342))
% 1.87/2.01 [1454]~P52(x14541)+~P5(x14541,x14542,f4(x14541))+~P5(x14541,f2(x14541),x14542)+~P5(x14541,f2(x14541),x14543)+P5(x14541,f21(f7(x14541,x14542),x14543),x14543)
% 1.87/2.01 [1455]~P52(x14551)+~P5(x14551,x14553,f4(x14551))+~P5(x14551,f2(x14551),x14553)+~P5(x14551,f2(x14551),x14552)+P5(x14551,f21(f7(x14551,x14552),x14553),x14552)
% 1.87/2.01 [1843]~P51(x18433)+E(x18431,x18432)+~P5(x18433,f2(x18433),x18432)+~P5(x18433,f2(x18433),x18431)+~E(f19(x18433,x18431,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(x18433,x18432,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))
% 1.87/2.01 [1403]~P9(x14031)+P6(x14031,f2(x14031),x14032)+~P6(x14031,x14033,f2(x14031))+P6(x14031,x14032,f2(x14031))+P6(x14031,x14033,f18(x14031,x14034,x14032))
% 1.87/2.01 [1404]~P9(x14041)+P6(x14041,f2(x14041),x14042)+~P5(x14041,x14043,f2(x14041))+P6(x14041,x14042,f2(x14041))+P5(x14041,x14043,f18(x14041,x14044,x14042))
% 1.87/2.01 [1405]~P9(x14051)+P6(x14051,f2(x14051),x14052)+~P6(x14051,f2(x14051),x14054)+P6(x14051,x14052,f2(x14051))+P6(x14051,f18(x14051,x14053,x14052),x14054)
% 1.87/2.01 [1406]~P9(x14061)+P6(x14061,f2(x14061),x14062)+~P5(x14061,f2(x14061),x14064)+P6(x14061,x14062,f2(x14061))+P5(x14061,f18(x14061,x14063,x14062),x14064)
% 1.87/2.01 [1468]~P9(x14681)+P6(x14681,f2(x14681),x14683)+P6(x14681,x14682,f2(x14681))+~P6(x14681,x14682,f18(x14681,x14684,x14683))+P6(x14681,x14683,f2(x14681))
% 1.87/2.01 [1469]~P9(x14691)+P6(x14691,f2(x14691),x14692)+P6(x14691,x14692,f2(x14691))+~P5(x14691,x14693,f18(x14691,x14694,x14692))+P5(x14691,x14693,f2(x14691))
% 1.87/2.01 [1470]~P9(x14701)+P6(x14701,f2(x14701),x14702)+P6(x14701,x14702,f2(x14701))+~P6(x14701,f18(x14701,x14704,x14702),x14703)+P6(x14701,f2(x14701),x14703)
% 1.87/2.01 [1471]~P9(x14711)+P6(x14711,f2(x14711),x14712)+P6(x14711,x14712,f2(x14711))+~P5(x14711,f18(x14711,x14714,x14712),x14713)+P5(x14711,f2(x14711),x14713)
% 1.87/2.01 [1611]~P51(x16111)+~P6(x16111,x16112,x16114)+~P5(x16111,f2(x16111),x16112)+P6(x16111,f19(x16111,x16112,x16113),f19(x16111,x16114,x16113))+~P6(a37,f2(a37),x16113)
% 1.87/2.01 [1617]~P51(x16171)+~P6(a37,x16174,x16173)+~P6(x16171,x16172,f4(x16171))+~P6(x16171,f2(x16171),x16172)+P6(x16171,f19(x16171,x16172,x16173),f19(x16171,x16172,x16174))
% 1.87/2.01 [1618]~P51(x16181)+~P5(a37,x16184,x16183)+~P5(x16181,x16182,f4(x16181))+~P5(x16181,f2(x16181),x16182)+P5(x16181,f19(x16181,x16182,x16183),f19(x16181,x16182,x16184))
% 1.87/2.01 [1597]~P9(x15971)+~P6(x15971,x15973,f2(x15971))+P6(x15971,x15972,f2(x15971))+P6(x15971,x15973,f18(x15971,x15974,x15972))+~P6(x15971,f21(f7(x15971,x15973),x15972),x15974)
% 1.87/2.01 [1598]~P9(x15981)+~P5(x15981,x15983,f2(x15981))+P6(x15981,x15982,f2(x15981))+P5(x15981,x15983,f18(x15981,x15984,x15982))+~P5(x15981,f21(f7(x15981,x15983),x15982),x15984)
% 1.87/2.01 [1599]~P9(x15991)+~P6(x15991,f2(x15991),x15994)+P6(x15991,x15992,f2(x15991))+P6(x15991,f18(x15991,x15993,x15992),x15994)+~P6(x15991,x15993,f21(f7(x15991,x15994),x15992))
% 1.87/2.01 [1600]~P9(x16001)+~P5(x16001,f2(x16001),x16004)+P6(x16001,x16002,f2(x16001))+P5(x16001,f18(x16001,x16003,x16002),x16004)+~P5(x16001,x16003,f21(f7(x16001,x16004),x16002))
% 1.87/2.01 [1601]~P9(x16011)+~P6(x16011,x16013,f2(x16011))+P6(x16011,f2(x16011),x16012)+P6(x16011,x16013,f18(x16011,x16014,x16012))+~P6(x16011,x16014,f21(f7(x16011,x16013),x16012))
% 1.87/2.01 [1602]~P9(x16021)+~P5(x16021,x16023,f2(x16021))+P6(x16021,f2(x16021),x16022)+P5(x16021,x16023,f18(x16021,x16024,x16022))+~P5(x16021,x16024,f21(f7(x16021,x16023),x16022))
% 1.87/2.01 [1603]~P9(x16031)+~P6(x16031,x16032,f2(x16031))+P6(x16031,f2(x16031),x16032)+P6(x16031,x16033,f18(x16031,x16034,x16032))+~P6(x16031,x16034,f21(f7(x16031,x16033),x16032))
% 1.87/2.01 [1604]~P9(x16041)+~P6(x16041,x16042,f2(x16041))+P6(x16041,f2(x16041),x16042)+P5(x16041,x16043,f18(x16041,x16044,x16042))+~P5(x16041,x16044,f21(f7(x16041,x16043),x16042))
% 1.87/2.01 [1605]~P9(x16051)+~P6(x16051,x16052,f2(x16051))+P6(x16051,f2(x16051),x16052)+P6(x16051,f18(x16051,x16053,x16052),x16054)+~P6(x16051,f21(f7(x16051,x16054),x16052),x16053)
% 1.87/2.01 [1606]~P9(x16061)+~P6(x16061,x16062,f2(x16061))+P6(x16061,f2(x16061),x16062)+P5(x16061,f18(x16061,x16063,x16062),x16064)+~P5(x16061,f21(f7(x16061,x16064),x16062),x16063)
% 1.87/2.01 [1607]~P9(x16071)+~P6(x16071,f2(x16071),x16074)+P6(x16071,f2(x16071),x16072)+P6(x16071,f18(x16071,x16073,x16072),x16074)+~P6(x16071,f21(f7(x16071,x16074),x16072),x16073)
% 1.87/2.01 [1608]~P9(x16081)+~P5(x16081,f2(x16081),x16084)+P6(x16081,f2(x16081),x16082)+P5(x16081,f18(x16081,x16083,x16082),x16084)+~P5(x16081,f21(f7(x16081,x16084),x16082),x16083)
% 1.87/2.01 [1613]~P9(x16131)+~P6(x16131,x16132,f2(x16131))+~P6(x16131,x16134,f18(x16131,x16133,x16132))+P6(x16131,f2(x16131),x16132)+P6(x16131,x16133,f21(f7(x16131,x16134),x16132))
% 1.87/2.01 [1614]~P9(x16141)+~P6(x16141,x16142,f2(x16141))+~P5(x16141,x16144,f18(x16141,x16143,x16142))+P6(x16141,f2(x16141),x16142)+P5(x16141,x16143,f21(f7(x16141,x16144),x16142))
% 1.87/2.01 [1615]~P9(x16151)+~P6(x16151,x16152,f2(x16151))+~P6(x16151,f18(x16151,x16154,x16152),x16153)+P6(x16151,f2(x16151),x16152)+P6(x16151,f21(f7(x16151,x16153),x16152),x16154)
% 1.87/2.01 [1616]~P9(x16161)+~P6(x16161,x16162,f2(x16161))+~P5(x16161,f18(x16161,x16164,x16162),x16163)+P6(x16161,f2(x16161),x16162)+P5(x16161,f21(f7(x16161,x16163),x16162),x16164)
% 1.87/2.01 [1690]~P2(x16901)+~P6(x16901,x16903,x16904)+~P6(x16901,x16902,f2(x16901))+P6(x16901,f18(x16901,x16902,x16903),f18(x16901,x16902,x16904))+~P6(x16901,f2(x16901),f21(f7(x16901,x16903),x16904))
% 1.87/2.01 [1691]~P9(x16911)+~P5(x16911,x16913,x16914)+~P5(x16911,x16912,f2(x16911))+P5(x16911,f18(x16911,x16912,x16913),f18(x16911,x16912,x16914))+~P6(x16911,f2(x16911),f21(f7(x16911,x16913),x16914))
% 1.87/2.01 [1692]~P2(x16921)+~P6(x16921,x16924,x16923)+~P6(x16921,f2(x16921),x16922)+P6(x16921,f18(x16921,x16922,x16923),f18(x16921,x16922,x16924))+~P6(x16921,f2(x16921),f21(f7(x16921,x16923),x16924))
% 1.87/2.01 [1693]~P2(x16931)+~P5(x16931,x16934,x16933)+~P5(x16931,f2(x16931),x16932)+P5(x16931,f18(x16931,x16932,x16933),f18(x16931,x16932,x16934))+~P6(x16931,f2(x16931),f21(f7(x16931,x16933),x16934))
% 1.87/2.01 [1694]~P9(x16941)+~P6(x16941,x16944,f2(x16941))+P6(x16941,x16942,f18(x16941,x16943,x16944))+~P6(x16941,x16943,f21(f7(x16941,x16942),x16944))+~P6(x16941,f21(f7(x16941,x16942),x16944),x16943)
% 1.87/2.01 [1695]~P9(x16951)+~P6(x16951,x16952,f2(x16951))+P6(x16951,x16952,f18(x16951,x16953,x16954))+~P6(x16951,x16953,f21(f7(x16951,x16952),x16954))+~P6(x16951,f21(f7(x16951,x16952),x16954),x16953)
% 1.87/2.01 [1696]~P9(x16961)+~P6(x16961,x16964,f2(x16961))+P5(x16961,x16962,f18(x16961,x16963,x16964))+~P5(x16961,x16963,f21(f7(x16961,x16962),x16964))+~P5(x16961,f21(f7(x16961,x16962),x16964),x16963)
% 1.87/2.01 [1697]~P9(x16971)+~P5(x16971,x16972,f2(x16971))+P5(x16971,x16972,f18(x16971,x16973,x16974))+~P5(x16971,x16973,f21(f7(x16971,x16972),x16974))+~P5(x16971,f21(f7(x16971,x16972),x16974),x16973)
% 1.87/2.01 [1698]~P9(x16981)+~P6(x16981,x16983,f2(x16981))+P6(x16981,f18(x16981,x16982,x16983),x16984)+~P6(x16981,x16982,f21(f7(x16981,x16984),x16983))+~P6(x16981,f21(f7(x16981,x16984),x16983),x16982)
% 1.87/2.01 [1699]~P9(x16991)+~P6(x16991,x16993,f2(x16991))+P5(x16991,f18(x16991,x16992,x16993),x16994)+~P5(x16991,x16992,f21(f7(x16991,x16994),x16993))+~P5(x16991,f21(f7(x16991,x16994),x16993),x16992)
% 1.87/2.01 [1700]~P9(x17001)+~P6(x17001,f2(x17001),x17004)+P6(x17001,f18(x17001,x17002,x17003),x17004)+~P6(x17001,x17002,f21(f7(x17001,x17004),x17003))+~P6(x17001,f21(f7(x17001,x17004),x17003),x17002)
% 1.87/2.01 [1701]~P9(x17011)+~P5(x17011,f2(x17011),x17014)+P5(x17011,f18(x17011,x17012,x17013),x17014)+~P5(x17011,x17012,f21(f7(x17011,x17014),x17013))+~P5(x17011,f21(f7(x17011,x17014),x17013),x17012)
% 1.87/2.01 [1790]~P7(a36,x17901,x17902,x17904)+~P6(a36,x17903,f33(x17904,x17902,x17901))+~P6(a36,f2(a36),x17904)+~P6(a36,f2(a36),x17903)+P6(a36,f21(x17901,x17902),f21(x17901,f8(a36,x17902,x17903)))
% 1.87/2.01 [1791]~P7(a36,x17911,x17912,x17914)+~P6(a36,x17913,f32(x17914,x17912,x17911))+~P6(a36,x17914,f2(a36))+~P6(a36,f2(a36),x17913)+P6(a36,f21(x17911,f8(a36,x17912,x17913)),f21(x17911,x17912))
% 1.87/2.01 [1779]~P6(a1,f2(a1),x17793)+~P5(a1,f2(a1),x17792)+~P78(f21(x17791,x17794))+P78(f21(x17791,f25(x17792,x17791,x17793)))+P78(f21(x17791,f8(a1,x17794,f21(f7(a1,x17792),x17793))))
% 1.87/2.01 [1804]~P6(a1,f2(a1),x18044)+~P5(a1,f2(a1),x18043)+~P78(f21(x18041,x18042))+~P78(f21(x18041,f8(a1,f25(x18043,x18041,x18044),x18044)))+P78(f21(x18041,f8(a1,x18042,f21(f7(a1,x18043),x18044))))
% 1.87/2.01 [1165]~P4(x11652)+E(f18(x11652,x11654,x11651),f18(x11652,x11655,x11653))+E(x11651,f2(x11652))+E(x11653,f2(x11652))+~E(f21(f7(x11652,x11654),x11653),f21(f7(x11652,x11655),x11651))
% 1.87/2.01 [1184]~P4(x11842)+~E(f18(x11842,x11844,x11843),f18(x11842,x11845,x11841))+E(x11841,f2(x11842))+E(x11843,f2(x11842))+E(f21(f7(x11842,x11844),x11841),f21(f7(x11842,x11845),x11843))
% 1.87/2.01 [1796]P5(a1,x17961,x17962)+~P6(a1,x17963,x17964)+~P6(a1,x17963,x17965)+~P5(a1,x17964,f2(a1))+~P5(a1,f8(a1,f21(f7(a1,x17963),x17962),x17965),f8(a1,f21(f7(a1,x17963),x17961),x17964))
% 1.87/2.01 [1797]P5(a1,x17971,x17972)+~P6(a1,x17973,x17974)+~P6(a1,x17975,x17974)+~P5(a1,f2(a1),x17975)+~P5(a1,f8(a1,f21(f7(a1,x17974),x17971),x17975),f8(a1,f21(f7(a1,x17974),x17972),x17973))
% 1.87/2.01 [1462]~P76(x14624)+E(x14621,x14622)+~E(x14625,x14626)+E(x14623,f2(x14624))+~E(f8(x14624,x14625,f21(f7(x14624,x14623),x14621)),f8(x14624,x14626,f21(f7(x14624,x14623),x14622)))
% 1.87/2.01 [830]~P57(x8302)+~P58(x8302)+~P72(x8302)+~P43(x8302)+~E(f19(x8302,x8301,x8303),f2(x8302))+E(x8301,f2(x8302))
% 1.87/2.01 [832]~P57(x8322)+~P58(x8322)+~P72(x8322)+~P43(x8322)+~E(f19(x8322,x8323,x8321),f2(x8322))+~E(x8321,f2(a37))
% 1.87/2.01 [1198]~P32(x11981)+~P5(x11981,f2(x11981),x11983)+~P5(x11981,f2(x11981),x11982)+~E(x11983,f2(x11981))+~E(x11982,f2(x11981))+E(f8(x11981,x11982,x11983),f2(x11981))
% 1.87/2.01 [1873]~P6(a36,f2(a36),x18733)+~P5(a36,f2(a36),x18732)+~P5(a36,f2(a36),x18731)+~P6(a36,x18731,f18(a36,x18733,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))+~P6(a36,x18732,f18(a36,x18733,f12(a36,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))+P6(a36,f21(a14,f8(a36,f19(a36,x18731,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))),f19(a36,x18732,f12(a37,f8(a1,f8(a1,f8(a1,a10,a10),f4(a1)),f8(a1,f8(a1,a10,a10),f4(a1))))))),x18733)
% 1.87/2.01 [1511]~P51(x15113)+E(x15111,x15112)+~P5(x15113,f2(x15113),x15112)+~P5(x15113,f2(x15113),x15111)+~E(f19(x15113,x15111,x15114),f19(x15113,x15112,x15114))+~P6(a37,f2(a37),x15114)
% 1.87/2.01 [1659]~P2(x16591)+~P6(x16591,x16595,x16593)+~P5(x16591,x16592,x16594)+~P6(x16591,f2(x16591),x16595)+~P6(x16591,f2(x16591),x16592)+P6(x16591,f18(x16591,x16592,x16593),f18(x16591,x16594,x16595))
% 1.87/2.01 [1660]~P2(x16601)+~P6(x16601,x16602,x16604)+~P5(x16601,x16605,x16603)+~P6(x16601,f2(x16601),x16605)+~P5(x16601,f2(x16601),x16602)+P6(x16601,f18(x16601,x16602,x16603),f18(x16601,x16604,x16605))
% 1.87/2.01 [1661]~P2(x16611)+~P5(x16611,x16615,x16613)+~P5(x16611,x16612,x16614)+~P6(x16611,f2(x16611),x16615)+~P5(x16611,f2(x16611),x16612)+P5(x16611,f18(x16611,x16612,x16613),f18(x16611,x16614,x16615))
% 1.87/2.01 [1638]~P59(x16381)+~P6(x16381,x16383,x16385)+~P6(x16381,x16382,x16384)+~P6(x16381,f2(x16381),x16384)+~P5(x16381,f2(x16381),x16383)+P6(x16381,f21(f7(x16381,x16382),x16383),f21(f7(x16381,x16384),x16385))
% 1.87/2.01 [1639]~P59(x16391)+~P6(x16391,x16393,x16395)+~P6(x16391,x16392,x16394)+~P5(x16391,f2(x16391),x16393)+~P5(x16391,f2(x16391),x16392)+P6(x16391,f21(f7(x16391,x16392),x16393),f21(f7(x16391,x16394),x16395))
% 1.87/2.01 [1640]~P59(x16401)+~P6(x16401,x16403,x16405)+~P5(x16401,x16402,x16404)+~P6(x16401,f2(x16401),x16402)+~P5(x16401,f2(x16401),x16403)+P6(x16401,f21(f7(x16401,x16402),x16403),f21(f7(x16401,x16404),x16405))
% 1.87/2.01 [1641]~P59(x16411)+~P6(x16411,x16412,x16414)+~P5(x16411,x16413,x16415)+~P6(x16411,f2(x16411),x16413)+~P5(x16411,f2(x16411),x16412)+P6(x16411,f21(f7(x16411,x16412),x16413),f21(f7(x16411,x16414),x16415))
% 1.87/2.01 [1642]~P67(x16421)+~P5(x16421,x16423,x16425)+~P5(x16421,x16422,x16424)+~P5(x16421,f2(x16421),x16423)+~P5(x16421,f2(x16421),x16424)+P5(x16421,f21(f7(x16421,x16422),x16423),f21(f7(x16421,x16424),x16425))
% 1.87/2.01 [1643]~P67(x16431)+~P5(x16431,x16433,x16435)+~P5(x16431,x16432,x16434)+~P5(x16431,f2(x16431),x16433)+~P5(x16431,f2(x16431),x16432)+P5(x16431,f21(f7(x16431,x16432),x16433),f21(f7(x16431,x16434),x16435))
% 1.87/2.01 [766]~P57(x7662)+~P58(x7662)+~P72(x7662)+~P43(x7662)+~E(x7663,f2(x7662))+E(f19(x7662,x7663,x7661),f2(x7662))+E(x7661,f2(a37))
% 1.87/2.01 [1769]~P61(x17691)+~P6(x17691,x17695,x17696)+~P6(x17691,x17693,x17696)+~P5(x17691,f2(x17691),x17694)+~P5(x17691,f2(x17691),x17692)+~E(f8(x17691,x17692,x17694),f4(x17691))+P6(x17691,f8(x17691,f21(f7(x17691,x17692),x17693),f21(f7(x17691,x17694),x17695)),x17696)
% 1.87/2.01 [1770]~P62(x17701)+~P5(x17701,x17705,x17706)+~P5(x17701,x17703,x17706)+~P5(x17701,f2(x17701),x17704)+~P5(x17701,f2(x17701),x17702)+~E(f8(x17701,x17702,x17704),f4(x17701))+P5(x17701,f8(x17701,f21(f7(x17701,x17702),x17703),f21(f7(x17701,x17704),x17705)),x17706)
% 1.87/2.01 [1798]~P6(a1,x17986,x17985)+~P5(a1,x17985,x17983)+P5(a1,x17981,x17982)+~P6(a1,f2(a1),x17985)+~P5(a1,f2(a1),x17984)+~P5(a1,f2(a1),f8(a1,f21(f7(a1,x17985),x17982),x17986))+~E(f8(a1,f21(f7(a1,x17983),x17981),x17984),f8(a1,f21(f7(a1,x17985),x17982),x17986))
% 1.87/2.01 [1799]~P6(a1,x17994,x17993)+~P5(a1,x17995,x17993)+P5(a1,x17991,x17992)+~P6(a1,f2(a1),x17995)+~P5(a1,f2(a1),x17996)+~P6(a1,f8(a1,f21(f7(a1,x17995),x17991),x17996),f2(a1))+~E(f8(a1,f21(f7(a1,x17993),x17992),x17994),f8(a1,f21(f7(a1,x17995),x17991),x17996))
% 1.87/2.01 %EqnAxiom
% 1.87/2.01 [1]E(x11,x11)
% 1.87/2.01 [2]E(x22,x21)+~E(x21,x22)
% 1.87/2.01 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.87/2.01 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 1.87/2.01 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 1.87/2.01 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 1.87/2.01 [7]~E(x71,x72)+E(f12(x71,x73),f12(x72,x73))
% 1.87/2.01 [8]~E(x81,x82)+E(f12(x83,x81),f12(x83,x82))
% 1.87/2.01 [9]~E(x91,x92)+E(f8(x91,x93,x94),f8(x92,x93,x94))
% 1.87/2.01 [10]~E(x101,x102)+E(f8(x103,x101,x104),f8(x103,x102,x104))
% 1.87/2.01 [11]~E(x111,x112)+E(f8(x113,x114,x111),f8(x113,x114,x112))
% 1.87/2.01 [12]~E(x121,x122)+E(f18(x121,x123,x124),f18(x122,x123,x124))
% 1.87/2.01 [13]~E(x131,x132)+E(f18(x133,x131,x134),f18(x133,x132,x134))
% 1.87/2.01 [14]~E(x141,x142)+E(f18(x143,x144,x141),f18(x143,x144,x142))
% 1.87/2.01 [15]~E(x151,x152)+E(f4(x151),f4(x152))
% 1.87/2.01 [16]~E(x161,x162)+E(f21(x161,x163),f21(x162,x163))
% 1.87/2.01 [17]~E(x171,x172)+E(f21(x173,x171),f21(x173,x172))
% 1.87/2.01 [18]~E(x181,x182)+E(f20(x181),f20(x182))
% 1.87/2.01 [19]~E(x191,x192)+E(f5(x191,x193),f5(x192,x193))
% 1.87/2.01 [20]~E(x201,x202)+E(f5(x203,x201),f5(x203,x202))
% 1.87/2.01 [21]~E(x211,x212)+E(f7(x211,x213),f7(x212,x213))
% 1.87/2.01 [22]~E(x221,x222)+E(f7(x223,x221),f7(x223,x222))
% 1.87/2.01 [23]~E(x231,x232)+E(f19(x231,x233,x234),f19(x232,x233,x234))
% 1.87/2.01 [24]~E(x241,x242)+E(f19(x243,x241,x244),f19(x243,x242,x244))
% 1.87/2.01 [25]~E(x251,x252)+E(f19(x253,x254,x251),f19(x253,x254,x252))
% 1.87/2.01 [26]~E(x261,x262)+E(f28(x261,x263),f28(x262,x263))
% 1.87/2.01 [27]~E(x271,x272)+E(f28(x273,x271),f28(x273,x272))
% 1.87/2.01 [28]~E(x281,x282)+E(f17(x281,x283),f17(x282,x283))
% 1.87/2.01 [29]~E(x291,x292)+E(f17(x293,x291),f17(x293,x292))
% 1.87/2.01 [30]~E(x301,x302)+E(f24(x301,x303),f24(x302,x303))
% 1.87/2.01 [31]~E(x311,x312)+E(f24(x313,x311),f24(x313,x312))
% 1.87/2.01 [32]~E(x321,x322)+E(f9(x321,x323),f9(x322,x323))
% 1.87/2.01 [33]~E(x331,x332)+E(f9(x333,x331),f9(x333,x332))
% 1.87/2.01 [34]~E(x341,x342)+E(f25(x341,x343,x344),f25(x342,x343,x344))
% 1.87/2.01 [35]~E(x351,x352)+E(f25(x353,x351,x354),f25(x353,x352,x354))
% 1.87/2.01 [36]~E(x361,x362)+E(f25(x363,x364,x361),f25(x363,x364,x362))
% 1.87/2.01 [37]~E(x371,x372)+E(f40(x371,x373),f40(x372,x373))
% 1.87/2.01 [38]~E(x381,x382)+E(f40(x383,x381),f40(x383,x382))
% 1.87/2.01 [39]~E(x391,x392)+E(f32(x391,x393,x394),f32(x392,x393,x394))
% 1.87/2.01 [40]~E(x401,x402)+E(f32(x403,x401,x404),f32(x403,x402,x404))
% 1.87/2.01 [41]~E(x411,x412)+E(f32(x413,x414,x411),f32(x413,x414,x412))
% 1.87/2.01 [42]~E(x421,x422)+E(f15(x421),f15(x422))
% 1.87/2.01 [43]~E(x431,x432)+E(f23(x431,x433),f23(x432,x433))
% 1.87/2.01 [44]~E(x441,x442)+E(f23(x443,x441),f23(x443,x442))
% 1.87/2.01 [45]~E(x451,x452)+E(f29(x451,x453,x454),f29(x452,x453,x454))
% 1.87/2.01 [46]~E(x461,x462)+E(f29(x463,x461,x464),f29(x463,x462,x464))
% 1.87/2.01 [47]~E(x471,x472)+E(f29(x473,x474,x471),f29(x473,x474,x472))
% 1.87/2.01 [48]~E(x481,x482)+E(f31(x481,x483,x484),f31(x482,x483,x484))
% 1.87/2.01 [49]~E(x491,x492)+E(f31(x493,x491,x494),f31(x493,x492,x494))
% 1.87/2.01 [50]~E(x501,x502)+E(f31(x503,x504,x501),f31(x503,x504,x502))
% 1.87/2.01 [51]~E(x511,x512)+E(f26(x511,x513,x514,x515),f26(x512,x513,x514,x515))
% 1.87/2.01 [52]~E(x521,x522)+E(f26(x523,x521,x524,x525),f26(x523,x522,x524,x525))
% 1.87/2.01 [53]~E(x531,x532)+E(f26(x533,x534,x531,x535),f26(x533,x534,x532,x535))
% 1.87/2.01 [54]~E(x541,x542)+E(f26(x543,x544,x545,x541),f26(x543,x544,x545,x542))
% 1.87/2.01 [55]~E(x551,x552)+E(f6(x551),f6(x552))
% 1.87/2.01 [56]~E(x561,x562)+E(f33(x561,x563,x564),f33(x562,x563,x564))
% 1.87/2.01 [57]~E(x571,x572)+E(f33(x573,x571,x574),f33(x573,x572,x574))
% 1.87/2.01 [58]~E(x581,x582)+E(f33(x583,x584,x581),f33(x583,x584,x582))
% 1.87/2.01 [59]~E(x591,x592)+E(f30(x591,x593,x594,x595),f30(x592,x593,x594,x595))
% 1.87/2.01 [60]~E(x601,x602)+E(f30(x603,x601,x604,x605),f30(x603,x602,x604,x605))
% 1.87/2.01 [61]~E(x611,x612)+E(f30(x613,x614,x611,x615),f30(x613,x614,x612,x615))
% 1.87/2.01 [62]~E(x621,x622)+E(f30(x623,x624,x625,x621),f30(x623,x624,x625,x622))
% 1.87/2.01 [63]~P1(x631)+P1(x632)+~E(x631,x632)
% 1.87/2.01 [64]P6(x642,x643,x644)+~E(x641,x642)+~P6(x641,x643,x644)
% 1.87/2.01 [65]P6(x653,x652,x654)+~E(x651,x652)+~P6(x653,x651,x654)
% 1.87/2.01 [66]P6(x663,x664,x662)+~E(x661,x662)+~P6(x663,x664,x661)
% 1.87/2.01 [67]~P51(x671)+P51(x672)+~E(x671,x672)
% 1.87/2.01 [68]~P52(x681)+P52(x682)+~E(x681,x682)
% 1.87/2.01 [69]~P37(x691)+P37(x692)+~E(x691,x692)
% 1.87/2.01 [70]~P2(x701)+P2(x702)+~E(x701,x702)
% 1.87/2.01 [71]~P9(x711)+P9(x712)+~E(x711,x712)
% 1.87/2.01 [72]~P3(x721)+P3(x722)+~E(x721,x722)
% 1.87/2.01 [73]P5(x732,x733,x734)+~E(x731,x732)+~P5(x731,x733,x734)
% 1.87/2.01 [74]P5(x743,x742,x744)+~E(x741,x742)+~P5(x743,x741,x744)
% 1.87/2.01 [75]P5(x753,x754,x752)+~E(x751,x752)+~P5(x753,x754,x751)
% 1.87/2.01 [76]~P4(x761)+P4(x762)+~E(x761,x762)
% 1.87/2.01 [77]~P36(x771)+P36(x772)+~E(x771,x772)
% 1.87/2.01 [78]~P49(x781)+P49(x782)+~E(x781,x782)
% 1.87/2.01 [79]~P41(x791)+P41(x792)+~E(x791,x792)
% 1.87/2.01 [80]~P50(x801)+P50(x802)+~E(x801,x802)
% 1.87/2.01 [81]~P73(x811)+P73(x812)+~E(x811,x812)
% 1.87/2.01 [82]P8(x822,x823)+~E(x821,x822)+~P8(x821,x823)
% 1.87/2.01 [83]P8(x833,x832)+~E(x831,x832)+~P8(x833,x831)
% 1.87/2.01 [84]~P27(x841)+P27(x842)+~E(x841,x842)
% 1.87/2.01 [85]~P26(x851)+P26(x852)+~E(x851,x852)
% 1.87/2.01 [86]~P58(x861)+P58(x862)+~E(x861,x862)
% 1.87/2.01 [87]~P55(x871)+P55(x872)+~E(x871,x872)
% 1.87/2.01 [88]~P43(x881)+P43(x882)+~E(x881,x882)
% 1.87/2.01 [89]~P57(x891)+P57(x892)+~E(x891,x892)
% 1.87/2.01 [90]~P28(x901)+P28(x902)+~E(x901,x902)
% 1.87/2.01 [91]~P34(x911)+P34(x912)+~E(x911,x912)
% 1.87/2.01 [92]~P56(x921)+P56(x922)+~E(x921,x922)
% 1.87/2.01 [93]~P22(x931)+P22(x932)+~E(x931,x932)
% 1.87/2.01 [94]~P63(x941)+P63(x942)+~E(x941,x942)
% 1.87/2.01 [95]~P70(x951)+P70(x952)+~E(x951,x952)
% 1.87/2.01 [96]~P67(x961)+P67(x962)+~E(x961,x962)
% 1.87/2.01 [97]~P35(x971)+P35(x972)+~E(x971,x972)
% 1.87/2.01 [98]P7(x982,x983,x984,x985)+~E(x981,x982)+~P7(x981,x983,x984,x985)
% 1.87/2.01 [99]P7(x993,x992,x994,x995)+~E(x991,x992)+~P7(x993,x991,x994,x995)
% 1.87/2.01 [100]P7(x1003,x1004,x1002,x1005)+~E(x1001,x1002)+~P7(x1003,x1004,x1001,x1005)
% 1.87/2.01 [101]P7(x1013,x1014,x1015,x1012)+~E(x1011,x1012)+~P7(x1013,x1014,x1015,x1011)
% 1.87/2.01 [102]~P29(x1021)+P29(x1022)+~E(x1021,x1022)
% 1.87/2.01 [103]~P72(x1031)+P72(x1032)+~E(x1031,x1032)
% 1.87/2.01 [104]~P23(x1041)+P23(x1042)+~E(x1041,x1042)
% 1.87/2.01 [105]~P59(x1051)+P59(x1052)+~E(x1051,x1052)
% 1.87/2.01 [106]~P42(x1061)+P42(x1062)+~E(x1061,x1062)
% 1.87/2.01 [107]~P38(x1071)+P38(x1072)+~E(x1071,x1072)
% 1.87/2.01 [108]~P74(x1081)+P74(x1082)+~E(x1081,x1082)
% 1.87/2.01 [109]~P19(x1091)+P19(x1092)+~E(x1091,x1092)
% 1.87/2.01 [110]~P75(x1101)+P75(x1102)+~E(x1101,x1102)
% 1.87/2.01 [111]~P15(x1111)+P15(x1112)+~E(x1111,x1112)
% 1.87/2.01 [112]~P53(x1121)+P53(x1122)+~E(x1121,x1122)
% 1.87/2.01 [113]~P39(x1131)+P39(x1132)+~E(x1131,x1132)
% 1.87/2.01 [114]~P77(x1141)+P77(x1142)+~E(x1141,x1142)
% 1.87/2.01 [115]~P30(x1151)+P30(x1152)+~E(x1151,x1152)
% 1.87/2.01 [116]~P21(x1161)+P21(x1162)+~E(x1161,x1162)
% 1.87/2.01 [117]~P47(x1171)+P47(x1172)+~E(x1171,x1172)
% 1.87/2.01 [118]~P10(x1181)+P10(x1182)+~E(x1181,x1182)
% 1.87/2.01 [119]~P40(x1191)+P40(x1192)+~E(x1191,x1192)
% 1.87/2.01 [120]~P13(x1201)+P13(x1202)+~E(x1201,x1202)
% 1.87/2.01 [121]~P31(x1211)+P31(x1212)+~E(x1211,x1212)
% 1.87/2.01 [122]~P17(x1221)+P17(x1222)+~E(x1221,x1222)
% 1.87/2.01 [123]~P33(x1231)+P33(x1232)+~E(x1231,x1232)
% 1.87/2.01 [124]~P11(x1241)+P11(x1242)+~E(x1241,x1242)
% 1.87/2.01 [125]~P14(x1251)+P14(x1252)+~E(x1251,x1252)
% 1.87/2.01 [126]~P54(x1261)+P54(x1262)+~E(x1261,x1262)
% 1.87/2.01 [127]~P32(x1271)+P32(x1272)+~E(x1271,x1272)
% 1.87/2.01 [128]~P69(x1281)+P69(x1282)+~E(x1281,x1282)
% 1.87/2.01 [129]~P64(x1291)+P64(x1292)+~E(x1291,x1292)
% 1.87/2.01 [130]~P68(x1301)+P68(x1302)+~E(x1301,x1302)
% 1.87/2.01 [131]~P78(x1311)+P78(x1312)+~E(x1311,x1312)
% 1.87/2.01 [132]~P45(x1321)+P45(x1322)+~E(x1321,x1322)
% 1.87/2.01 [133]~P76(x1331)+P76(x1332)+~E(x1331,x1332)
% 1.87/2.01 [134]~P60(x1341)+P60(x1342)+~E(x1341,x1342)
% 1.87/2.01 [135]~P46(x1351)+P46(x1352)+~E(x1351,x1352)
% 1.87/2.01 [136]~P71(x1361)+P71(x1362)+~E(x1361,x1362)
% 1.87/2.01 [137]~P16(x1371)+P16(x1372)+~E(x1371,x1372)
% 1.87/2.01 [138]~P48(x1381)+P48(x1382)+~E(x1381,x1382)
% 1.87/2.01 [139]~P18(x1391)+P18(x1392)+~E(x1391,x1392)
% 1.87/2.01 [140]~P65(x1401)+P65(x1402)+~E(x1401,x1402)
% 1.87/2.01 [141]~P66(x1411)+P66(x1412)+~E(x1411,x1412)
% 1.87/2.01 [142]~P62(x1421)+P62(x1422)+~E(x1421,x1422)
% 1.87/2.01 [143]~P61(x1431)+P61(x1432)+~E(x1431,x1432)
% 1.87/2.01 [144]~P20(x1441)+P20(x1442)+~E(x1441,x1442)
% 1.87/2.01 [145]~P44(x1451)+P44(x1452)+~E(x1451,x1452)
% 1.87/2.01 [146]~P12(x1461)+P12(x1462)+~E(x1461,x1462)
% 1.87/2.01 [147]~P25(x1471)+P25(x1472)+~E(x1471,x1472)
% 1.87/2.01 [148]~P24(x1481)+P24(x1482)+~E(x1481,x1482)
% 1.87/2.01
% 1.87/2.01 %-------------------------------------------
% 1.87/2.02 cnf(1890,plain,
% 1.87/2.02 (P5(a1,x18901,x18901)),
% 1.87/2.02 inference(rename_variables,[],[425])).
% 1.87/2.02 cnf(1893,plain,
% 1.87/2.02 (P5(a37,x18931,f8(a37,x18932,x18931))),
% 1.87/2.02 inference(rename_variables,[],[473])).
% 1.87/2.02 cnf(1899,plain,
% 1.87/2.02 (~P6(a37,f8(a37,x18991,x18992),x18992)),
% 1.87/2.02 inference(rename_variables,[],[555])).
% 1.87/2.02 cnf(1917,plain,
% 1.87/2.02 (P5(a36,x19171,f21(a14,f8(a36,f21(f7(a36,x19171),x19171),f21(f7(a36,x19172),x19172))))),
% 1.87/2.02 inference(rename_variables,[],[512])).
% 1.87/2.02 cnf(1926,plain,
% 1.87/2.02 (~E(f8(a1,x19261,x19261),f8(a1,f8(a1,x19262,x19262),f4(a1)))),
% 1.87/2.02 inference(rename_variables,[],[561])).
% 1.87/2.02 cnf(1942,plain,
% 1.87/2.02 (E(f12(a1,x19421),x19421)),
% 1.87/2.02 inference(rename_variables,[],[399])).
% 1.87/2.02 cnf(1946,plain,
% 1.87/2.02 (P5(a1,x19461,x19461)),
% 1.87/2.02 inference(rename_variables,[],[425])).
% 1.87/2.02 cnf(1948,plain,
% 1.87/2.02 (P5(a36,x19481,x19481)),
% 1.87/2.02 inference(rename_variables,[],[424])).
% 1.87/2.02 cnf(1975,plain,
% 1.87/2.02 (~P6(a37,x19751,x19751)),
% 1.87/2.02 inference(rename_variables,[],[547])).
% 1.87/2.02 cnf(1981,plain,
% 1.87/2.02 (P5(a1,x19811,x19811)),
% 1.87/2.02 inference(rename_variables,[],[425])).
% 1.87/2.02 cnf(2004,plain,
% 1.87/2.02 (~P6(a37,x20041,f2(a37))),
% 1.87/2.02 inference(rename_variables,[],[551])).
% 1.87/2.02 cnf(2066,plain,
% 1.87/2.02 (P5(a36,x20661,x20661)),
% 1.87/2.02 inference(rename_variables,[],[424])).
% 1.87/2.02 cnf(2081,plain,
% 1.87/2.02 (~P6(a36,f21(f20(a36),x20811),f2(a36))),
% 1.87/2.02 inference(rename_variables,[],[552])).
% 1.87/2.02 cnf(2088,plain,
% 1.87/2.02 (P5(a1,x20881,x20881)),
% 1.87/2.02 inference(rename_variables,[],[425])).
% 1.87/2.02 cnf(2091,plain,
% 1.87/2.02 (P5(a1,x20911,x20911)),
% 1.87/2.02 inference(rename_variables,[],[425])).
% 1.87/2.02 cnf(2096,plain,
% 1.87/2.02 (P5(a1,x20961,x20961)),
% 1.87/2.02 inference(rename_variables,[],[425])).
% 1.87/2.02 cnf(2148,plain,
% 1.87/2.02 (E(f21(f7(a36,x21481),x21482),f21(f7(a36,x21482),x21481))),
% 1.87/2.02 inference(rename_variables,[],[453])).
% 1.87/2.02 cnf(2155,plain,
% 1.87/2.02 ($false),
% 1.87/2.02 inference(scs_inference,[],[554,424,1948,2066,425,1890,1946,1981,2088,2091,2096,426,547,1975,155,156,157,161,163,165,167,169,170,248,249,253,254,257,259,262,277,296,297,298,303,311,312,324,334,341,349,350,352,353,371,374,375,545,439,551,2004,471,427,431,432,433,468,548,149,398,400,403,445,543,544,404,405,520,526,525,524,519,399,1942,473,1893,555,1899,556,443,448,459,552,2081,553,415,558,418,453,2148,561,1926,478,559,512,1917,532,530,542,2,753,736,731,730,641,744,1249,1239,1238,1144,1142,885,865,1822,1333,942,911,975,974,973,972,11,10,1518,1308,1231,1071,768,1865,100,75,74,66,65,3,959,958,955,954,805,765,764,594,575,800,1181,1824,1456,1241,965,1022,1021,767,596,1548,1342,1340,1087,619,1051,1050,1049,1047,1045,773,610,609,608,607,606,605,604,586,1280,1279,1278,1277,1276,772,689,688,797,796,795,750,743,742,1819,1126,1123,979,893,818,1826,1042,1040,984,982,981,1678,1677,1676,1588,1586,1132,1131,1334,1636,1634,1330,1329,1328,1477,1476,1475,783,782,705,704,1637,1262,1227,852,851,1571,1569]),
% 1.87/2.02 ['proof']).
% 1.87/2.02 % SZS output end Proof
% 1.87/2.02 % Total time :0.660000s
%------------------------------------------------------------------------------