TSTP Solution File: SWW204+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW204+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n005.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 00:13:06 EDT 2023
% Result : Theorem 2.58s 2.53s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW204+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 17:51:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 2.30/2.46 %-------------------------------------------
% 2.30/2.46 % File :CSE---1.6
% 2.30/2.46 % Problem :theBenchmark
% 2.30/2.46 % Transform :cnf
% 2.30/2.46 % Format :tptp:raw
% 2.30/2.46 % Command :java -jar mcs_scs.jar %d %s
% 2.30/2.46
% 2.30/2.46 % Result :Theorem 0.970000s
% 2.30/2.46 % Output :CNFRefutation 0.970000s
% 2.30/2.46 %-------------------------------------------
% 2.30/2.47 %------------------------------------------------------------------------------
% 2.30/2.47 % File : SWW204+1 : TPTP v8.1.2. Released v5.2.0.
% 2.30/2.47 % Domain : Software Verification
% 2.30/2.47 % Problem : Fundamental Theorem of Algebra 436686, 1000 axioms selected
% 2.30/2.47 % Version : Especial.
% 2.30/2.47 % English :
% 2.30/2.47
% 2.30/2.47 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 2.30/2.47 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 2.30/2.47 % Source : [Bla11]
% 2.30/2.47 % Names : fta_436686.1000.p [Bla11]
% 2.30/2.47
% 2.30/2.47 % Status : Theorem
% 2.30/2.47 % Rating : 0.31 v8.1.0, 0.28 v7.5.0, 0.31 v7.4.0, 0.23 v7.3.0, 0.21 v7.2.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.20 v6.4.0, 0.31 v6.3.0, 0.21 v6.2.0, 0.32 v6.1.0, 0.37 v6.0.0, 0.26 v5.5.0, 0.48 v5.4.0, 0.46 v5.3.0, 0.52 v5.2.0
% 2.30/2.47 % Syntax : Number of formulae : 1264 ( 419 unt; 0 def)
% 2.30/2.47 % Number of atoms : 2886 ( 714 equ)
% 2.30/2.47 % Maximal formula atoms : 13 ( 2 avg)
% 2.30/2.47 % Number of connectives : 1762 ( 140 ~; 57 |; 110 &)
% 2.30/2.47 % ( 221 <=>;1234 =>; 0 <=; 0 <~>)
% 2.30/2.47 % Maximal formula depth : 13 ( 4 avg)
% 2.30/2.47 % Maximal term depth : 10 ( 2 avg)
% 2.30/2.47 % Number of predicates : 73 ( 72 usr; 0 prp; 1-2 aty)
% 2.30/2.47 % Number of functors : 51 ( 51 usr; 12 con; 0-5 aty)
% 2.30/2.47 % Number of variables : 2706 (2663 !; 43 ?)
% 2.30/2.47 % SPC : FOF_THM_RFO_SEQ
% 2.30/2.47
% 2.30/2.47 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2.30/2.47 % 2011-03-01 11:28:42
% 2.40/2.47 %------------------------------------------------------------------------------
% 2.40/2.47 %----Relevant facts (997)
% 2.40/2.47 fof(fact_ext,axiom,
% 2.40/2.47 ! [V_gb_2,V_fa_2] :
% 2.40/2.47 ( ! [B_x] : hAPP(V_fa_2,B_x) = hAPP(V_gb_2,B_x)
% 2.40/2.47 => V_fa_2 = V_gb_2 ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_g_I1_J,axiom,
% 2.40/2.47 c_SEQ_Osubseq(v_ga____) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_order__refl,axiom,
% 2.40/2.47 ! [V_x,T_a] :
% 2.40/2.47 ( class_Orderings_Opreorder(T_a)
% 2.40/2.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_assms,axiom,
% 2.40/2.47 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)) ).
% 2.40/2.47
% 2.40/2.47 fof(fact__096cmod_A_Is_A0_J_A_060_061_Ar_096,axiom,
% 2.40/2.47 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_f_I1_J,axiom,
% 2.40/2.47 c_SEQ_Osubseq(v_f____) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_real__le__refl,axiom,
% 2.40/2.47 ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_real__le__linear,axiom,
% 2.40/2.47 ! [V_w,V_z] :
% 2.40/2.47 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
% 2.40/2.47 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_real__le__trans,axiom,
% 2.40/2.47 ! [V_k,V_j,V_i] :
% 2.40/2.47 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
% 2.40/2.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_real__le__antisym,axiom,
% 2.40/2.47 ! [V_w,V_z] :
% 2.40/2.47 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
% 2.40/2.47 => V_z = V_w ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_le__fun__def,axiom,
% 2.40/2.47 ! [V_gb_2,V_fa_2,T_a,T_b] :
% 2.40/2.47 ( class_Orderings_Oord(T_b)
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 2.40/2.47 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x)),hAPP(V_gb_2,B_x))) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_linorder__linear,axiom,
% 2.40/2.47 ! [V_y,V_x,T_a] :
% 2.40/2.47 ( class_Orderings_Olinorder(T_a)
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 2.40/2.47 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_order__eq__iff,axiom,
% 2.40/2.47 ! [V_y_2,V_x_2,T_a] :
% 2.40/2.47 ( class_Orderings_Oorder(T_a)
% 2.40/2.47 => ( V_x_2 = V_y_2
% 2.40/2.47 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 2.40/2.47 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_order__eq__refl,axiom,
% 2.40/2.47 ! [V_y,V_x,T_a] :
% 2.40/2.47 ( class_Orderings_Opreorder(T_a)
% 2.40/2.47 => ( V_x = V_y
% 2.40/2.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact__0960_A_060_061_Acmod_A_Is_A0_J_096,axiom,
% 2.40/2.47 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_linorder__le__cases,axiom,
% 2.40/2.47 ! [V_y,V_x,T_a] :
% 2.40/2.47 ( class_Orderings_Olinorder(T_a)
% 2.40/2.47 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 2.40/2.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_le__funE,axiom,
% 2.40/2.47 ! [V_x_2,V_gb_2,V_fa_2,T_a,T_b] :
% 2.40/2.47 ( class_Orderings_Oord(T_b)
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 2.40/2.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_xt1_I6_J,axiom,
% 2.40/2.47 ! [V_z,V_x,V_y,T_a] :
% 2.40/2.47 ( class_Orderings_Oorder(T_a)
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 2.40/2.47 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_xt1_I5_J,axiom,
% 2.40/2.47 ! [V_x,V_y,T_a] :
% 2.40/2.47 ( class_Orderings_Oorder(T_a)
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 2.40/2.47 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 2.40/2.47 => V_x = V_y ) ) ) ).
% 2.40/2.47
% 2.40/2.47 fof(fact_order__trans,axiom,
% 2.40/2.47 ! [V_z,V_y,V_x,T_a] :
% 2.40/2.47 ( class_Orderings_Opreorder(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_order__antisym,axiom,
% 2.40/2.48 ! [V_y,V_x,T_a] :
% 2.40/2.48 ( class_Orderings_Oorder(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 2.40/2.48 => V_x = V_y ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_xt1_I4_J,axiom,
% 2.40/2.48 ! [V_c,V_a,V_b,T_a] :
% 2.40/2.48 ( class_Orderings_Oorder(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 2.40/2.48 => ( V_b = V_c
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_ord__le__eq__trans,axiom,
% 2.40/2.48 ! [V_c,V_b,V_a,T_a] :
% 2.40/2.48 ( class_Orderings_Oord(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.40/2.48 => ( V_b = V_c
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_xt1_I3_J,axiom,
% 2.40/2.48 ! [V_c,V_b,V_a,T_a] :
% 2.40/2.48 ( class_Orderings_Oorder(T_a)
% 2.40/2.48 => ( V_a = V_b
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_ord__eq__le__trans,axiom,
% 2.40/2.48 ! [V_c,V_b,V_a,T_a] :
% 2.40/2.48 ( class_Orderings_Oord(T_a)
% 2.40/2.48 => ( V_a = V_b
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_order__antisym__conv,axiom,
% 2.40/2.48 ! [V_x_2,V_y_2,T_a] :
% 2.40/2.48 ( class_Orderings_Oorder(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 2.40/2.48 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_le__funD,axiom,
% 2.40/2.48 ! [V_x_2,V_gb_2,V_fa_2,T_a,T_b] :
% 2.40/2.48 ( class_Orderings_Oord(T_b)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_norm__le__zero__iff,axiom,
% 2.40/2.48 ! [V_x_2,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.40/2.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_norm__ge__zero,axiom,
% 2.40/2.48 ! [V_x,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x))) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_norm__eq__zero,axiom,
% 2.40/2.48 ! [V_x_2,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.40/2.48 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.40/2.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_norm__zero,axiom,
% 2.40/2.48 ! [T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.40/2.48 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_le0,axiom,
% 2.40/2.48 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_seq__suble,axiom,
% 2.40/2.48 ! [V_n_2,V_fa_2] :
% 2.40/2.48 ( c_SEQ_Osubseq(V_fa_2)
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),hAPP(V_fa_2,V_n_2))) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 2.40/2.48 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_le__0__eq,axiom,
% 2.40/2.48 ! [V_n_2] :
% 2.40/2.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 2.40/2.48 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_zero__reorient,axiom,
% 2.40/2.48 ! [V_x_2,T_a] :
% 2.40/2.48 ( class_Groups_Ozero(T_a)
% 2.40/2.48 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 2.40/2.48 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 2.40/2.48 ! [V_n_2] :
% 2.40/2.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.40/2.48 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_norm__ratiotest__lemma,axiom,
% 2.40/2.48 ! [V_y,V_x,V_c,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y))))
% 2.40/2.48 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__of__nat__ge__zero,axiom,
% 2.40/2.48 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n))) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_le__refl,axiom,
% 2.40/2.48 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_norm__mult,axiom,
% 2.40/2.48 ! [V_y,V_x,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 2.40/2.48 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__mult__commute,axiom,
% 2.40/2.48 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_nat__le__linear,axiom,
% 2.40/2.48 ! [V_n,V_m] :
% 2.40/2.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.40/2.48 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__of__nat__inject,axiom,
% 2.40/2.48 ! [V_m_2,V_n_2] :
% 2.40/2.48 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
% 2.40/2.48 <=> V_n_2 = V_m_2 ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__mult__assoc,axiom,
% 2.40/2.48 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_eq__imp__le,axiom,
% 2.40/2.48 ! [V_n,V_m] :
% 2.40/2.48 ( V_m = V_n
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_le__trans,axiom,
% 2.40/2.48 ! [V_k,V_j,V_i] :
% 2.40/2.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_le__antisym,axiom,
% 2.40/2.48 ! [V_n,V_m] :
% 2.40/2.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 2.40/2.48 => V_m = V_n ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.40/2.48 ! [V_c,V_b,V_a,T_a] :
% 2.40/2.48 ( class_Groups_Oab__semigroup__mult(T_a)
% 2.40/2.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult_Ozero__left,axiom,
% 2.40/2.48 ! [V_b,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__left_Ozero,axiom,
% 2.40/2.48 ! [V_y,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult_Ozero__right,axiom,
% 2.40/2.48 ! [V_a,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__right_Ozero,axiom,
% 2.40/2.48 ! [V_x,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.48 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_norm__mult__ineq,axiom,
% 2.40/2.48 ! [V_y,V_x,T_a] :
% 2.40/2.48 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__of__nat__le__iff,axiom,
% 2.40/2.48 ! [V_m_2,V_n_2] :
% 2.40/2.48 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))
% 2.40/2.48 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__mult__right__cancel,axiom,
% 2.40/2.48 ! [V_b_2,V_a_2,V_c_2] :
% 2.40/2.48 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.40/2.48 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)
% 2.40/2.48 <=> V_a_2 = V_b_2 ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__mult__left__cancel,axiom,
% 2.40/2.48 ! [V_b_2,V_a_2,V_c_2] :
% 2.40/2.48 ( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.40/2.48 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)
% 2.40/2.48 <=> V_a_2 = V_b_2 ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__of__nat__zero__iff,axiom,
% 2.40/2.48 ! [V_n_2] :
% 2.40/2.48 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.40/2.48 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_real__of__nat__zero,axiom,
% 2.40/2.48 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_zero__le__square,axiom,
% 2.40/2.48 ! [V_a,T_a] :
% 2.40/2.48 ( class_Rings_Olinordered__ring(T_a)
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_zero__le__mult__iff,axiom,
% 2.40/2.48 ! [V_b_2,V_a_2,T_a] :
% 2.40/2.48 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))
% 2.40/2.48 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 2.40/2.48 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) )
% 2.40/2.48 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.48 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__le__0__iff,axiom,
% 2.40/2.48 ! [V_b_2,V_a_2,T_a] :
% 2.40/2.48 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.48 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
% 2.40/2.48 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))) )
% 2.40/2.48 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.48 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__nonneg__nonneg,axiom,
% 2.40/2.48 ! [V_b,V_a,T_a] :
% 2.40/2.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__nonneg__nonpos,axiom,
% 2.40/2.48 ! [V_b,V_a,T_a] :
% 2.40/2.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__nonneg__nonpos2,axiom,
% 2.40/2.48 ! [V_b,V_a,T_a] :
% 2.40/2.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__nonpos__nonneg,axiom,
% 2.40/2.48 ! [V_b,V_a,T_a] :
% 2.40/2.48 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__nonpos__nonpos,axiom,
% 2.40/2.48 ! [V_b,V_a,T_a] :
% 2.40/2.48 ( class_Rings_Oordered__ring(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__right__mono,axiom,
% 2.40/2.48 ! [V_c,V_b,V_a,T_a] :
% 2.40/2.48 ( class_Rings_Oordered__semiring(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_mult__left__mono,axiom,
% 2.40/2.48 ! [V_c,V_b,V_a,T_a] :
% 2.40/2.48 ( class_Rings_Oordered__semiring(T_a)
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.40/2.48 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.40/2.48 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 2.40/2.48
% 2.40/2.48 fof(fact_comm__mult__left__mono,axiom,
% 2.40/2.49 ! [V_c,V_b,V_a,T_a] :
% 2.40/2.49 ( class_Rings_Oordered__comm__semiring(T_a)
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__0,axiom,
% 2.40/2.49 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__0__right,axiom,
% 2.40/2.49 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__is__0,axiom,
% 2.40/2.49 ! [V_n_2,V_m_2] :
% 2.40/2.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.40/2.49 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.40/2.49 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__cancel1,axiom,
% 2.40/2.49 ! [V_n_2,V_m_2,V_k_2] :
% 2.40/2.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 2.40/2.49 <=> ( V_m_2 = V_n_2
% 2.40/2.49 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__cancel2,axiom,
% 2.40/2.49 ! [V_n_2,V_k_2,V_m_2] :
% 2.40/2.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
% 2.40/2.49 <=> ( V_m_2 = V_n_2
% 2.40/2.49 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__le__mono,axiom,
% 2.40/2.49 ! [V_l,V_k,V_j,V_i] :
% 2.40/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__le__mono2,axiom,
% 2.40/2.49 ! [V_k,V_j,V_i] :
% 2.40/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__le__mono1,axiom,
% 2.40/2.49 ! [V_k,V_j,V_i] :
% 2.40/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_le__cube,axiom,
% 2.40/2.49 ! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_le__square,axiom,
% 2.40/2.49 ! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_real__of__nat__mult,axiom,
% 2.40/2.49 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_divisors__zero,axiom,
% 2.40/2.49 ! [V_b,V_a,T_a] :
% 2.40/2.49 ( class_Rings_Ono__zero__divisors(T_a)
% 2.40/2.49 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 2.40/2.49 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 2.40/2.49 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_no__zero__divisors,axiom,
% 2.40/2.49 ! [V_b,V_a,T_a] :
% 2.40/2.49 ( class_Rings_Ono__zero__divisors(T_a)
% 2.40/2.49 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 2.40/2.49 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__eq__0__iff,axiom,
% 2.40/2.49 ! [V_b_2,V_a_2,T_a] :
% 2.40/2.49 ( class_Rings_Oring__no__zero__divisors(T_a)
% 2.40/2.49 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.40/2.49 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.40/2.49 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__zero__right,axiom,
% 2.40/2.49 ! [V_a,T_a] :
% 2.40/2.49 ( class_Rings_Omult__zero(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__zero__left,axiom,
% 2.40/2.49 ! [V_a,T_a] :
% 2.40/2.49 ( class_Rings_Omult__zero(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_split__mult__neg__le,axiom,
% 2.40/2.49 ! [V_b,V_a,T_a] :
% 2.40/2.49 ( class_Rings_Oordered__cancel__semiring(T_a)
% 2.40/2.49 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.40/2.49 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 2.40/2.49 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.49 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_split__mult__pos__le,axiom,
% 2.40/2.49 ! [V_b,V_a,T_a] :
% 2.40/2.49 ( class_Rings_Oordered__ring(T_a)
% 2.40/2.49 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.40/2.49 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 2.40/2.49 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.49 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__mono,axiom,
% 2.40/2.49 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.40/2.49 ( class_Rings_Oordered__semiring(T_a)
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__mono_H,axiom,
% 2.40/2.49 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.40/2.49 ( class_Rings_Oordered__semiring(T_a)
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__left__mono__neg,axiom,
% 2.40/2.49 ! [V_c,V_a,V_b,T_a] :
% 2.40/2.49 ( class_Rings_Oordered__ring(T_a)
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__right__mono__neg,axiom,
% 2.40/2.49 ! [V_c,V_a,V_b,T_a] :
% 2.40/2.49 ( class_Rings_Oordered__ring(T_a)
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 2.40/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_decseq__def,axiom,
% 2.40/2.49 ! [V_X_2,T_a] :
% 2.40/2.49 ( class_Orderings_Oorder(T_a)
% 2.40/2.49 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 2.40/2.49 <=> ! [B_m,B_n] :
% 2.40/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 2.40/2.49 ! [V_a,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 2.40/2.49 ! [V_a,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult_Ononneg__bounded,axiom,
% 2.40/2.49 ! [T_a] :
% 2.40/2.49 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.49 => ? [B_K] :
% 2.40/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.40/2.49 & ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__right_Ononneg__bounded,axiom,
% 2.40/2.49 ! [V_x,T_a] :
% 2.40/2.49 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.49 => ? [B_K] :
% 2.40/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.40/2.49 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__left_Ononneg__bounded,axiom,
% 2.40/2.49 ! [V_y,T_a] :
% 2.40/2.49 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.49 => ? [B_K] :
% 2.40/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.40/2.49 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_incseq__def,axiom,
% 2.40/2.49 ! [V_X_2,T_a] :
% 2.40/2.49 ( class_Orderings_Oorder(T_a)
% 2.40/2.49 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 2.40/2.49 <=> ! [B_m,B_n] :
% 2.40/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 2.40/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) ) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult_Obounded,axiom,
% 2.40/2.49 ! [T_a] :
% 2.40/2.49 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.49 => ? [B_K] :
% 2.40/2.49 ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__right_Obounded,axiom,
% 2.40/2.49 ! [V_x,T_a] :
% 2.40/2.49 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.49 => ? [B_K] :
% 2.40/2.49 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_mult__left_Obounded,axiom,
% 2.40/2.49 ! [V_y,T_a] :
% 2.40/2.49 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.40/2.49 => ? [B_K] :
% 2.40/2.49 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_nat__mult__assoc,axiom,
% 2.40/2.49 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_nat__mult__commute,axiom,
% 2.40/2.49 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 2.40/2.49 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 2.40/2.49 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 2.40/2.49 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 2.40/2.49 ! [V_rx,V_ly,V_lx,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 2.40/2.49 ! [V_rx,V_ly,V_lx,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 2.40/2.49 ! [V_ry,V_rx,V_lx,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 2.40/2.49 ! [V_ry,V_rx,V_lx,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 2.40/2.49 ! [V_b,V_a,T_a] :
% 2.40/2.49 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.40/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 2.40/2.49 ! [V_n_2,V_m_2,V_k_2] :
% 2.40/2.49 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 2.40/2.49 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.40/2.49 | V_m_2 = V_n_2 ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_psize__eq__0__iff,axiom,
% 2.40/2.49 ! [V_p_2,T_a] :
% 2.40/2.49 ( class_Groups_Ozero(T_a)
% 2.40/2.49 => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.40/2.49 <=> V_p_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 2.40/2.49
% 2.40/2.49 fof(fact_le__mult__natfloor,axiom,
% 2.40/2.49 ! [V_b,V_a] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 2.45/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_monoseq__def,axiom,
% 2.45/2.49 ! [V_X_2,T_a] :
% 2.45/2.49 ( class_Orderings_Oorder(T_a)
% 2.45/2.49 => ( c_SEQ_Omonoseq(T_a,V_X_2)
% 2.45/2.49 <=> ( ! [B_m,B_n] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) )
% 2.45/2.49 | ! [B_m,B_n] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) ) ) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natceiling__le__eq,axiom,
% 2.45/2.49 ! [V_a_2,V_x_2] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2))
% 2.45/2.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2))) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_le__natfloor__eq,axiom,
% 2.45/2.49 ! [V_a_2,V_x_2] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2)))
% 2.45/2.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2)) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_decseq__imp__monoseq,axiom,
% 2.45/2.49 ! [V_X_2,T_a] :
% 2.45/2.49 ( class_Orderings_Oorder(T_a)
% 2.45/2.49 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 2.45/2.49 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_mult__left__idem,axiom,
% 2.45/2.49 ! [V_b,V_a,T_a] :
% 2.45/2.49 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 2.45/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_mult__idem,axiom,
% 2.45/2.49 ! [V_x,T_a] :
% 2.45/2.49 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 2.45/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natfloor__real__of__nat,axiom,
% 2.45/2.49 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natceiling__real__of__nat,axiom,
% 2.45/2.49 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natfloor__zero,axiom,
% 2.45/2.49 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_zero__le__natfloor,axiom,
% 2.45/2.49 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x))) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natfloor__mono,axiom,
% 2.45/2.49 ! [V_y,V_x] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_RComplete_Onatfloor(V_y))) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natceiling__zero,axiom,
% 2.45/2.49 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_zero__le__natceiling,axiom,
% 2.45/2.49 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(V_x))) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natceiling__mono,axiom,
% 2.45/2.49 ! [V_y,V_x] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),c_RComplete_Onatceiling(V_y))) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_real__natceiling__ge,axiom,
% 2.45/2.49 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)))) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natfloor__neg,axiom,
% 2.45/2.49 ! [V_x] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.45/2.49 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_real__natfloor__le,axiom,
% 2.45/2.49 ! [V_x] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),V_x)) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_le__natfloor,axiom,
% 2.45/2.49 ! [V_a,V_x] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)),V_a))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a))) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natceiling__neg,axiom,
% 2.45/2.49 ! [V_x] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.45/2.49 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_natceiling__le,axiom,
% 2.45/2.49 ! [V_a,V_x] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a)) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_incseq__imp__monoseq,axiom,
% 2.45/2.49 ! [V_X_2,T_a] :
% 2.45/2.49 ( class_Orderings_Oorder(T_a)
% 2.45/2.49 => ( c_SEQ_Oincseq(T_a,V_X_2)
% 2.45/2.49 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_times_Oidem,axiom,
% 2.45/2.49 ! [V_a,T_a] :
% 2.45/2.49 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 2.45/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_monoI1,axiom,
% 2.45/2.49 ! [V_X_2,T_a] :
% 2.45/2.49 ( class_Orderings_Oorder(T_a)
% 2.45/2.49 => ( ! [B_m,B_n] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) )
% 2.45/2.49 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_monoI2,axiom,
% 2.45/2.49 ! [V_X_2,T_a] :
% 2.45/2.49 ( class_Orderings_Oorder(T_a)
% 2.45/2.49 => ( ! [B_m,B_n] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) )
% 2.45/2.49 => c_SEQ_Omonoseq(T_a,V_X_2) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_mult__poly__0__left,axiom,
% 2.45/2.49 ! [V_q,T_a] :
% 2.45/2.49 ( class_Rings_Ocomm__semiring__0(T_a)
% 2.45/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_mult__poly__0__right,axiom,
% 2.45/2.49 ! [V_p,T_a] :
% 2.45/2.49 ( class_Rings_Ocomm__semiring__0(T_a)
% 2.45/2.49 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_g_I2_J,axiom,
% 2.45/2.49 c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_nat__mult__le__cancel1,axiom,
% 2.45/2.49 ! [V_n_2,V_m_2,V_k_2] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 2.45/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 2.45/2.49 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_mult__le__cancel2,axiom,
% 2.45/2.49 ! [V_n_2,V_k_2,V_m_2] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 2.45/2.49 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_mult__le__cancel1,axiom,
% 2.45/2.49 ! [V_n_2,V_m_2,V_k_2] :
% 2.45/2.49 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 2.45/2.49 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_norm__mult__less,axiom,
% 2.45/2.49 ! [V_s,V_y,V_r,V_x,T_a] :
% 2.45/2.49 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.45/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))
% 2.45/2.49 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))) ) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_less__zeroE,axiom,
% 2.45/2.49 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_f_I2_J,axiom,
% 2.45/2.49 c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_linorder__neqE__linordered__idom,axiom,
% 2.45/2.49 ! [V_y,V_x,T_a] :
% 2.45/2.49 ( class_Rings_Olinordered__idom(T_a)
% 2.45/2.49 => ( V_x != V_y
% 2.45/2.49 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.49 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ).
% 2.45/2.49
% 2.45/2.49 fof(fact_order__less__irrefl,axiom,
% 2.45/2.49 ! [V_x,T_a] :
% 2.45/2.49 ( class_Orderings_Opreorder(T_a)
% 2.45/2.49 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)) ) ).
% 2.45/2.49
% 2.45/2.50 fof(fact_linorder__neq__iff,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( V_x_2 != V_y_2
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_not__less__iff__gr__or__eq,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
% 2.45/2.50 | V_x_2 = V_y_2 ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__less__linear,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 | V_x = V_y
% 2.45/2.50 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__antisym__conv3,axiom,
% 2.45/2.50 ! [V_x_2,V_y_2,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__neqE,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( V_x != V_y
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__imp__neq,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => V_x != V_y ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__not__sym,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__imp__not__less,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__imp__not__eq,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => V_x != V_y ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__imp__not__eq2,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => V_y != V_x ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__asym_H,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.50 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_xt1_I9_J,axiom,
% 2.45/2.50 ! [V_a,V_b,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
% 2.45/2.50 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_ord__eq__less__trans,axiom,
% 2.45/2.50 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Orderings_Oord(T_a)
% 2.45/2.50 => ( V_a = V_b
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_xt1_I1_J,axiom,
% 2.45/2.50 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( V_a = V_b
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_ord__less__eq__trans,axiom,
% 2.45/2.50 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Orderings_Oord(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.50 => ( V_b = V_c
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_xt1_I2_J,axiom,
% 2.45/2.50 ! [V_c,V_a,V_b,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
% 2.45/2.50 => ( V_b = V_c
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__trans,axiom,
% 2.45/2.50 ! [V_z,V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_xt1_I10_J,axiom,
% 2.45/2.50 ! [V_z,V_x,V_y,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__asym,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__cases,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => ( V_x != V_y
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__not__refl,axiom,
% 2.45/2.50 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat__neq__iff,axiom,
% 2.45/2.50 ! [V_n_2,V_m_2] :
% 2.45/2.50 ( V_m_2 != V_n_2
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.50 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__neqE__nat,axiom,
% 2.45/2.50 ! [V_y,V_x] :
% 2.45/2.50 ( V_x != V_y
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__irrefl__nat,axiom,
% 2.45/2.50 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__not__refl2,axiom,
% 2.45/2.50 ! [V_m,V_n] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))
% 2.45/2.50 => V_m != V_n ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__not__refl3,axiom,
% 2.45/2.50 ! [V_t,V_s] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))
% 2.45/2.50 => V_s != V_t ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat__less__cases,axiom,
% 2.45/2.50 ! [V_P_2,V_n_2,V_m_2] :
% 2.45/2.50 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 2.45/2.50 => ( ( V_m_2 = V_n_2
% 2.45/2.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 2.45/2.50 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
% 2.45/2.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 2.45/2.50 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_real__of__nat__less__iff,axiom,
% 2.45/2.50 ! [V_m_2,V_n_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__not__less,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__not__le,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__le__less__linear,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 2.45/2.50 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__le,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 2.45/2.50 & V_x_2 != V_y_2 ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__le__not__le,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 2.45/2.50 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__le__less,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 | V_x_2 = V_y_2 ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_leI,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_not__leE,axiom,
% 2.45/2.50 ! [V_x,V_y,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__antisym__conv1,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__neq__le__trans,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( V_a != V_b
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_xt1_I12_J,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( V_a != V_b
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_leD,axiom,
% 2.45/2.50 ! [V_x,V_y,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 2.45/2.50 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__imp__le,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_linorder__antisym__conv2,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.50 ( class_Orderings_Olinorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
% 2.45/2.50 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__le__imp__less__or__eq,axiom,
% 2.45/2.50 ! [V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 | V_x = V_y ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__le__neq__trans,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.45/2.50 => ( V_a != V_b
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_xt1_I11_J,axiom,
% 2.45/2.50 ! [V_a,V_b,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 2.45/2.50 => ( V_a != V_b
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__less__le__trans,axiom,
% 2.45/2.50 ! [V_z,V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_xt1_I7_J,axiom,
% 2.45/2.50 ! [V_z,V_x,V_y,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_order__le__less__trans,axiom,
% 2.45/2.50 ! [V_z,V_y,V_x,T_a] :
% 2.45/2.50 ( class_Orderings_Opreorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_xt1_I8_J,axiom,
% 2.45/2.50 ! [V_z,V_x,V_y,T_a] :
% 2.45/2.50 ( class_Orderings_Oorder(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_gr0I,axiom,
% 2.45/2.50 ! [V_n] :
% 2.45/2.50 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_gr__implies__not0,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.45/2.50 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__nat__zero__code,axiom,
% 2.45/2.50 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_neq0__conv,axiom,
% 2.45/2.50 ! [V_n_2] :
% 2.45/2.50 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_not__less0,axiom,
% 2.45/2.50 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_real__less__def,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 2.45/2.50 & V_x_2 != V_y_2 ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__eq__real__def,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
% 2.45/2.50 | V_x_2 = V_y_2 ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat__less__le,axiom,
% 2.45/2.50 ! [V_n_2,V_m_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.50 & V_m_2 != V_n_2 ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_le__eq__less__or__eq,axiom,
% 2.45/2.50 ! [V_n_2,V_m_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.50 | V_m_2 = V_n_2 ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__imp__le__nat,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_le__neq__implies__less,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.45/2.50 => ( V_m != V_n
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__or__eq__imp__le,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.45/2.50 | V_m = V_n )
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 2.45/2.50 ! [V_n_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_subseq__def,axiom,
% 2.45/2.50 ! [V_fa_2] :
% 2.45/2.50 ( c_SEQ_Osubseq(V_fa_2)
% 2.45/2.50 <=> ! [B_m,B_n] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m)),hAPP(V_fa_2,B_n))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_not__square__less__zero,axiom,
% 2.45/2.50 ! [V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring(T_a)
% 2.45/2.50 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__cancel__right__disj,axiom,
% 2.45/2.50 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
% 2.45/2.50 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 2.45/2.50 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) )
% 2.45/2.50 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__cancel__left__disj,axiom,
% 2.45/2.50 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 2.45/2.50 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 2.45/2.50 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) )
% 2.45/2.50 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__cancel__left__pos,axiom,
% 2.45/2.50 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__pos__pos,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__pos__neg,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__pos__neg2,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_zero__less__mult__pos,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_zero__less__mult__pos2,axiom,
% 2.45/2.50 ! [V_a,V_b,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__cancel__left__neg,axiom,
% 2.45/2.50 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__neg__pos,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__neg__neg,axiom,
% 2.45/2.50 ! [V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__strict__right__mono,axiom,
% 2.45/2.50 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__strict__left__mono,axiom,
% 2.45/2.50 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_comm__mult__strict__left__mono,axiom,
% 2.45/2.50 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__strict__right__mono__neg,axiom,
% 2.45/2.50 ! [V_c,V_a,V_b,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__strict__left__mono__neg,axiom,
% 2.45/2.50 ! [V_c,V_a,V_b,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__natfloor,axiom,
% 2.45/2.50 ! [V_n,V_x] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n)))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_n)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat__0__less__mult__iff,axiom,
% 2.45/2.50 ! [V_n_2,V_m_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 2.45/2.50 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__cancel1,axiom,
% 2.45/2.50 ! [V_n_2,V_m_2,V_k_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 2.45/2.50 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__cancel2,axiom,
% 2.45/2.50 ! [V_n_2,V_k_2,V_m_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 2.45/2.50 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__mono1,axiom,
% 2.45/2.50 ! [V_k,V_j,V_i] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__mono2,axiom,
% 2.45/2.50 ! [V_k,V_j,V_i] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat__mult__less__cancel1,axiom,
% 2.45/2.50 ! [V_n_2,V_m_2,V_k_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat__mult__eq__cancel1,axiom,
% 2.45/2.50 ! [V_n_2,V_m_2,V_k_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 2.45/2.50 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 2.45/2.50 <=> V_m_2 = V_n_2 ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_real__mult__less__mono2,axiom,
% 2.45/2.50 ! [V_y,V_x,V_z] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_real__mult__order,axiom,
% 2.45/2.50 ! [V_y,V_x] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_real__mult__less__iff1,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,V_z_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_norm__not__less__zero,axiom,
% 2.45/2.50 ! [V_x,T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.50 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_not__real__of__nat__less__zero,axiom,
% 2.45/2.50 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__le__cancel__left__pos,axiom,
% 2.45/2.50 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__le__cancel__left__neg,axiom,
% 2.45/2.50 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),V_a_2)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__strict__mono,axiom,
% 2.45/2.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__strict__mono_H,axiom,
% 2.45/2.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__le__imp__less,axiom,
% 2.45/2.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__le__less__imp__less,axiom,
% 2.45/2.50 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__right__less__imp__less,axiom,
% 2.45/2.50 ! [V_b,V_c,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__imp__less__right,axiom,
% 2.45/2.50 ! [V_b,V_c,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__left__less__imp__less,axiom,
% 2.45/2.50 ! [V_b,V_a,V_c,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__less__imp__less__left,axiom,
% 2.45/2.50 ! [V_b,V_a,V_c,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__right__le__imp__le,axiom,
% 2.45/2.50 ! [V_b,V_c,V_a,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__left__le__imp__le,axiom,
% 2.45/2.50 ! [V_b,V_a,V_c,T_a] :
% 2.45/2.50 ( class_Rings_Olinordered__semiring__strict(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_zero__less__norm__iff,axiom,
% 2.45/2.50 ! [V_x_2,T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)))
% 2.45/2.50 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_real__mult__le__cancel__iff1,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,V_z_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_real__mult__le__cancel__iff2,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2,V_z_2] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2)))
% 2.45/2.50 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 2.45/2.50 ~ ! [B_g] :
% 2.45/2.50 ( c_SEQ_Osubseq(B_g)
% 2.45/2.50 => ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,B_g)))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_not__real__square__gt__zero,axiom,
% 2.45/2.50 ! [V_x_2] :
% 2.45/2.50 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)))
% 2.45/2.50 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__left_Opos__bounded,axiom,
% 2.45/2.50 ! [V_y,T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.45/2.50 => ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult__right_Opos__bounded,axiom,
% 2.45/2.50 ! [V_x,T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.45/2.50 => ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_mult_Opos__bounded,axiom,
% 2.45/2.50 ! [T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.45/2.50 => ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_a,B_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Im_Ozero,axiom,
% 2.45/2.50 hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_termination__basic__simps_I5_J,axiom,
% 2.45/2.50 ! [V_y,V_x] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Bseq__def,axiom,
% 2.45/2.50 ! [V_X_2,T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.50 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.45/2.50 <=> ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Im_Opos__bounded,axiom,
% 2.45/2.50 ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_complex__equality,axiom,
% 2.45/2.50 ! [V_y,V_x] :
% 2.45/2.50 ( hAPP(c_Complex_ORe,V_x) = hAPP(c_Complex_ORe,V_y)
% 2.45/2.50 => ( hAPP(c_Complex_OIm,V_x) = hAPP(c_Complex_OIm,V_y)
% 2.45/2.50 => V_x = V_y ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_expand__complex__eq,axiom,
% 2.45/2.50 ! [V_y_2,V_x_2] :
% 2.45/2.50 ( V_x_2 = V_y_2
% 2.45/2.50 <=> ( hAPP(c_Complex_ORe,V_x_2) = hAPP(c_Complex_ORe,V_y_2)
% 2.45/2.50 & hAPP(c_Complex_OIm,V_x_2) = hAPP(c_Complex_OIm,V_y_2) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Re_Ozero,axiom,
% 2.45/2.50 hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__fun__def,axiom,
% 2.45/2.50 ! [V_gb_2,V_fa_2,T_a,T_b] :
% 2.45/2.50 ( class_Orderings_Oord(T_b)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 2.45/2.50 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
% 2.45/2.50 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_gb_2),V_fa_2)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_complex__Re__le__cmod,axiom,
% 2.45/2.50 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Re_Opos__bounded,axiom,
% 2.45/2.50 ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Im_Ononneg__bounded,axiom,
% 2.45/2.50 ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Re_Ononneg__bounded,axiom,
% 2.45/2.50 ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Im_Obounded,axiom,
% 2.45/2.50 ? [B_K] :
% 2.45/2.50 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Re_Obounded,axiom,
% 2.45/2.50 ? [B_K] :
% 2.45/2.50 ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_BseqD,axiom,
% 2.45/2.50 ! [V_X_2,T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.50 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.45/2.50 => ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K)) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_BseqI,axiom,
% 2.45/2.50 ! [V_X_2,V_K_2,T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_K_2))
% 2.45/2.50 => ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2))
% 2.45/2.50 => c_SEQ_OBseq(T_a,V_X_2) ) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_BseqI2_H,axiom,
% 2.45/2.50 ! [V_K_2,V_X_2,V_N_2,T_a] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.50 => ( ! [B_n] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2),B_n))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2)) )
% 2.45/2.50 => c_SEQ_OBseq(T_a,V_X_2) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_lemma__NBseq__def,axiom,
% 2.45/2.50 ! [V_X_2,T_b] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__vector(T_b)
% 2.45/2.50 => ( ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K)) )
% 2.45/2.50 <=> ? [B_N] :
% 2.45/2.50 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_lemma__NBseq__def2,axiom,
% 2.45/2.50 ! [V_X_2,T_b] :
% 2.45/2.50 ( class_RealVector_Oreal__normed__vector(T_b)
% 2.45/2.50 => ( ? [B_K] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))
% 2.45/2.50 & ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K)) )
% 2.45/2.50 <=> ? [B_N] :
% 2.45/2.50 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_reals__Archimedean3,axiom,
% 2.45/2.50 ! [V_x] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.50 => ! [B_y] :
% 2.45/2.50 ? [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact__096EX_Af_O_Asubseq_Af_A_G_Amonoseq_A_I_Fn_O_A_IRe_Ao_As_J_A_If_An_J_J_096,axiom,
% 2.45/2.50 ? [B_f] :
% 2.45/2.50 ( c_SEQ_Osubseq(B_f)
% 2.45/2.50 & c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,v_s),B_f)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Suc__mono,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_lessI,axiom,
% 2.45/2.50 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_n))) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_zero__less__Suc,axiom,
% 2.45/2.50 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(V_n))) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Suc__inject,axiom,
% 2.45/2.50 ! [V_y,V_x] :
% 2.45/2.50 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 2.45/2.50 => V_x = V_y ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat_Oinject,axiom,
% 2.45/2.50 ! [V_nat_H_2,V_nat_2] :
% 2.45/2.50 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 2.45/2.50 <=> V_nat_2 = V_nat_H_2 ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Suc__n__not__n,axiom,
% 2.45/2.50 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 2.45/2.50
% 2.45/2.50 fof(fact_n__not__Suc__n,axiom,
% 2.45/2.50 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_comp__cong,axiom,
% 2.45/2.50 ! [T_e,T_d,T_c,T_a,T_b,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_gb_2,V_fa_2] :
% 2.45/2.50 ( hAPP(V_fa_2,hAPP(V_gb_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))
% 2.45/2.50 => hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2) = hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2,V_g_H_2),V_x_H_2) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Zero__not__Suc,axiom,
% 2.45/2.50 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat_Osimps_I2_J,axiom,
% 2.45/2.50 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Suc__not__Zero,axiom,
% 2.45/2.50 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_nat_Osimps_I3_J,axiom,
% 2.45/2.50 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Zero__neq__Suc,axiom,
% 2.45/2.50 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Suc__neq__Zero,axiom,
% 2.45/2.50 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Suc__less__SucD,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n)))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Suc__lessD,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__SucE,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
% 2.45/2.50 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.45/2.50 => V_m = V_n ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__trans__Suc,axiom,
% 2.45/2.50 ! [V_k,V_j,V_i] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i)),V_k)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_Suc__lessI,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.45/2.50 => ( c_Nat_OSuc(V_m) != V_n
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) ) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__SucI,axiom,
% 2.45/2.50 ! [V_n,V_m] :
% 2.45/2.50 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.45/2.50 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ).
% 2.45/2.50
% 2.45/2.50 fof(fact_less__antisym,axiom,
% 2.45/2.50 ! [V_m,V_n] :
% 2.45/2.50 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))
% 2.45/2.50 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_m)))
% 2.45/2.50 => V_m = V_n ) ) ).
% 2.45/2.50
% 2.45/2.51 fof(fact_not__less__less__Suc__eq,axiom,
% 2.45/2.51 ! [V_m_2,V_n_2] :
% 2.45/2.51 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
% 2.45/2.51 <=> V_n_2 = V_m_2 ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__less__eq,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_less__Suc__eq,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 2.45/2.51 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.51 | V_m_2 = V_n_2 ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_not__less__eq,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__leD,axiom,
% 2.45/2.51 ! [V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_le__SucE,axiom,
% 2.45/2.51 ! [V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
% 2.45/2.51 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.45/2.51 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_le__SucI,axiom,
% 2.45/2.51 ! [V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__le__mono,axiom,
% 2.45/2.51 ! [V_m_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_le__Suc__eq,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 2.45/2.51 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.51 | V_m_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_not__less__eq__eq,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__n__not__le__n,axiom,
% 2.45/2.51 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n)) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__mult__cancel1,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2,V_k_2] :
% 2.45/2.51 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
% 2.45/2.51 <=> V_m_2 = V_n_2 ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_less__Suc__eq__0__disj,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 2.45/2.51 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.51 | ? [B_j] :
% 2.45/2.51 ( V_m_2 = c_Nat_OSuc(B_j)
% 2.45/2.51 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_less__Suc0,axiom,
% 2.45/2.51 ! [V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 2.45/2.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_gr0__conv__Suc,axiom,
% 2.45/2.51 ! [V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__eq__1__iff,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.45/2.51 <=> ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.45/2.51 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_less__eq__Suc__le,axiom,
% 2.45/2.51 ! [V_m_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_less__Suc__eq__le,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__le__eq,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_le__imp__less__Suc,axiom,
% 2.45/2.51 ! [V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__leI,axiom,
% 2.45/2.51 ! [V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_le__less__Suc__eq,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
% 2.45/2.51 <=> V_n_2 = V_m_2 ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__le__lessD,axiom,
% 2.45/2.51 ! [V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__mult__less__cancel1,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2,V_k_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Suc__mult__le__cancel1,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2,V_k_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_monoseq__Suc,axiom,
% 2.45/2.51 ! [V_X_2,T_a] :
% 2.45/2.51 ( class_Orderings_Oorder(T_a)
% 2.45/2.51 => ( c_SEQ_Omonoseq(T_a,V_X_2)
% 2.45/2.51 <=> ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n))))
% 2.45/2.51 | ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n))),hAPP(V_X_2,B_n))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_subseq__Suc__iff,axiom,
% 2.45/2.51 ! [V_fa_2] :
% 2.45/2.51 ( c_SEQ_Osubseq(V_fa_2)
% 2.45/2.51 <=> ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n)))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_less__eq__Suc__le__raw,axiom,
% 2.45/2.51 ! [V_n_2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_n__less__m__mult__n,axiom,
% 2.45/2.51 ! [V_m,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_n__less__n__mult__m,axiom,
% 2.45/2.51 ! [V_m,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_one__less__mult,axiom,
% 2.45/2.51 ! [V_m,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_one__le__mult__iff,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
% 2.45/2.51 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))
% 2.45/2.51 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__of__nat__Suc__gt__zero,axiom,
% 2.45/2.51 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)))) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Bseq__iff,axiom,
% 2.45/2.51 ! [V_X_2,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.51 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.45/2.51 <=> ? [B_N] :
% 2.45/2.51 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Bseq__iff1a,axiom,
% 2.45/2.51 ! [V_X_2,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.51 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.45/2.51 <=> ? [B_N] :
% 2.45/2.51 ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 2.45/2.51 ! [V_x] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
% 2.45/2.51 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.51 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact__096EX_Afa_O_Asubseq_Afa_A_G_Amonoseq_A_I_Fn_O_A_IIm_Ao_As_Ao_Af_J_A_Ifa_An_J_J_096,axiom,
% 2.45/2.51 ? [B_f] :
% 2.45/2.51 ( c_SEQ_Osubseq(B_f)
% 2.45/2.51 & c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,v_s),v_f____),B_f)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_reals__Archimedean6a,axiom,
% 2.45/2.51 ! [V_r] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))
% 2.45/2.51 => ? [B_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_r))
% 2.45/2.51 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_reals__Archimedean4,axiom,
% 2.45/2.51 ! [V_x,V_y] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => ? [B_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y)),V_x))
% 2.45/2.51 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_K__record__comp,axiom,
% 2.45/2.51 ! [V_x_2,V_fa_2,V_c_2,T_c,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_a,T_c,c_COMBK(T_a,T_b,V_c_2),V_fa_2),V_x_2) = V_c_2 ).
% 2.45/2.51
% 2.45/2.51 fof(fact_o__eq__dest__lhs,axiom,
% 2.45/2.51 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] :
% 2.45/2.51 ( c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2) = V_c_2
% 2.45/2.51 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_o__def,axiom,
% 2.45/2.51 ! [V_x_2,V_gb_2,V_fa_2,T_c,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2) = hAPP(V_fa_2,hAPP(V_gb_2,V_x_2)) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__pos__mult__exp,axiom,
% 2.45/2.51 ! [V_x,V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_x) = c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__mult__lemma,axiom,
% 2.45/2.51 ! [V_y,V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 2.45/2.51 => c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__less__mono__lemma,axiom,
% 2.45/2.51 ! [V_y,V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__pos__pos,axiom,
% 2.45/2.51 ! [V_x_1,V_n_1] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_1))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_1))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_1,V_x_1))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__zero,axiom,
% 2.45/2.51 ! [V_n] : c_NthRoot_Oroot(V_n,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__Suc__0,axiom,
% 2.45/2.51 ! [V_x] : c_NthRoot_Oroot(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x) = V_x ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__commute,axiom,
% 2.45/2.51 ! [V_x,V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x)) = c_NthRoot_Oroot(V_n,c_NthRoot_Oroot(V_m,V_x)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__eq__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( c_NthRoot_Oroot(V_n_2,V_x_2) = c_NthRoot_Oroot(V_n_2,V_y_2)
% 2.45/2.51 <=> V_x_2 = V_y_2 ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__le__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_NthRoot_Oroot(V_n_2,V_y_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__le__mono,axiom,
% 2.45/2.51 ! [V_y,V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__eq__0__iff,axiom,
% 2.45/2.51 ! [V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( c_NthRoot_Oroot(V_n_2,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.45/2.51 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__less__mono,axiom,
% 2.45/2.51 ! [V_y,V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__less__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_NthRoot_Oroot(V_n_2,V_y_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__mult,axiom,
% 2.45/2.51 ! [V_y,V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__mult__exp,axiom,
% 2.45/2.51 ! [V_x,V_n,V_m] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_x) = c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_o__assoc,axiom,
% 2.45/2.51 ! [V_h_2,V_gb_2,T_d,V_fa_2,T_a,T_b,T_c] : c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2,c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2,V_h_2)) = c_Fun_Ocomp(T_d,T_b,T_a,c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2,V_gb_2),V_h_2) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_o__apply,axiom,
% 2.45/2.51 ! [V_x_2,V_gb_2,V_fa_2,T_c,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2) = hAPP(V_fa_2,hAPP(V_gb_2,V_x_2)) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_o__eq__dest,axiom,
% 2.45/2.51 ! [V_v_2,V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 2.45/2.51 ( c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2) = c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)
% 2.45/2.51 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_o__eq__elim,axiom,
% 2.45/2.51 ! [V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] :
% 2.45/2.51 ( c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2) = c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)
% 2.45/2.51 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__ge__zero,axiom,
% 2.45/2.51 ! [V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n,V_x))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__le__0__iff,axiom,
% 2.45/2.51 ! [V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__ge__0__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__gt__0__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__lt__0__iff,axiom,
% 2.45/2.51 ! [V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__gt__zero,axiom,
% 2.45/2.51 ! [V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n,V_x))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__strict__increasing,axiom,
% 2.45/2.51 ! [V_x,V_N,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_N,V_x))) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__increasing,axiom,
% 2.45/2.51 ! [V_x,V_N,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_N,V_x))) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__pow__pos,axiom,
% 2.45/2.51 ! [V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_n) = V_x ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__pos2,axiom,
% 2.45/2.51 ! [V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = V_x ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__pow__pos2,axiom,
% 2.45/2.51 ! [V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_n) = V_x ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_norm__power,axiom,
% 2.45/2.51 ! [V_n,V_x,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 2.45/2.51 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_norm__one,axiom,
% 2.45/2.51 ! [T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 2.45/2.51 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 2.45/2.51 ! [V_x,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_one__reorient,axiom,
% 2.45/2.51 ! [V_x_2,T_a] :
% 2.45/2.51 ( class_Groups_Oone(T_a)
% 2.45/2.51 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 2.45/2.51 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_norm__power__ineq,axiom,
% 2.45/2.51 ! [V_n,V_x,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 2.45/2.51 ! [V_q,V_y,V_x,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_one__neq__zero,axiom,
% 2.45/2.51 ! [T_a] :
% 2.45/2.51 ( class_Rings_Ozero__neq__one(T_a)
% 2.45/2.51 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_zero__neq__one,axiom,
% 2.45/2.51 ! [T_a] :
% 2.45/2.51 ( class_Rings_Ozero__neq__one(T_a)
% 2.45/2.51 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult_Ocomm__neutral,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Ocomm__monoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__1__right,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__1,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Ocomm__monoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__1__left,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 2.45/2.51 ! [V_q,V_p,V_x,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_Bseq__realpow,axiom,
% 2.45/2.51 ! [V_x_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.45/2.51 => c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__zero__not__eq__one,axiom,
% 2.45/2.51 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__mult__1,axiom,
% 2.45/2.51 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 2.45/2.51
% 2.45/2.51 fof(fact_realpow__Suc__le__self,axiom,
% 2.45/2.51 ! [V_n,V_r,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n))),V_r)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_monoseq__realpow,axiom,
% 2.45/2.51 ! [V_x_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.45/2.51 => c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 2.45/2.51 ! [V_q,V_x,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 2.45/2.51 ! [V_q,V_x,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 2.45/2.51 ! [V_q,V_x,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_not__one__le__zero,axiom,
% 2.45/2.51 ! [T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_zero__le__one,axiom,
% 2.45/2.51 ! [T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_zero__less__one,axiom,
% 2.45/2.51 ! [T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_not__one__less__zero,axiom,
% 2.45/2.51 ! [T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_less__1__mult,axiom,
% 2.45/2.51 ! [V_n,V_m,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__right__le__one__le,axiom,
% 2.45/2.51 ! [V_y,V_x,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__idom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__left__le__one__le,axiom,
% 2.45/2.51 ! [V_y,V_x,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__idom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__power,axiom,
% 2.45/2.51 ! [V_k,V_x,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_k)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_k) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__of__nat__one,axiom,
% 2.45/2.51 c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__eq__1__iff,axiom,
% 2.45/2.51 ! [V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( c_NthRoot_Oroot(V_n_2,V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 2.45/2.51 <=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__one,axiom,
% 2.45/2.51 ! [V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => c_NthRoot_Oroot(V_n,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__pos,axiom,
% 2.45/2.51 ! [V_n,V_x] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => c_NthRoot_Oroot(c_Nat_OSuc(V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),c_Nat_OSuc(V_n))) = V_x ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__decreasing,axiom,
% 2.45/2.51 ! [V_x,V_N,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_N,V_x)),c_NthRoot_Oroot(V_n,V_x))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__le__1__iff,axiom,
% 2.45/2.51 ! [V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__ge__1__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_y_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__gt__1__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_y_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__lt__1__iff,axiom,
% 2.45/2.51 ! [V_x_2,V_n_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__strict__decreasing,axiom,
% 2.45/2.51 ! [V_x,V_N,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_N,V_x)),c_NthRoot_Oroot(V_n,V_x))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__root__pos__unique,axiom,
% 2.45/2.51 ! [V_x,V_y,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 2.45/2.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),V_n) = V_x
% 2.45/2.51 => c_NthRoot_Oroot(V_n,V_x) = V_y ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__strict__mono,axiom,
% 2.45/2.51 ! [V_n,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_one__less__power,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__increasing__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__le__imp__le__exp,axiom,
% 2.45/2.51 ! [V_n,V_m,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__decreasing,axiom,
% 2.45/2.51 ! [V_a,V_N,V_n,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__one__right,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 2.45/2.51 ! [V_x,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__mult__1,axiom,
% 2.45/2.51 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__1__eq__mult__iff,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 2.45/2.51 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 2.45/2.51 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__mult__1__right,axiom,
% 2.45/2.51 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__mult__eq__1__iff,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2] :
% 2.45/2.51 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 2.45/2.51 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 2.45/2.51 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__Suc__0,axiom,
% 2.45/2.51 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 2.45/2.51 ! [V_m_2,V_x_2] :
% 2.45/2.51 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.45/2.51 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.51 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__power__less__imp__less,axiom,
% 2.45/2.51 ! [V_n,V_m,V_i] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__zero__less__power__iff,axiom,
% 2.45/2.51 ! [V_n_2,V_x_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
% 2.45/2.51 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 2.45/2.51 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_nat__one__le__power,axiom,
% 2.45/2.51 ! [V_n,V_i] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_zero__less__power__nat__eq,axiom,
% 2.45/2.51 ! [V_n_2,V_x_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
% 2.45/2.51 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.51 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__of__nat__power,axiom,
% 2.45/2.51 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__real__of__nat,axiom,
% 2.45/2.51 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_One__nat__def,axiom,
% 2.45/2.51 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__eq__self__implies__10,axiom,
% 2.45/2.51 ! [V_n,V_m] :
% 2.45/2.51 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 2.45/2.51 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 2.45/2.51 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_complex__Im__one,axiom,
% 2.45/2.51 hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_complex__Re__one,axiom,
% 2.45/2.51 hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__of__nat__1,axiom,
% 2.45/2.51 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_natfloor__one,axiom,
% 2.45/2.51 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_natceiling__one,axiom,
% 2.45/2.51 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_natfloor__power,axiom,
% 2.45/2.51 ! [V_n,V_x] :
% 2.45/2.51 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
% 2.45/2.51 => c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_le__natfloor__eq__one,axiom,
% 2.45/2.51 ! [V_x_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_natceiling__le__eq__one,axiom,
% 2.45/2.51 ! [V_x_2] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_field__power__not__zero,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 2.45/2.51 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__commutes,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__mult__distrib,axiom,
% 2.45/2.51 ! [V_n,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Ocomm__monoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__one,axiom,
% 2.45/2.51 ! [V_n,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__mult,axiom,
% 2.45/2.51 ! [V_n,V_m,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__mono,axiom,
% 2.45/2.51 ! [V_n,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_zero__le__power,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_zero__less__power,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_one__le__power,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__eq__0__iff,axiom,
% 2.45/2.51 ! [V_n_2,V_a_2,T_a] :
% 2.45/2.51 ( ( class_Power_Opower(T_a)
% 2.45/2.51 & class_Rings_Omult__zero(T_a)
% 2.45/2.51 & class_Rings_Ono__zero__divisors(T_a)
% 2.45/2.51 & class_Rings_Ozero__neq__one(T_a) )
% 2.45/2.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.51 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.51 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__inject__exp,axiom,
% 2.45/2.51 ! [V_n_2,V_m_2,V_a_2,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a_2))
% 2.45/2.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
% 2.45/2.51 <=> V_m_2 = V_n_2 ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__0__Suc,axiom,
% 2.45/2.51 ! [V_n,T_a] :
% 2.45/2.51 ( ( class_Power_Opower(T_a)
% 2.45/2.51 & class_Rings_Osemiring__0(T_a) )
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__Suc,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Power_Opower(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__Suc2,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__mult(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__0,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Power_Opower(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__less__imp__less__base,axiom,
% 2.45/2.51 ! [V_b,V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__inject__base,axiom,
% 2.45/2.51 ! [V_b,V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.51 => V_a = V_b ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__le__imp__le__base,axiom,
% 2.45/2.51 ! [V_b,V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__less__power__Suc,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__gt1__lemma,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__0__left,axiom,
% 2.45/2.51 ! [V_n,T_a] :
% 2.45/2.51 ( ( class_Power_Opower(T_a)
% 2.45/2.51 & class_Rings_Osemiring__0(T_a) )
% 2.45/2.51 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 2.45/2.51 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.51 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__gt1,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__strict__increasing__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__less__imp__less__exp,axiom,
% 2.45/2.51 ! [V_n,V_m,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__strict__increasing,axiom,
% 2.45/2.51 ! [V_a,V_N,V_n,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__increasing,axiom,
% 2.45/2.51 ! [V_a,V_N,V_n,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__Suc__less,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__Suc__less__one,axiom,
% 2.45/2.51 ! [V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__strict__decreasing,axiom,
% 2.45/2.51 ! [V_a,V_N,V_n,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__eq__imp__eq__base,axiom,
% 2.45/2.51 ! [V_b,V_n,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.51 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => V_a = V_b ) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_power__power__power,axiom,
% 2.45/2.51 ! [T_a] :
% 2.45/2.51 ( class_Power_Opower(T_a)
% 2.45/2.51 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_realpow__pos__nth__unique,axiom,
% 2.45/2.51 ! [V_a,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 2.45/2.51 => ? [B_x] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_x))
% 2.45/2.51 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
% 2.45/2.51 & ! [B_y] :
% 2.45/2.51 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_y))
% 2.45/2.51 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a )
% 2.45/2.51 => B_y = B_x ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_realpow__pos__nth,axiom,
% 2.45/2.51 ! [V_a,V_n] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 2.45/2.51 => ? [B_r] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r))
% 2.45/2.51 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 2.45/2.51 ! [V_n,V_x] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_ln__realpow,axiom,
% 2.45/2.51 ! [V_n,V_x] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__add__left__mono,axiom,
% 2.45/2.51 ! [V_z,V_y,V_x] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_real__add__mult__distrib,axiom,
% 2.45/2.51 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oab__semigroup__add(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__left__cancel,axiom,
% 2.45/2.51 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 2.45/2.51 ( class_Groups_Ocancel__semigroup__add(T_a)
% 2.45/2.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)
% 2.45/2.51 <=> V_b_2 = V_c_2 ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__right__cancel,axiom,
% 2.45/2.51 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 2.45/2.51 ( class_Groups_Ocancel__semigroup__add(T_a)
% 2.45/2.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)
% 2.45/2.51 <=> V_b_2 = V_c_2 ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__left__imp__eq,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Ocancel__semigroup__add(T_a)
% 2.45/2.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 2.45/2.51 => V_b = V_c ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__imp__eq,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 2.45/2.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 2.45/2.51 => V_b = V_c ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__right__imp__eq,axiom,
% 2.45/2.51 ! [V_c,V_a,V_b,T_a] :
% 2.45/2.51 ( class_Groups_Ocancel__semigroup__add(T_a)
% 2.45/2.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
% 2.45/2.51 => V_b = V_c ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 2.45/2.51 ! [V_c,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 2.45/2.51 ! [V_d,V_c,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 2.45/2.51 ! [V_d,V_c,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 2.45/2.51 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_norm__add__less,axiom,
% 2.45/2.51 ! [V_s,V_y,V_r,V_x,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_norm__triangle__ineq,axiom,
% 2.45/2.51 ! [V_y,V_x,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__class_Odistrib,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_combine__common__factor,axiom,
% 2.45/2.51 ! [V_c,V_b,V_e,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Osemiring(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult_Oadd__right,axiom,
% 2.45/2.51 ! [V_b_H,V_b,V_a,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__right_Oadd,axiom,
% 2.45/2.51 ! [V_y,V_x,V_xa,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult_Oadd__left,axiom,
% 2.45/2.51 ! [V_b,V_a_H,V_a,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_mult__left_Oadd,axiom,
% 2.45/2.51 ! [V_ya,V_y,V_x,T_a] :
% 2.45/2.51 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 2.45/2.51 ! [V_z,V_y,V_x,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_crossproduct__noteq,axiom,
% 2.45/2.51 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 2.45/2.51 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 2.45/2.51 => ( ( V_a_2 != V_b_2
% 2.45/2.51 & V_c_2 != V_d_2 )
% 2.45/2.51 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 2.45/2.51 ! [V_b,V_m,V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_crossproduct__eq,axiom,
% 2.45/2.51 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
% 2.45/2.51 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 2.45/2.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 2.45/2.51 <=> ( V_w_2 = V_x_2
% 2.45/2.51 | V_y_2 = V_z_2 ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__less__imp__less__left,axiom,
% 2.45/2.51 ! [V_b,V_a,V_c,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__less__imp__less__right,axiom,
% 2.45/2.51 ! [V_b,V_c,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__strict__mono,axiom,
% 2.45/2.51 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__strict__left__mono,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__strict__right__mono,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__less__cancel__left,axiom,
% 2.45/2.51 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__less__cancel__right,axiom,
% 2.45/2.51 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__le__imp__le__left,axiom,
% 2.45/2.51 ! [V_b,V_a,V_c,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__le__imp__le__right,axiom,
% 2.45/2.51 ! [V_b,V_c,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__mono,axiom,
% 2.45/2.51 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__left__mono,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__right__mono,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__le__cancel__left,axiom,
% 2.45/2.51 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__le__cancel__right,axiom,
% 2.45/2.51 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add_Ocomm__neutral,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Ocomm__monoid__add(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__0__right,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__add(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_double__zero__sym,axiom,
% 2.45/2.51 ! [V_a_2,T_a] :
% 2.45/2.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.45/2.51 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)
% 2.45/2.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__0,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Ocomm__monoid__add(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__0__left,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Groups_Omonoid__add(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__0__iff,axiom,
% 2.45/2.51 ! [V_a_2,V_b_2,T_a] :
% 2.45/2.51 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 2.45/2.51 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)
% 2.45/2.51 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 2.45/2.51 ! [V_a,T_a] :
% 2.45/2.51 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.51 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_ln__mult,axiom,
% 2.45/2.51 ! [V_y,V_x] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 2.45/2.51 => c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_ln__add__one__self__le__self,axiom,
% 2.45/2.51 ! [V_x] :
% 2.45/2.51 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))),V_x)) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.45/2.51 ! [V_a_2,T_a] :
% 2.45/2.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.45/2.51 ! [V_a_2,T_a] :
% 2.45/2.51 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.51 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__nonneg__nonneg,axiom,
% 2.45/2.51 ! [V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.51 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__nonneg__eq__0__iff,axiom,
% 2.45/2.51 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 2.45/2.51 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.51 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.51 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 2.45/2.51
% 2.45/2.51 fof(fact_add__increasing,axiom,
% 2.45/2.51 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.51 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.51 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__increasing2,axiom,
% 2.45/2.52 ! [V_a,V_b,V_c,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__nonpos__nonpos,axiom,
% 2.45/2.52 ! [V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.45/2.52 ! [V_a_2,T_a] :
% 2.45/2.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.45/2.52 ! [V_a_2,T_a] :
% 2.45/2.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__pos__pos,axiom,
% 2.45/2.52 ! [V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__neg__neg,axiom,
% 2.45/2.52 ! [V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_pos__add__strict,axiom,
% 2.45/2.52 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__le__less__mono,axiom,
% 2.45/2.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__less__le__mono,axiom,
% 2.45/2.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_sum__squares__eq__zero__iff,axiom,
% 2.45/2.52 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.52 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.52 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__scale__eq__noteq,axiom,
% 2.45/2.52 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 2.45/2.52 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 2.45/2.52 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.52 => ( ( V_a = V_b
% 2.45/2.52 & V_c != V_d )
% 2.45/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_less__add__one,axiom,
% 2.45/2.52 ! [V_a,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 2.45/2.52 ! [V_m,V_a,T_a] :
% 2.45/2.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 2.45/2.52 ! [V_a,V_m,T_a] :
% 2.45/2.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 2.45/2.52 ! [V_m,T_a] :
% 2.45/2.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.45/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_real__two__squares__add__zero__iff,axiom,
% 2.45/2.52 ! [V_y_2,V_x_2] :
% 2.45/2.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.45/2.52 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.45/2.52 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__less__self,axiom,
% 2.45/2.52 ! [V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),V_x)) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__inj__iff,axiom,
% 2.45/2.52 ! [V_y_2,V_x_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
% 2.45/2.52 => ( c_Transcendental_Oln(V_x_2) = c_Transcendental_Oln(V_y_2)
% 2.45/2.52 <=> V_x_2 = V_y_2 ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__less__cancel__iff,axiom,
% 2.45/2.52 ! [V_y_2,V_x_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__one,axiom,
% 2.45/2.52 c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__pos__nonneg,axiom,
% 2.45/2.52 ! [V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__nonneg__pos,axiom,
% 2.45/2.52 ! [V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__strict__increasing,axiom,
% 2.45/2.52 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__strict__increasing2,axiom,
% 2.45/2.52 ! [V_c,V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__neg__nonpos,axiom,
% 2.45/2.52 ! [V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__nonpos__neg,axiom,
% 2.45/2.52 ! [V_b,V_a,T_a] :
% 2.45/2.52 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_sum__squares__ge__zero,axiom,
% 2.45/2.52 ! [V_y,V_x,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__ring(T_a)
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_sum__squares__le__zero__iff,axiom,
% 2.45/2.52 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.52 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_not__sum__squares__lt__zero,axiom,
% 2.45/2.52 ! [V_y,V_x,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__ring(T_a)
% 2.45/2.52 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_sum__squares__gt__zero__iff,axiom,
% 2.45/2.52 ! [V_y_2,V_x_2,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__ring__strict(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))
% 2.45/2.52 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.52 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_zero__less__two,axiom,
% 2.45/2.52 ! [T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__semidom(T_a)
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_power_Opower_Opower__0,axiom,
% 2.45/2.52 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 2.45/2.52
% 2.45/2.52 fof(fact_power_Opower_Opower__Suc,axiom,
% 2.45/2.52 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_real__of__nat__Suc,axiom,
% 2.45/2.52 ! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_complex__Im__mult,axiom,
% 2.45/2.52 ! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__le__cancel__iff,axiom,
% 2.45/2.52 ! [V_y_2,V_x_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__ge__zero,axiom,
% 2.45/2.52 ! [V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__gt__zero__imp__gt__one,axiom,
% 2.45/2.52 ! [V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__less__zero,axiom,
% 2.45/2.52 ! [V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__less__zero__iff,axiom,
% 2.45/2.52 ! [V_x_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__eq__zero__iff,axiom,
% 2.45/2.52 ! [V_x_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.52 => ( c_Transcendental_Oln(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.45/2.52 <=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__gt__zero__iff,axiom,
% 2.45/2.52 ! [V_x_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__gt__zero,axiom,
% 2.45/2.52 ! [V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_convex__bound__le,axiom,
% 2.45/2.52 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__semiring__1(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 2.45/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_nat__less__real__le,axiom,
% 2.45/2.52 ! [V_m_2,V_n_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_nat__le__real__less,axiom,
% 2.45/2.52 ! [V_m_2,V_n_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_real__natfloor__add__one__gt,axiom,
% 2.45/2.52 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__ge__zero__iff,axiom,
% 2.45/2.52 ! [V_x_2] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_ln__ge__zero__imp__ge__one,axiom,
% 2.45/2.52 ! [V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_convex__bound__lt,axiom,
% 2.45/2.52 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 2.45/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_natfloor__eq,axiom,
% 2.45/2.52 ! [V_x,V_n] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
% 2.45/2.52 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_even__less__0__iff,axiom,
% 2.45/2.52 ! [V_a_2,T_a] :
% 2.45/2.52 ( class_Rings_Olinordered__idom(T_a)
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 2.45/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_natceiling__eq,axiom,
% 2.45/2.52 ! [V_x,V_n] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))
% 2.45/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
% 2.45/2.52 => c_RComplete_Onatceiling(V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_double__eq__0__iff,axiom,
% 2.45/2.52 ! [V_a_2,T_a] :
% 2.45/2.52 ( class_Groups_Olinordered__ab__group__add(T_a)
% 2.45/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.45/2.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_natceiling__add__one,axiom,
% 2.45/2.52 ! [V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.45/2.52 => c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_zpower__zadd__distrib,axiom,
% 2.45/2.52 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_plus__nat_Oadd__0,axiom,
% 2.45/2.52 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 2.45/2.52
% 2.45/2.52 fof(fact_Nat_Oadd__0__right,axiom,
% 2.45/2.52 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__is__0,axiom,
% 2.45/2.52 ! [V_n_2,V_m_2] :
% 2.45/2.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.52 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.45/2.52 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__eq__self__zero,axiom,
% 2.45/2.52 ! [V_n,V_m] :
% 2.45/2.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 2.45/2.52 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__Suc__shift,axiom,
% 2.45/2.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__Suc,axiom,
% 2.45/2.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__Suc__right,axiom,
% 2.45/2.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_termination__basic__simps_I2_J,axiom,
% 2.45/2.52 ! [V_y,V_z,V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_termination__basic__simps_I1_J,axiom,
% 2.45/2.52 ! [V_z,V_y,V_x] :
% 2.45/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
% 2.45/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 2.45/2.52
% 2.45/2.52 fof(fact_add__lessD1,axiom,
% 2.45/2.52 ! [V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_less__add__eq__less,axiom,
% 2.56/2.52 ! [V_n,V_m,V_l,V_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
% 2.56/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__less__mono,axiom,
% 2.56/2.52 ! [V_l,V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__less__mono1,axiom,
% 2.56/2.52 ! [V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_trans__less__add2,axiom,
% 2.56/2.52 ! [V_m,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_trans__less__add1,axiom,
% 2.56/2.52 ! [V_m,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_nat__add__left__cancel__less,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2,V_k_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_not__add__less2,axiom,
% 2.56/2.52 ! [V_i,V_j] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_not__add__less1,axiom,
% 2.56/2.52 ! [V_j,V_i] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_termination__basic__simps_I3_J,axiom,
% 2.56/2.52 ! [V_z,V_y,V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_termination__basic__simps_I4_J,axiom,
% 2.56/2.52 ! [V_y,V_z,V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__leE,axiom,
% 2.56/2.52 ! [V_n,V_k,V_m] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 2.56/2.52 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.56/2.52 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__leD1,axiom,
% 2.56/2.52 ! [V_n,V_k,V_m] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__leD2,axiom,
% 2.56/2.52 ! [V_n,V_k,V_m] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__le__mono,axiom,
% 2.56/2.52 ! [V_l,V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__le__mono1,axiom,
% 2.56/2.52 ! [V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_trans__le__add2,axiom,
% 2.56/2.52 ! [V_m,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_trans__le__add1,axiom,
% 2.56/2.52 ! [V_m,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_nat__add__left__cancel__le,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2,V_k_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__iff__add,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
% 2.56/2.52 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__Suc__ex__iff,axiom,
% 2.56/2.52 ! [V_l_2,V_k_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_l_2))
% 2.56/2.52 <=> ? [B_n] : V_l_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__add1,axiom,
% 2.56/2.52 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__add2,axiom,
% 2.56/2.52 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_left__add__mult__distrib,axiom,
% 2.56/2.52 ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__mult__distrib2,axiom,
% 2.56/2.52 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__mult__distrib,axiom,
% 2.56/2.52 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__poly__code_I1_J,axiom,
% 2.56/2.52 ! [V_q,T_a] :
% 2.56/2.52 ( class_Groups_Ocomm__monoid__add(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = V_q ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__poly__code_I2_J,axiom,
% 2.56/2.52 ! [V_p,T_a] :
% 2.56/2.52 ( class_Groups_Ocomm__monoid__add(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_nat__add__commute,axiom,
% 2.56/2.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_nat__add__left__commute,axiom,
% 2.56/2.52 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_nat__add__assoc,axiom,
% 2.56/2.52 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_nat__add__left__cancel,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2,V_k_2] :
% 2.56/2.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
% 2.56/2.52 <=> V_m_2 = V_n_2 ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_nat__add__right__cancel,axiom,
% 2.56/2.52 ! [V_n_2,V_k_2,V_m_2] :
% 2.56/2.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
% 2.56/2.52 <=> V_m_2 = V_n_2 ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult__poly__add__left,axiom,
% 2.56/2.52 ! [V_r,V_q,V_p,T_a] :
% 2.56/2.52 ( class_Rings_Ocomm__semiring__0(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Bseq__ignore__initial__segment,axiom,
% 2.56/2.52 ! [V_k_2,V_X_2,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.56/2.52 => ( c_SEQ_OBseq(T_a,V_X_2)
% 2.56/2.52 => c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Bseq__offset,axiom,
% 2.56/2.52 ! [V_k_2,V_X_2,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.56/2.52 => ( c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))
% 2.56/2.52 => c_SEQ_OBseq(T_a,V_X_2) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_power__add,axiom,
% 2.56/2.52 ! [V_n,V_m,V_a,T_a] :
% 2.56/2.52 ( class_Groups_Omonoid__mult(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 2.56/2.52 ! [V_q,V_p,V_x,T_a] :
% 2.56/2.52 ( class_Rings_Ocomm__semiring__1(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_one__is__add,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2] :
% 2.56/2.52 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
% 2.56/2.52 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.56/2.52 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.56/2.52 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.56/2.52 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__is__1,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2] :
% 2.56/2.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.56/2.52 <=> ( ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 2.56/2.52 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.56/2.52 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.56/2.52 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__gr__0,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
% 2.56/2.52 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 2.56/2.52 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_less__add__Suc1,axiom,
% 2.56/2.52 ! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_less__add__Suc2,axiom,
% 2.56/2.52 ! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_less__iff__Suc__add,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
% 2.56/2.52 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult__Suc__right,axiom,
% 2.56/2.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult__Suc,axiom,
% 2.56/2.52 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Suc__eq__plus1__left,axiom,
% 2.56/2.52 ! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Suc__eq__plus1,axiom,
% 2.56/2.52 ! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Re_Oadd,axiom,
% 2.56/2.52 ! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Im_Oadd,axiom,
% 2.56/2.52 ! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_real__of__nat__add,axiom,
% 2.56/2.52 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_complex__mod__triangle__sub,axiom,
% 2.56/2.52 ! [V_z,V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zpower__zpower,axiom,
% 2.56/2.52 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_natfloor__add,axiom,
% 2.56/2.52 ! [V_a,V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.56/2.52 => c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 2.56/2.52 ! [V_n,V_z] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z),c_RealDef_Oreal(tc_Nat_Onat,V_n))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_natceiling__add,axiom,
% 2.56/2.52 ! [V_a,V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.56/2.52 => c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_natfloor__add__one,axiom,
% 2.56/2.52 ! [V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
% 2.56/2.52 => c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_reduce__poly__simple,axiom,
% 2.56/2.52 ! [V_n,V_b] :
% 2.56/2.52 ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 2.56/2.52 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.56/2.52 => ? [B_z] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_ex__least__nat__less,axiom,
% 2.56/2.52 ! [V_n_2,V_P_2] :
% 2.56/2.52 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 2.56/2.52 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 2.56/2.52 => ? [B_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k),V_n_2))
% 2.56/2.52 & ! [B_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k))
% 2.56/2.52 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 2.56/2.52 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_cis__real__of__nat__Suc__mult,axiom,
% 2.56/2.52 ! [V_a,V_n] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zmult__1__right,axiom,
% 2.56/2.52 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zmult__1,axiom,
% 2.56/2.52 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 2.56/2.52
% 2.56/2.52 fof(fact_pos__zmult__eq__1__iff,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 2.56/2.52 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 2.56/2.52 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 2.56/2.52 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__zmult__distrib,axiom,
% 2.56/2.52 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__zmult__distrib2,axiom,
% 2.56/2.52 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zmult__zless__mono2,axiom,
% 2.56/2.52 ! [V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zmult__commute,axiom,
% 2.56/2.52 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zmult__assoc,axiom,
% 2.56/2.52 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_DeMoivre,axiom,
% 2.56/2.52 ! [V_n,V_a] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_cis__mult,axiom,
% 2.56/2.52 ! [V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_cis__zero,axiom,
% 2.56/2.52 c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_DeMoivre2,axiom,
% 2.56/2.52 ! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_expi__zero,axiom,
% 2.56/2.52 c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_cos__n__Re__cis__pow__n,axiom,
% 2.56/2.52 ! [V_a,V_n] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_odd__nonzero,axiom,
% 2.56/2.52 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zle__add1__eq__le,axiom,
% 2.56/2.52 ! [V_z_2,V_w_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add1__zle__eq,axiom,
% 2.56/2.52 ! [V_z_2,V_w_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zless__imp__add1__zle,axiom,
% 2.56/2.52 ! [V_z,V_w] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zless__add1__eq,axiom,
% 2.56/2.52 ! [V_z_2,V_w_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 2.56/2.52 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))
% 2.56/2.52 | V_w_2 = V_z_2 ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__imp__0__less,axiom,
% 2.56/2.52 ! [V_z] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_odd__less__0,axiom,
% 2.56/2.52 ! [V_z_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__0__right,axiom,
% 2.56/2.52 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__0,axiom,
% 2.56/2.52 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__assoc,axiom,
% 2.56/2.52 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__left__commute,axiom,
% 2.56/2.52 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__commute,axiom,
% 2.56/2.52 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__left__mono,axiom,
% 2.56/2.52 ! [V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__zless__mono,axiom,
% 2.56/2.52 ! [V_z,V_z_H,V_w,V_w_H] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zadd__strict__right__mono,axiom,
% 2.56/2.52 ! [V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Re__rcis,axiom,
% 2.56/2.52 ! [V_a,V_r] : hAPP(c_Complex_ORe,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_cos__le__one,axiom,
% 2.56/2.52 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_cos__zero,axiom,
% 2.56/2.52 c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zless__le,axiom,
% 2.56/2.52 ! [V_w_2,V_z_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))
% 2.56/2.52 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2))
% 2.56/2.52 & V_z_2 != V_w_2 ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zless__linear,axiom,
% 2.56/2.52 ! [V_y,V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y))
% 2.56/2.52 | V_x = V_y
% 2.56/2.52 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_int__0__less__1,axiom,
% 2.56/2.52 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_int__one__le__iff__zero__less,axiom,
% 2.56/2.52 ! [V_z_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_int__0__neq__1,axiom,
% 2.56/2.52 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Re__cis,axiom,
% 2.56/2.52 ! [V_a] : hAPP(c_Complex_ORe,c_Complex_Ocis(V_a)) = c_Transcendental_Ocos(V_a) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_cis__rcis__eq,axiom,
% 2.56/2.52 ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_rcis__zero__mod,axiom,
% 2.56/2.52 ! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_rcis__mult,axiom,
% 2.56/2.52 ! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_expi__add,axiom,
% 2.56/2.52 ! [V_b,V_a] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_self__quotient__aux2,axiom,
% 2.56/2.52 ! [V_q,V_r,V_a] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 2.56/2.52 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_self__quotient__aux1,axiom,
% 2.56/2.52 ! [V_q,V_r,V_a] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 2.56/2.52 => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_q__pos__lemma,axiom,
% 2.56/2.52 ! [V_r_H,V_q_H,V_b_H] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zle__refl,axiom,
% 2.56/2.52 ! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zle__linear,axiom,
% 2.56/2.52 ! [V_w,V_z] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w))
% 2.56/2.52 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zle__trans,axiom,
% 2.56/2.52 ! [V_k,V_j,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_k)) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zle__antisym,axiom,
% 2.56/2.52 ! [V_w,V_z] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z))
% 2.56/2.52 => V_z = V_w ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 2.56/2.52 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 2.56/2.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_unique__quotient__lemma__neg,axiom,
% 2.56/2.52 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zdiv__mono2__lemma,axiom,
% 2.56/2.52 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 2.56/2.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_unique__quotient__lemma,axiom,
% 2.56/2.52 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_q__neg__lemma,axiom,
% 2.56/2.52 ! [V_r_H,V_q_H,V_b_H] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 2.56/2.52 ! [V_n,V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 2.56/2.52 ! [V_y,V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 2.56/2.52 ! [V_y,V_x] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 2.56/2.52 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 2.56/2.52 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_sin__n__Im__cis__pow__n,axiom,
% 2.56/2.52 ! [V_a,V_n] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_realpow__pos__nth2,axiom,
% 2.56/2.52 ! [V_n,V_a] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
% 2.56/2.52 => ? [B_r] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r))
% 2.56/2.52 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),c_Nat_OSuc(V_n)) = V_a ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_sin__zero,axiom,
% 2.56/2.52 c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_sin__le__one,axiom,
% 2.56/2.52 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Im__cis,axiom,
% 2.56/2.52 ! [V_a] : hAPP(c_Complex_OIm,c_Complex_Ocis(V_a)) = c_Transcendental_Osin(V_a) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_cos__one__sin__zero,axiom,
% 2.56/2.52 ! [V_x] :
% 2.56/2.52 ( c_Transcendental_Ocos(V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 2.56/2.52 => c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_sin__add,axiom,
% 2.56/2.52 ! [V_y,V_x] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Im__rcis,axiom,
% 2.56/2.52 ! [V_a,V_r] : hAPP(c_Complex_OIm,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_sin__cos__squared__add3,axiom,
% 2.56/2.52 ! [V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_x))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_realpow__minus__mult,axiom,
% 2.56/2.52 ! [V_x,V_n,T_a] :
% 2.56/2.52 ( class_Groups_Omonoid__mult(T_a)
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.56/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_realpow__num__eq__if,axiom,
% 2.56/2.52 ! [V_m,V_n,T_a] :
% 2.56/2.52 ( class_Power_Opower(T_a)
% 2.56/2.52 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.56/2.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 2.56/2.52 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.56/2.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__iff__diff__le__0,axiom,
% 2.56/2.52 ! [V_b_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__diff__iff,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2,V_k_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Nat_Odiff__diff__eq,axiom,
% 2.56/2.52 ! [V_n,V_m,V_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_m))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_eq__diff__iff,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2,V_k_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 2.56/2.52 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
% 2.56/2.52 <=> V_m_2 = V_n_2 ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__diff__cancel,axiom,
% 2.56/2.52 ! [V_n,V_i] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_n))
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__le__mono,axiom,
% 2.56/2.52 ! [V_l,V_n,V_m] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__le__mono2,axiom,
% 2.56/2.52 ! [V_l,V_n,V_m] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__le__self,axiom,
% 2.56/2.52 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__eq__diff__less__eq,axiom,
% 2.56/2.52 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 2.56/2.52 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),V_d_2)) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_norm__triangle__ineq2,axiom,
% 2.56/2.52 ! [V_b,V_a,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__less__Suc,axiom,
% 2.56/2.52 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),c_Nat_OSuc(V_m))) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__add__0,axiom,
% 2.56/2.52 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__is__0__eq_H,axiom,
% 2.56/2.52 ! [V_n,V_m] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__is__0__eq,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2] :
% 2.56/2.52 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Suc__diff__le,axiom,
% 2.56/2.52 ! [V_m,V_n] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_less__diff__conv,axiom,
% 2.56/2.52 ! [V_k_2,V_j_2,V_i_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__diff__inverse,axiom,
% 2.56/2.52 ! [V_n,V_m] :
% 2.56/2.52 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.56/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_less__diff__iff,axiom,
% 2.56/2.52 ! [V_n_2,V_m_2,V_k_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__less__mono,axiom,
% 2.56/2.52 ! [V_c,V_b,V_a] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c),V_a))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__diff__right,axiom,
% 2.56/2.52 ! [V_i,V_j,V_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__diff__conv,axiom,
% 2.56/2.52 ! [V_i_2,V_k_2,V_j_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__add__diff,axiom,
% 2.56/2.52 ! [V_m,V_n,V_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__add__diff__inverse,axiom,
% 2.56/2.52 ! [V_m,V_n] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 2.56/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__diff__assoc,axiom,
% 2.56/2.52 ! [V_i,V_j,V_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 2.56/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__diff__conv2,axiom,
% 2.56/2.52 ! [V_i_2,V_j_2,V_k_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_j_2))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__add__diff__inverse2,axiom,
% 2.56/2.52 ! [V_m,V_n] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 2.56/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n) = V_m ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_le__imp__diff__is__add,axiom,
% 2.56/2.52 ! [V_k_2,V_j_2,V_i_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 2.56/2.52 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 2.56/2.52 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__add__assoc,axiom,
% 2.56/2.52 ! [V_i,V_j,V_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__diff__assoc2,axiom,
% 2.56/2.52 ! [V_i,V_j,V_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 2.56/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__add__assoc2,axiom,
% 2.56/2.52 ! [V_i,V_j,V_k] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__Suc__1,axiom,
% 2.56/2.52 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 2.56/2.52 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult__left_Odiff,axiom,
% 2.56/2.52 ! [V_ya,V_y,V_x,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult_Odiff__left,axiom,
% 2.56/2.52 ! [V_b,V_a_H,V_a,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult__right_Odiff,axiom,
% 2.56/2.52 ! [V_y,V_x,V_xa,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult_Odiff__right,axiom,
% 2.56/2.52 ! [V_b_H,V_b,V_a,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.56/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__mult__distrib,axiom,
% 2.56/2.52 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__mult__distrib2,axiom,
% 2.56/2.52 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_norm__minus__commute,axiom,
% 2.56/2.52 ! [V_b,V_a,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.56/2.52 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__Suc__Suc,axiom,
% 2.56/2.52 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_Suc__diff__diff,axiom,
% 2.56/2.52 ! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_fun__diff__def,axiom,
% 2.56/2.52 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 2.56/2.52 ( class_Groups_Ominus(T_a)
% 2.56/2.52 => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__eq__diff__eq,axiom,
% 2.56/2.52 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Groups_Oab__group__add(T_a)
% 2.56/2.52 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 2.56/2.52 => ( V_a_2 = V_b_2
% 2.56/2.52 <=> V_c_2 = V_d_2 ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__commute,axiom,
% 2.56/2.52 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_minus__apply,axiom,
% 2.56/2.52 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 2.56/2.52 ( class_Groups_Ominus(T_a)
% 2.56/2.52 => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_zero__less__diff,axiom,
% 2.56/2.52 ! [V_m_2,V_n_2] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__less,axiom,
% 2.56/2.52 ! [V_m,V_n] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__less__mono2,axiom,
% 2.56/2.52 ! [V_l,V_n,V_m] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_less__imp__diff__less,axiom,
% 2.56/2.52 ! [V_n,V_k,V_j] :
% 2.56/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))
% 2.56/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__eq__diff__less,axiom,
% 2.56/2.52 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 2.56/2.52 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)) ) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_right__minus__eq,axiom,
% 2.56/2.52 ! [V_b_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Groups_Ogroup__add(T_a)
% 2.56/2.52 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.56/2.52 <=> V_a_2 = V_b_2 ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_eq__iff__diff__eq__0,axiom,
% 2.56/2.52 ! [V_b_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Groups_Oab__group__add(T_a)
% 2.56/2.52 => ( V_a_2 = V_b_2
% 2.56/2.52 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__self,axiom,
% 2.56/2.52 ! [V_a,T_a] :
% 2.56/2.52 ( class_Groups_Ogroup__add(T_a)
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__0__right,axiom,
% 2.56/2.52 ! [V_a,T_a] :
% 2.56/2.52 ( class_Groups_Ogroup__add(T_a)
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__0__eq__0,axiom,
% 2.56/2.52 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_minus__nat_Odiff__0,axiom,
% 2.56/2.52 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__self__eq__0,axiom,
% 2.56/2.52 ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diffs0__imp__equal,axiom,
% 2.56/2.52 ! [V_n,V_m] :
% 2.56/2.52 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.56/2.52 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.56/2.52 => V_m = V_n ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult__diff__mult,axiom,
% 2.56/2.52 ! [V_b,V_a,V_y,V_x,T_a] :
% 2.56/2.52 ( class_Rings_Oring(T_a)
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_mult_Oprod__diff__prod,axiom,
% 2.56/2.52 ! [V_b,V_a,V_y,V_x,T_a] :
% 2.56/2.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_eq__add__iff2,axiom,
% 2.56/2.52 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Rings_Oring(T_a)
% 2.56/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
% 2.56/2.52 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_eq__add__iff1,axiom,
% 2.56/2.52 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Rings_Oring(T_a)
% 2.56/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)
% 2.56/2.52 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_less__iff__diff__less__0,axiom,
% 2.56/2.52 ! [V_b_2,V_a_2,T_a] :
% 2.56/2.52 ( class_Groups_Oordered__ab__group__add(T_a)
% 2.56/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
% 2.56/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__cancel2,axiom,
% 2.56/2.52 ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__cancel,axiom,
% 2.56/2.52 ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__diff__left,axiom,
% 2.56/2.52 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__add__inverse,axiom,
% 2.56/2.52 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n) = V_m ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__add__inverse2,axiom,
% 2.56/2.52 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n) = V_m ).
% 2.56/2.52
% 2.56/2.52 fof(fact_add__diff__cancel,axiom,
% 2.56/2.52 ! [V_b,V_a,T_a] :
% 2.56/2.52 ( class_Groups_Ogroup__add(T_a)
% 2.56/2.52 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = V_a ) ).
% 2.56/2.52
% 2.56/2.52 fof(fact_diff__add__cancel,axiom,
% 2.58/2.52 ! [V_b,V_a,T_a] :
% 2.58/2.52 ( class_Groups_Ogroup__add(T_a)
% 2.58/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b) = V_a ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_le__add__iff2,axiom,
% 2.58/2.52 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.58/2.52 ( class_Rings_Oordered__ring(T_a)
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_le__add__iff1,axiom,
% 2.58/2.52 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.58/2.52 ( class_Rings_Oordered__ring(T_a)
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_less__add__iff2,axiom,
% 2.58/2.52 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.58/2.52 ( class_Rings_Oordered__ring(T_a)
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_less__add__iff1,axiom,
% 2.58/2.52 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
% 2.58/2.52 ( class_Rings_Oordered__ring(T_a)
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_real__squared__diff__one__factored,axiom,
% 2.58/2.52 ! [V_x,T_a] :
% 2.58/2.52 ( class_Rings_Oring__1(T_a)
% 2.58/2.52 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_norm__triangle__ineq4,axiom,
% 2.58/2.52 ! [V_b,V_a,T_a] :
% 2.58/2.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.58/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)))) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_diff__Suc__less,axiom,
% 2.58/2.52 ! [V_i,V_n] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i))),V_n)) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_Suc__pred,axiom,
% 2.58/2.52 ! [V_n] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.52 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__diff__split,axiom,
% 2.58/2.52 ! [V_b_2,V_a_2,V_P_2] :
% 2.58/2.52 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 2.58/2.52 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))
% 2.58/2.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 2.58/2.52 & ! [B_d] :
% 2.58/2.52 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 2.58/2.52 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__diff__split__asm,axiom,
% 2.58/2.52 ! [V_b_2,V_a_2,V_P_2] :
% 2.58/2.52 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 2.58/2.52 <=> ~ ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))
% 2.58/2.52 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 2.58/2.52 | ? [B_d] :
% 2.58/2.52 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 2.58/2.52 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_diff__Suc__diff__eq1,axiom,
% 2.58/2.52 ! [V_m,V_j,V_k] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 2.58/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j)) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_diff__Suc__diff__eq2,axiom,
% 2.58/2.52 ! [V_m,V_j,V_k] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
% 2.58/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__le__add__iff1,axiom,
% 2.58/2.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__diff__add__eq1,axiom,
% 2.58/2.52 ! [V_n,V_m,V_u,V_i,V_j] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_i))
% 2.58/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__eq__add__iff1,axiom,
% 2.58/2.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 2.58/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 2.58/2.52 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__le__add__iff2,axiom,
% 2.58/2.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__diff__add__eq2,axiom,
% 2.58/2.52 ! [V_n,V_m,V_u,V_j,V_i] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 2.58/2.52 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n)) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__eq__add__iff2,axiom,
% 2.58/2.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 2.58/2.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 2.58/2.52 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_norm__diff__triangle__ineq,axiom,
% 2.58/2.52 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.58/2.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.58/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_lemma__realpow__diff,axiom,
% 2.58/2.52 ! [V_y,V_n,V_p,T_a] :
% 2.58/2.52 ( class_Groups_Omonoid__mult(T_a)
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p),V_n))
% 2.58/2.52 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_Suc__diff__1,axiom,
% 2.58/2.52 ! [V_n] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.52 => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_Suc__pred_H,axiom,
% 2.58/2.52 ! [V_n] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.52 => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_add__eq__if,axiom,
% 2.58/2.52 ! [V_n,V_m] :
% 2.58/2.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 2.58/2.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__less__add__iff2,axiom,
% 2.58/2.52 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_nat__less__add__iff1,axiom,
% 2.58/2.52 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_mult__eq__if,axiom,
% 2.58/2.52 ! [V_n,V_m] :
% 2.58/2.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.58/2.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.52 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_power__eq__if,axiom,
% 2.58/2.52 ! [V_p,V_m] :
% 2.58/2.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.52 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 2.58/2.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.52 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_realpow__two__diff,axiom,
% 2.58/2.52 ! [V_y,V_x,T_a] :
% 2.58/2.52 ( class_Rings_Ocomm__ring__1(T_a)
% 2.58/2.52 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_reals__Archimedean6,axiom,
% 2.58/2.52 ! [V_r] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))
% 2.58/2.52 => ? [B_n] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r))
% 2.58/2.52 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,B_n))) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_lemmaCauchy,axiom,
% 2.58/2.52 ! [V_X_2,V_M_2,T_a,T_b] :
% 2.58/2.52 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 2.58/2.52 & class_Orderings_Oord(T_a) )
% 2.58/2.52 => ( ! [B_n] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n))
% 2.58/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
% 2.58/2.52 => ! [B_n] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n))
% 2.58/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))) ) ) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_real__le__eq__diff,axiom,
% 2.58/2.52 ! [V_y_2,V_x_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_zdiff__zmult__distrib2,axiom,
% 2.58/2.52 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_zdiff__zmult__distrib,axiom,
% 2.58/2.52 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_Re_Odiff,axiom,
% 2.58/2.52 ! [V_y,V_x] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_Im_Odiff,axiom,
% 2.58/2.52 ! [V_y,V_x] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_less__bin__lemma,axiom,
% 2.58/2.52 ! [V_l_2,V_k_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_diff__poly__code_I2_J,axiom,
% 2.58/2.52 ! [V_p,T_a] :
% 2.58/2.52 ( class_Groups_Oab__group__add(T_a)
% 2.58/2.52 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_norm__diff__ineq,axiom,
% 2.58/2.52 ! [V_b,V_a,T_a] :
% 2.58/2.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.58/2.52 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_zle__diff1__eq,axiom,
% 2.58/2.52 ! [V_z_2,V_w_2] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 2.58/2.52 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_real__of__nat__diff,axiom,
% 2.58/2.52 ! [V_m,V_n] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 2.58/2.52 => c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_sin__diff,axiom,
% 2.58/2.52 ! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_sin__diff2,axiom,
% 2.58/2.52 ! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Osin(V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Ocos(V_x))) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_complex__mod__triangle__ineq2,axiom,
% 2.58/2.52 ! [V_a,V_b] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a))) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_cos__add,axiom,
% 2.58/2.52 ! [V_y,V_x] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_cos__diff,axiom,
% 2.58/2.52 ! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_cos__diff2,axiom,
% 2.58/2.52 ! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Osin(V_x))) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_natfloor__subtract,axiom,
% 2.58/2.52 ! [V_x,V_a] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x))
% 2.58/2.52 => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_real__natfloor__gt__diff__one,axiom,
% 2.58/2.52 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)))) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_natceiling__subtract,axiom,
% 2.58/2.52 ! [V_x,V_a] :
% 2.58/2.52 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x))
% 2.58/2.52 => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_complex__Re__mult,axiom,
% 2.58/2.52 ! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))) ).
% 2.58/2.52
% 2.58/2.52 fof(fact_unimodular__reduce__norm,axiom,
% 2.58/2.52 ! [V_z] :
% 2.58/2.52 ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 2.58/2.52 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.58/2.52 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.58/2.52 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 2.58/2.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_int__power__div__base,axiom,
% 2.58/2.53 ! [V_k,V_m] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__mult1__if,axiom,
% 2.58/2.53 ! [V_b,V_a,V_c,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 2.58/2.53 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__self2__is__id,axiom,
% 2.58/2.53 ! [V_a,V_b,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__self1__is__id,axiom,
% 2.58/2.53 ! [V_a,V_b,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__mult2,axiom,
% 2.58/2.53 ! [V_b,V_a,V_c,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__mult1,axiom,
% 2.58/2.53 ! [V_b,V_a,V_c,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zdiv__self,axiom,
% 2.58/2.53 ! [V_a] :
% 2.58/2.53 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__by__1,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__self,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 2.58/2.53 ! [V_a_2,V_b_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 2.58/2.53 ! [V_a_2,V_b_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__neg__pos__less0,axiom,
% 2.58/2.53 ! [V_b,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zdiv__zero,axiom,
% 2.58/2.53 ! [V_b] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 2.58/2.53 ! [V_y,V_x] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__by__0,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__0,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__i__not__one,axiom,
% 2.58/2.53 c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__i__not__zero,axiom,
% 2.58/2.53 c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__Re__i,axiom,
% 2.58/2.53 hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zdiv__mono1__neg,axiom,
% 2.58/2.53 ! [V_b,V_a_H,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zdiv__mono1,axiom,
% 2.58/2.53 ! [V_b,V_a_H,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__neg__neg__trivial,axiom,
% 2.58/2.53 ! [V_b,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_a))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zdiv__mono2__neg,axiom,
% 2.58/2.53 ! [V_b,V_b_H,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__nonpos__pos__le0,axiom,
% 2.58/2.53 ! [V_b,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 2.58/2.53 ! [V_a_2,V_b_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))
% 2.58/2.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__pos__pos__trivial,axiom,
% 2.58/2.53 ! [V_b,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),V_b))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__nonneg__neg__le0,axiom,
% 2.58/2.53 ! [V_b,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zdiv__mono2,axiom,
% 2.58/2.53 ! [V_b,V_b_H,V_a] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 2.58/2.53 ! [V_b_2,V_a_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))
% 2.58/2.53 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 2.58/2.53 ! [V_i_2,V_k_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)))
% 2.58/2.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2),V_i_2)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 2.58/2.53 ! [V_a_2,V_b_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))
% 2.58/2.53 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zdiv__eq__0__iff,axiom,
% 2.58/2.53 ! [V_k_2,V_i_2] :
% 2.58/2.53 ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.58/2.53 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.58/2.53 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2)) )
% 2.58/2.53 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_int__div__less__self,axiom,
% 2.58/2.53 ! [V_k,V_x] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zdiv__zmult2__eq,axiom,
% 2.58/2.53 ! [V_b,V_a,V_c] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__Im__i,axiom,
% 2.58/2.53 hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__self2,axiom,
% 2.58/2.53 ! [V_c,V_a,V_b,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__self1,axiom,
% 2.58/2.53 ! [V_c,V_a,V_b,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__add__self2,axiom,
% 2.58/2.53 ! [V_a,V_b,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__add__self1,axiom,
% 2.58/2.53 ! [V_a,V_b,T_a] :
% 2.58/2.53 ( class_Divides_Osemiring__div(T_a)
% 2.58/2.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_divmod__int__rel__div__eq,axiom,
% 2.58/2.53 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 2.58/2.53 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
% 2.58/2.53 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1)) ) )
% 2.58/2.53 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 2.58/2.53 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_split__zdiv,axiom,
% 2.58/2.53 ! [V_k_2,V_n_2,V_P_2] :
% 2.58/2.53 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
% 2.58/2.53 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.58/2.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 2.58/2.53 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 2.58/2.53 => ! [B_i] :
% 2.58/2.53 ( ? [B_j] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))
% 2.58/2.53 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 2.58/2.53 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 2.58/2.53 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 => ! [B_i] :
% 2.58/2.53 ( ? [B_j] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 2.58/2.53 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 2.58/2.53 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_metric__bound__lemma,axiom,
% 2.58/2.53 ! [V_y,V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)))))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_tsub__def,axiom,
% 2.58/2.53 ! [V_x,V_y] :
% 2.58/2.53 ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 2.58/2.53 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 2.58/2.53 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 2.58/2.53 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__triangle__ineq2__sym,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__triangle__ineq2,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__triangle__ineq3,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__minus__commute,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__triangle__ineq4,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__diff__triangle__ineq,axiom,
% 2.58/2.53 ! [V_d,V_c,V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__diff__less__iff,axiom,
% 2.58/2.53 ! [V_ra_2,V_a_2,V_x_2,T_a] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_a)
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2))),V_ra_2))
% 2.58/2.53 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2))) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__less,axiom,
% 2.58/2.53 ! [V_n,V_m] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__1,axiom,
% 2.58/2.53 ! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__le__mono,axiom,
% 2.58/2.53 ! [V_k,V_n,V_m] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__le__dividend,axiom,
% 2.58/2.53 ! [V_n,V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult2__eq,axiom,
% 2.58/2.53 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_poly__div__mult__right,axiom,
% 2.58/2.53 ! [V_z,V_y,V_x,T_a] :
% 2.58/2.53 ( class_Fields_Ofield(T_a)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_nat__mult__div__cancel__disj,axiom,
% 2.58/2.53 ! [V_n,V_m,V_k] :
% 2.58/2.53 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.58/2.53 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__add__abs,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__not__less__zero,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zero__less__abs__iff,axiom,
% 2.58/2.53 ! [V_a_2,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))
% 2.58/2.53 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__of__pos,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__mult__less,axiom,
% 2.58/2.53 ! [V_d,V_b,V_c,V_a,T_a] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_a)
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_c))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b)),V_d))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__one,axiom,
% 2.58/2.53 ! [T_a] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_a)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__zero,axiom,
% 2.58/2.53 ! [T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__eq__0,axiom,
% 2.58/2.53 ! [V_a_2,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 2.58/2.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__idempotent,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__real__of__nat__cancel,axiom,
% 2.58/2.53 ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__norm__cancel,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_real__norm__def,axiom,
% 2.58/2.53 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_power__abs,axiom,
% 2.58/2.53 ! [V_n,V_a,T_a] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_a)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__mult,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_a)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__mult__self,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_a)
% 2.58/2.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__ge__self,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__le__D1,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_b))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__triangle__ineq,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__of__nonneg,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__le__zero__iff,axiom,
% 2.58/2.53 ! [V_a_2,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 2.58/2.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__ge__zero,axiom,
% 2.58/2.53 ! [V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zero__le__power__abs,axiom,
% 2.58/2.53 ! [V_n,V_a,T_a] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__eq__mult,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_Rings_Oordered__ring__abs(T_a)
% 2.58/2.53 => ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 2.58/2.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 2.58/2.53 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 2.58/2.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__mult__pos,axiom,
% 2.58/2.53 ! [V_y,V_x,T_a] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_a)
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 2.58/2.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__mod__rcis,axiom,
% 2.58/2.53 ! [V_a,V_r] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__le__mono2,axiom,
% 2.58/2.53 ! [V_k,V_n,V_m] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__self__is__m,axiom,
% 2.58/2.53 ! [V_m,V_n] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__mult__self1__is__m,axiom,
% 2.58/2.53 ! [V_m,V_n] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_nat__mult__div__cancel1,axiom,
% 2.58/2.53 ! [V_n,V_m,V_k] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__less__dividend,axiom,
% 2.58/2.53 ! [V_m,V_n] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_rabs__ratiotest__lemma,axiom,
% 2.58/2.53 ! [V_y,V_x,V_c] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y))))
% 2.58/2.53 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__add__one__not__less__self,axiom,
% 2.58/2.53 ! [V_x] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x)) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_real__root__abs,axiom,
% 2.58/2.53 ! [V_x,V_n] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.53 => c_NthRoot_Oroot(V_n,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__cos__le__one,axiom,
% 2.58/2.53 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__sin__le__one,axiom,
% 2.58/2.53 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__Re__le__cmod,axiom,
% 2.58/2.53 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__Im__le__cmod,axiom,
% 2.58/2.53 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__if,axiom,
% 2.58/2.53 ! [V_m,V_n] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.53 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 2.58/2.53 & ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_div__geq,axiom,
% 2.58/2.53 ! [V_m,V_n] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.53 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_split__div,axiom,
% 2.58/2.53 ! [V_k_2,V_n_2,V_P_2] :
% 2.58/2.53 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
% 2.58/2.53 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.53 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 2.58/2.53 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.53 => ! [B_i,B_j] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_k_2))
% 2.58/2.53 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 2.58/2.53 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_norm__triangle__ineq3,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__add__one__gt__zero,axiom,
% 2.58/2.53 ! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_sin__zero__abs__cos__one,axiom,
% 2.58/2.53 ! [V_x] :
% 2.58/2.53 ( c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_split__div_H,axiom,
% 2.58/2.53 ! [V_n_2,V_m_2,V_P_2] :
% 2.58/2.53 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
% 2.58/2.53 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 2.58/2.53 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 2.58/2.53 | ? [B_q] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q))))
% 2.58/2.53 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_split__div__lemma,axiom,
% 2.58/2.53 ! [V_m_2,V_q_2,V_n_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 2.58/2.53 => ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))
% 2.58/2.53 & hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))) )
% 2.58/2.53 <=> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_le__div__geq,axiom,
% 2.58/2.53 ! [V_m,V_n] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 2.58/2.53 => c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 2.58/2.53 ! [V_y,V_x] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_tsub__eq,axiom,
% 2.58/2.53 ! [V_x,V_y] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
% 2.58/2.53 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_Deriv_Oadd__diff__add,axiom,
% 2.58/2.53 ! [V_d,V_b,V_c,V_a,T_a] :
% 2.58/2.53 ( class_Groups_Oab__group__add(T_a)
% 2.58/2.53 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__mult__def,axiom,
% 2.58/2.53 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_abs__zmult__eq__1,axiom,
% 2.58/2.53 ! [V_n,V_m] :
% 2.58/2.53 ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 2.58/2.53 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zabs__less__one__iff,axiom,
% 2.58/2.53 ! [V_z_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 2.58/2.53 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_Complex__eq__0,axiom,
% 2.58/2.53 ! [V_b_2,V_a_2] :
% 2.58/2.53 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 2.58/2.53 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.58/2.53 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__zero__def,axiom,
% 2.58/2.53 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__add,axiom,
% 2.58/2.53 ! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d)) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex_Oinject,axiom,
% 2.58/2.53 ! [V_real2_H_2,V_real1_H_2,V_real2_2,V_real1_2] :
% 2.58/2.53 ( c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)
% 2.58/2.53 <=> ( V_real1_2 = V_real1_H_2
% 2.58/2.53 & V_real2_2 = V_real2_H_2 ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_Im,axiom,
% 2.58/2.53 ! [V_y,V_x] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_y ).
% 2.58/2.53
% 2.58/2.53 fof(fact_Re,axiom,
% 2.58/2.53 ! [V_y,V_x] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_x ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__surj,axiom,
% 2.58/2.53 ! [V_z] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z)) = V_z ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__diff,axiom,
% 2.58/2.53 ! [V_d,V_c,V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zero__le__zpower__abs,axiom,
% 2.58/2.53 ! [V_n,V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_Complex__eq__i,axiom,
% 2.58/2.53 ! [V_y_2,V_x_2] :
% 2.58/2.53 ( c_Complex_Ocomplex_OComplex(V_x_2,V_y_2) = c_Complex_Oii
% 2.58/2.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.58/2.53 & V_y_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_i__def,axiom,
% 2.58/2.53 c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_Complex__eq__1,axiom,
% 2.58/2.53 ! [V_b_2,V_a_2] :
% 2.58/2.53 ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
% 2.58/2.53 <=> ( V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 2.58/2.53 & V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__one__def,axiom,
% 2.58/2.53 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_cis__def,axiom,
% 2.58/2.53 ! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a)) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_zero__less__zpower__abs__iff,axiom,
% 2.58/2.53 ! [V_n_2,V_x_2] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)))
% 2.58/2.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 2.58/2.53 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_cmod__unit__one,axiom,
% 2.58/2.53 ! [V_a] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__mult,axiom,
% 2.58/2.53 ! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex__add__def,axiom,
% 2.58/2.53 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_decr__lemma,axiom,
% 2.58/2.53 ! [V_z,V_x,V_d] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_incr__lemma,axiom,
% 2.58/2.53 ! [V_x,V_z,V_d] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 2.58/2.53 => hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex_Osize_I1_J,axiom,
% 2.58/2.53 ! [V_real2,V_real1] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_cos__arg__i__mult__zero__pos,axiom,
% 2.58/2.53 ! [V_y] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
% 2.58/2.53 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_cos__arg__i__mult__zero,axiom,
% 2.58/2.53 ! [V_y] :
% 2.58/2.53 ( V_y != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 2.58/2.53 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_cos__arg__i__mult__zero__neg,axiom,
% 2.58/2.53 ! [V_y] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.58/2.53 => c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex_Osize_I2_J,axiom,
% 2.58/2.53 ! [V_real2,V_real1] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex_Osimps_I2_J,axiom,
% 2.58/2.53 ! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_complex_Orecs,axiom,
% 2.58/2.53 ! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_natfloor__div__nat,axiom,
% 2.58/2.53 ! [V_y,V_x] :
% 2.58/2.53 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
% 2.58/2.53 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y))
% 2.58/2.53 => c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_real__0__le__divide__iff,axiom,
% 2.58/2.53 ! [V_y_2,V_x_2] :
% 2.58/2.53 ( hBOOL(hAPP(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)))
% 2.58/2.53 <=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
% 2.58/2.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)) )
% 2.58/2.53 & ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
% 2.58/2.53 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_times__divide__eq__right,axiom,
% 2.58/2.53 ! [V_c,V_b,V_a,T_a] :
% 2.58/2.53 ( class_Rings_Odivision__ring(T_a)
% 2.58/2.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_real__divide__square__eq,axiom,
% 2.58/2.53 ! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_power__divide,axiom,
% 2.58/2.53 ! [V_n,V_b,V_a,T_a] :
% 2.58/2.53 ( class_Fields_Ofield__inverse__zero(T_a)
% 2.58/2.53 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(fact_norm__divide,axiom,
% 2.58/2.53 ! [V_b,V_a,T_a] :
% 2.58/2.53 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 2.58/2.53 & class_RealVector_Oreal__normed__field(T_a) )
% 2.58/2.53 => c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)) ) ).
% 2.58/2.53
% 2.58/2.53 %----Arity declarations (263)
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Oidom(T_1)
% 2.58/2.53 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 2.58/2.53 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__ring(T_1)
% 2.58/2.53 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 2.58/2.53 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 2.58/2.53 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 2.58/2.53 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 2.58/2.53 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 2.58/2.53 class_Rings_Oidom(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 2.58/2.53 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_fun__Orderings_Opreorder,axiom,
% 2.58/2.53 ! [T_2,T_1] :
% 2.58/2.53 ( class_Orderings_Opreorder(T_1)
% 2.58/2.53 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_fun__Orderings_Oorder,axiom,
% 2.58/2.53 ! [T_2,T_1] :
% 2.58/2.53 ( class_Orderings_Oorder(T_1)
% 2.58/2.53 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_fun__Orderings_Oord,axiom,
% 2.58/2.53 ! [T_2,T_1] :
% 2.58/2.53 ( class_Orderings_Oord(T_1)
% 2.58/2.53 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_fun__Groups_Ominus,axiom,
% 2.58/2.53 ! [T_2,T_1] :
% 2.58/2.53 ( class_Groups_Ominus(T_1)
% 2.58/2.53 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.58/2.53 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 2.58/2.53 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 2.58/2.53 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 2.58/2.53 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 2.58/2.53 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 2.58/2.53 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 2.58/2.53 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 2.58/2.53 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 2.58/2.53 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 2.58/2.53 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 2.58/2.53 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 2.58/2.53 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 2.58/2.53 class_Orderings_Opreorder(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 2.58/2.53 class_Orderings_Olinorder(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 2.58/2.53 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 2.58/2.53 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 2.58/2.53 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 2.58/2.53 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 2.58/2.53 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 2.58/2.53 class_Rings_Omult__zero(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 2.58/2.53 class_Orderings_Oorder(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 2.58/2.53 class_Rings_Osemiring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 2.58/2.53 class_Orderings_Oord(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 2.58/2.53 class_Rings_Oring__1(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 2.58/2.53 class_Groups_Ominus(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Power_Opower,axiom,
% 2.58/2.53 class_Power_Opower(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 2.58/2.53 class_Groups_Ozero(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Rings_Oring,axiom,
% 2.58/2.53 class_Rings_Oring(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Int__Oint__Groups_Oone,axiom,
% 2.58/2.53 class_Groups_Oone(tc_Int_Oint) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.58/2.53 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 2.58/2.53 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 2.58/2.53 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 2.58/2.53 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 2.58/2.53 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 2.58/2.53 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 2.58/2.53 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 2.58/2.53 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 2.58/2.53 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 2.58/2.53 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 2.58/2.53 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 2.58/2.53 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 2.58/2.53 class_Orderings_Oorder(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 2.58/2.53 class_Rings_Osemiring(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 2.58/2.53 class_Orderings_Oord(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 2.58/2.53 class_Groups_Ominus(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Power_Opower,axiom,
% 2.58/2.53 class_Power_Opower(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 2.58/2.53 class_Groups_Ozero(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 2.58/2.53 class_Groups_Oone(tc_Nat_Onat) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 2.58/2.53 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 2.58/2.53 class_Orderings_Oorder(tc_HOL_Obool) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 2.58/2.53 class_Orderings_Oord(tc_HOL_Obool) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 2.58/2.53 class_Groups_Ominus(tc_HOL_Obool) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.58/2.53 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 2.58/2.53 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 2.58/2.53 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 2.58/2.53 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 2.58/2.53 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
% 2.58/2.53 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 2.58/2.53 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 2.58/2.53 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 2.58/2.53 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 2.58/2.53 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 2.58/2.53 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 2.58/2.53 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 2.58/2.53 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
% 2.58/2.53 class_Rings_Odivision__ring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 2.58/2.53 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 2.58/2.53 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 2.58/2.53 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 2.58/2.53 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 2.58/2.53 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 2.58/2.53 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 2.58/2.53 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 2.58/2.53 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 2.58/2.53 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 2.58/2.53 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 2.58/2.53 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 2.58/2.53 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 2.58/2.53 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 2.58/2.53 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 2.58/2.53 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
% 2.58/2.53 class_Groups_Ominus(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 2.58/2.53 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 2.58/2.53 class_Power_Opower(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 2.58/2.53 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 2.58/2.53 class_Rings_Oring(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 2.58/2.53 class_Groups_Oone(tc_RealDef_Oreal) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.58/2.53 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
% 2.58/2.53 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
% 2.58/2.53 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 2.58/2.53 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 2.58/2.53 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 2.58/2.53 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 2.58/2.53 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 2.58/2.53 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
% 2.58/2.53 class_Rings_Odivision__ring(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 2.58/2.53 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 2.58/2.53 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 2.58/2.53 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 2.58/2.53 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 2.58/2.53 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 2.58/2.53 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 2.58/2.53 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 2.58/2.53 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 2.58/2.53 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 2.58/2.53 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 2.58/2.53 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
% 2.58/2.53 class_Groups_Ominus(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 2.58/2.53 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 2.58/2.53 class_Power_Opower(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 2.58/2.53 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 2.58/2.53 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 2.58/2.53 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Oidom(T_1)
% 2.58/2.53 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 2.58/2.53 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Oidom(T_1)
% 2.58/2.53 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Oidom(T_1)
% 2.58/2.53 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 2.58/2.53 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.58/2.53 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.58/2.53 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Ocomm__monoid__add(T_1)
% 2.58/2.53 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Oidom(T_1)
% 2.58/2.53 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Ocomm__monoid__add(T_1)
% 2.58/2.53 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.58/2.53 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.58/2.53 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Fields_Ofield(T_1)
% 2.58/2.53 => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.58/2.53 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Oab__group__add(T_1)
% 2.58/2.53 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.58/2.53 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.58/2.53 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__ring__1(T_1)
% 2.58/2.53 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Ocomm__monoid__add(T_1)
% 2.58/2.53 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.58/2.53 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Oab__group__add(T_1)
% 2.58/2.53 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.58/2.53 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__0(T_1)
% 2.58/2.53 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Olinordered__idom(T_1)
% 2.58/2.53 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__ring__1(T_1)
% 2.58/2.53 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Oab__group__add(T_1)
% 2.58/2.53 => class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.58/2.53 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Groups_Ozero(T_1)
% 2.58/2.53 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__ring(T_1)
% 2.58/2.53 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 2.58/2.53 ! [T_1] :
% 2.58/2.53 ( class_Rings_Ocomm__semiring__1(T_1)
% 2.58/2.53 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 2.58/2.53
% 2.58/2.53 %----Helper facts (3)
% 2.58/2.53 fof(help_c__COMBK__1,axiom,
% 2.58/2.53 ! [V_Q,V_P,T_b,T_a] : hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P ).
% 2.58/2.53
% 2.58/2.53 fof(help_c__COMBB__1,axiom,
% 2.58/2.53 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ).
% 2.58/2.53
% 2.58/2.53 fof(help_c__COMBC__1,axiom,
% 2.58/2.53 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ).
% 2.58/2.53
% 2.58/2.53 %----Conjectures (1)
% 2.58/2.53 fof(conj_0,conjecture,
% 2.58/2.53 hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)) ).
% 2.58/2.53
% 2.58/2.53 %------------------------------------------------------------------------------
% 2.58/2.53 %-------------------------------------------
% 2.58/2.53 % Proof found
% 2.58/2.53 % SZS status Theorem for theBenchmark
% 2.58/2.53 % SZS output start Proof
% 2.58/2.53 %ClaNum:1970(EqnAxiom:308)
% 2.58/2.53 %VarNum:8740(SingletonVarNum:3148)
% 2.58/2.53 %MaxLitNum:7
% 2.58/2.53 %MaxfuncDepth:7
% 2.58/2.53 %SharedTerms:359
% 2.58/2.53 %goalClause: 731
% 2.58/2.53 %singleGoalClaCount:1
% 2.58/2.53 [309]P1(a1)
% 2.58/2.53 [310]P1(a2)
% 2.58/2.53 [311]P1(a3)
% 2.58/2.53 [312]P1(a53)
% 2.58/2.53 [313]P1(a79)
% 2.58/2.53 [314]P6(a90)
% 2.58/2.53 [315]P6(a91)
% 2.58/2.53 [316]P6(a92)
% 2.58/2.53 [317]P6(a93)
% 2.58/2.53 [318]P7(a90)
% 2.58/2.53 [319]P7(a91)
% 2.58/2.53 [320]P7(a92)
% 2.58/2.53 [321]P7(a93)
% 2.58/2.53 [322]P8(a90)
% 2.58/2.53 [323]P8(a91)
% 2.58/2.53 [324]P8(a92)
% 2.58/2.53 [325]P34(a90)
% 2.58/2.53 [326]P34(a91)
% 2.58/2.53 [327]P34(a92)
% 2.58/2.53 [328]P34(a93)
% 2.58/2.53 [329]P35(a90)
% 2.58/2.53 [330]P35(a94)
% 2.58/2.53 [331]P9(a90)
% 2.58/2.53 [332]P9(a94)
% 2.58/2.53 [333]P9(a91)
% 2.58/2.53 [334]P9(a92)
% 2.58/2.53 [335]P36(a90)
% 2.58/2.53 [336]P36(a94)
% 2.58/2.53 [337]P10(a90)
% 2.58/2.53 [338]P10(a94)
% 2.58/2.53 [339]P10(a91)
% 2.58/2.53 [340]P10(a92)
% 2.58/2.53 [341]P37(a90)
% 2.58/2.53 [342]P37(a94)
% 2.58/2.53 [343]P41(a90)
% 2.58/2.53 [344]P41(a92)
% 2.58/2.53 [345]P51(a90)
% 2.58/2.53 [346]P51(a92)
% 2.58/2.53 [347]P52(a90)
% 2.58/2.53 [348]P52(a91)
% 2.58/2.53 [349]P52(a92)
% 2.58/2.53 [350]P60(a90)
% 2.58/2.53 [351]P60(a92)
% 2.58/2.53 [352]P62(a90)
% 2.58/2.53 [353]P62(a91)
% 2.58/2.53 [354]P62(a92)
% 2.58/2.53 [355]P61(a90)
% 2.58/2.53 [356]P61(a91)
% 2.58/2.53 [357]P61(a92)
% 2.58/2.53 [358]P53(a90)
% 2.58/2.53 [359]P53(a94)
% 2.58/2.53 [360]P53(a91)
% 2.58/2.53 [361]P53(a92)
% 2.58/2.53 [362]P64(a90)
% 2.58/2.53 [363]P64(a94)
% 2.58/2.53 [364]P64(a92)
% 2.58/2.53 [365]P54(a90)
% 2.58/2.53 [366]P54(a94)
% 2.58/2.53 [367]P54(a91)
% 2.58/2.53 [368]P54(a92)
% 2.58/2.53 [369]P42(a90)
% 2.58/2.53 [370]P42(a94)
% 2.58/2.53 [371]P42(a91)
% 2.58/2.53 [372]P42(a92)
% 2.58/2.53 [373]P43(a90)
% 2.58/2.53 [374]P43(a94)
% 2.58/2.53 [375]P43(a91)
% 2.58/2.53 [376]P43(a92)
% 2.58/2.53 [377]P47(a90)
% 2.58/2.53 [378]P47(a92)
% 2.58/2.53 [379]P55(a90)
% 2.58/2.53 [380]P55(a91)
% 2.58/2.53 [381]P55(a92)
% 2.58/2.53 [382]P48(a90)
% 2.58/2.53 [383]P48(a91)
% 2.58/2.53 [384]P48(a92)
% 2.58/2.53 [385]P56(a90)
% 2.58/2.53 [386]P56(a91)
% 2.58/2.53 [387]P56(a92)
% 2.58/2.53 [388]P39(a90)
% 2.58/2.53 [389]P39(a94)
% 2.58/2.53 [390]P16(a90)
% 2.58/2.53 [391]P16(a94)
% 2.58/2.53 [392]P16(a91)
% 2.58/2.53 [393]P16(a92)
% 2.58/2.53 [394]P68(a90)
% 2.58/2.53 [395]P68(a94)
% 2.58/2.53 [396]P68(a91)
% 2.58/2.53 [397]P68(a92)
% 2.58/2.53 [398]P17(a90)
% 2.58/2.53 [399]P17(a94)
% 2.58/2.53 [400]P17(a91)
% 2.58/2.53 [401]P17(a92)
% 2.58/2.53 [402]P22(a90)
% 2.58/2.53 [403]P22(a94)
% 2.58/2.53 [404]P22(a91)
% 2.58/2.53 [405]P22(a92)
% 2.58/2.53 [406]P57(a90)
% 2.58/2.53 [407]P57(a91)
% 2.58/2.53 [408]P57(a92)
% 2.58/2.53 [409]P65(a90)
% 2.58/2.53 [410]P65(a94)
% 2.58/2.53 [411]P65(a92)
% 2.58/2.53 [412]P38(a90)
% 2.58/2.53 [413]P38(a94)
% 2.58/2.53 [414]P38(a91)
% 2.58/2.53 [415]P38(a92)
% 2.58/2.53 [416]P69(a90)
% 2.58/2.53 [417]P69(a94)
% 2.58/2.53 [418]P69(a91)
% 2.58/2.53 [419]P69(a92)
% 2.58/2.53 [420]P11(a90)
% 2.58/2.53 [421]P11(a94)
% 2.58/2.53 [422]P11(a91)
% 2.58/2.53 [423]P11(a92)
% 2.58/2.53 [424]P18(a90)
% 2.58/2.53 [425]P18(a94)
% 2.58/2.53 [426]P18(a91)
% 2.58/2.53 [427]P18(a92)
% 2.58/2.53 [428]P19(a90)
% 2.58/2.53 [429]P19(a94)
% 2.58/2.53 [430]P19(a91)
% 2.58/2.53 [431]P19(a92)
% 2.58/2.53 [432]P44(a90)
% 2.58/2.53 [433]P44(a94)
% 2.58/2.53 [434]P44(a91)
% 2.58/2.53 [435]P44(a92)
% 2.58/2.53 [436]P70(a90)
% 2.58/2.53 [437]P70(a94)
% 2.58/2.53 [438]P70(a91)
% 2.58/2.53 [439]P70(a92)
% 2.58/2.53 [440]P71(a90)
% 2.58/2.53 [441]P71(a94)
% 2.58/2.53 [442]P71(a91)
% 2.58/2.53 [443]P71(a92)
% 2.58/2.53 [444]P27(a90)
% 2.58/2.53 [445]P27(a91)
% 2.58/2.53 [446]P27(a92)
% 2.58/2.53 [447]P31(a90)
% 2.58/2.53 [448]P31(a91)
% 2.58/2.53 [449]P31(a92)
% 2.58/2.53 [450]P28(a90)
% 2.58/2.53 [451]P28(a91)
% 2.58/2.53 [452]P28(a92)
% 2.58/2.53 [453]P21(a90)
% 2.58/2.53 [454]P21(a94)
% 2.58/2.53 [455]P21(a91)
% 2.58/2.53 [456]P21(a92)
% 2.58/2.53 [457]P23(a90)
% 2.58/2.53 [458]P23(a94)
% 2.58/2.53 [459]P23(a91)
% 2.58/2.53 [460]P23(a92)
% 2.58/2.53 [461]P24(a90)
% 2.58/2.53 [462]P24(a92)
% 2.58/2.53 [463]P32(a90)
% 2.58/2.53 [464]P32(a91)
% 2.58/2.53 [465]P32(a92)
% 2.58/2.53 [466]P58(a90)
% 2.58/2.53 [467]P58(a92)
% 2.58/2.53 [468]P59(a90)
% 2.58/2.53 [469]P59(a92)
% 2.58/2.53 [470]P29(a90)
% 2.58/2.53 [471]P29(a92)
% 2.58/2.53 [472]P26(a90)
% 2.58/2.53 [473]P26(a94)
% 2.58/2.53 [474]P26(a91)
% 2.58/2.53 [475]P26(a92)
% 2.58/2.53 [476]P26(a93)
% 2.58/2.53 [477]P12(a90)
% 2.58/2.53 [478]P12(a94)
% 2.58/2.53 [479]P12(a92)
% 2.58/2.53 [480]P25(a90)
% 2.58/2.53 [481]P25(a94)
% 2.58/2.53 [482]P25(a92)
% 2.58/2.53 [483]P66(a90)
% 2.58/2.53 [484]P66(a94)
% 2.58/2.53 [485]P66(a92)
% 2.58/2.53 [486]P67(a90)
% 2.58/2.53 [487]P67(a94)
% 2.58/2.53 [488]P67(a92)
% 2.58/2.53 [489]P45(a90)
% 2.58/2.53 [490]P45(a94)
% 2.58/2.53 [491]P45(a92)
% 2.58/2.53 [492]P13(a91)
% 2.58/2.53 [493]P13(a92)
% 2.58/2.53 [494]P30(a90)
% 2.58/2.53 [495]P30(a92)
% 2.58/2.53 [496]P14(a90)
% 2.58/2.53 [497]P14(a94)
% 2.58/2.53 [498]P63(a90)
% 2.58/2.53 [499]P63(a92)
% 2.58/2.53 [500]P49(a90)
% 2.58/2.53 [501]P49(a94)
% 2.58/2.53 [502]P15(a90)
% 2.58/2.53 [503]P15(a94)
% 2.58/2.53 [504]P40(a90)
% 2.58/2.53 [505]P40(a94)
% 2.58/2.53 [506]P50(a90)
% 2.58/2.53 [507]P50(a94)
% 2.58/2.53 [508]P50(a92)
% 2.58/2.53 [509]P20(a90)
% 2.58/2.53 [510]P20(a94)
% 2.58/2.53 [511]P20(a91)
% 2.58/2.53 [512]P20(a92)
% 2.58/2.53 [513]P46(a90)
% 2.58/2.53 [514]P46(a94)
% 2.58/2.53 [515]P46(a92)
% 2.58/2.53 [522]E(f95(a7,a17),f5(a90))
% 2.58/2.53 [523]E(f95(a11,a17),f4(a90))
% 2.58/2.53 [714]~E(f4(a94),a17)
% 2.58/2.53 [715]~E(f5(a94),a17)
% 2.58/2.53 [716]~E(f5(a90),f4(a90))
% 2.58/2.53 [717]~E(f5(a92),f4(a92))
% 2.58/2.53 [516]E(f26(f4(a90)),f4(a91))
% 2.58/2.53 [517]E(f26(f5(a90)),f5(a91))
% 2.58/2.53 [518]E(f27(f4(a90)),f4(a91))
% 2.58/2.53 [519]E(f27(f5(a90)),f5(a91))
% 2.58/2.53 [520]E(f35(f5(a90)),f4(a90))
% 2.58/2.53 [521]E(f6(f4(a94)),f5(a94))
% 2.58/2.53 [524]E(f95(a7,f4(a94)),f4(a90))
% 2.58/2.53 [525]E(f95(a7,f5(a94)),f4(a90))
% 2.58/2.53 [526]E(f95(a11,f4(a94)),f4(a90))
% 2.58/2.53 [527]E(f95(a11,f5(a94)),f5(a90))
% 2.58/2.53 [528]E(f36(a91,f4(a91)),f4(a90))
% 2.58/2.53 [529]E(f36(a91,f5(a91)),f5(a90))
% 2.58/2.53 [532]E(f12(f4(a90),f5(a90)),a17)
% 2.58/2.53 [533]E(f12(f4(a90),f4(a90)),f4(a94))
% 2.58/2.53 [534]E(f12(f5(a90),f4(a90)),f5(a94))
% 2.58/2.53 [535]E(f18(f5(a90),f4(a90)),f5(a94))
% 2.58/2.53 [579]P72(f95(f31(a92,f4(a92)),f5(a92)))
% 2.58/2.53 [580]P72(f95(f32(a92,f4(a92)),f5(a92)))
% 2.58/2.53 [708]P2(a90,f9(a94,a90,a91,a11,f9(a91,a94,a91,a124,a2)))
% 2.58/2.53 [709]P2(a90,f9(a91,a90,a91,f21(a94,a90,a91,a11,a124),a53))
% 2.58/2.53 [555]E(f95(a7,f18(f5(a90),f4(a90))),f4(a90))
% 2.58/2.53 [556]E(f95(a11,f18(f5(a90),f4(a90))),f5(a90))
% 2.58/2.53 [567]P72(f95(f31(a90,f4(a90)),a54))
% 2.58/2.53 [568]P72(f95(f31(a90,f4(a90)),a63))
% 2.58/2.53 [569]P72(f95(f32(a90,f4(a90)),a55))
% 2.58/2.53 [570]P72(f95(f32(a90,f4(a90)),a61))
% 2.58/2.53 [589]E(f36(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),f5(a90))
% 2.58/2.53 [711]P2(a90,f9(a94,a90,a91,a7,f9(a91,a94,a91,a124,f9(a91,a91,a91,a2,a1))))
% 2.58/2.53 [712]P2(a90,f9(a94,a90,a91,a7,f9(a91,a94,a91,a124,f9(a91,a91,a91,a2,a3))))
% 2.58/2.53 [713]P2(a90,f9(a91,a90,a91,f21(a91,a90,a91,f21(a94,a90,a91,a7,a124),a2),a79))
% 2.58/2.53 [731]~P72(f95(f31(a90,f4(a90)),a125))
% 2.58/2.53 [612]P72(f95(f31(a90,f4(a90)),f37(a94,f95(a124,f4(a91)))))
% 2.58/2.53 [536]E(f37(a90,x5361),f19(a90,x5361))
% 2.58/2.53 [558]E(f23(a91,x5581,x5581),f4(a91))
% 2.58/2.53 [530]E(f28(x5301,f4(a90)),f4(a90))
% 2.58/2.53 [531]E(f18(f4(a90),x5311),f4(a94))
% 2.58/2.53 [537]E(f26(f36(a91,x5371)),x5371)
% 2.58/2.53 [538]E(f27(f36(a91,x5381)),x5381)
% 2.58/2.53 [543]E(f19(a90,f36(a91,x5431)),f36(a91,x5431))
% 2.58/2.53 [544]E(f95(f95(f24(a91),x5441),f5(a91)),x5441)
% 2.58/2.53 [545]E(f95(f95(f24(a92),x5451),f5(a92)),x5451)
% 2.58/2.53 [546]E(f95(f95(f25(a91),x5461),f4(a91)),x5461)
% 2.58/2.53 [547]E(f95(f95(f25(a92),x5471),f4(a92)),x5471)
% 2.58/2.53 [549]E(f95(f95(f24(a91),x5491),f4(a91)),f4(a91))
% 2.58/2.53 [559]E(f23(a91,x5591,f4(a91)),x5591)
% 2.58/2.53 [561]E(f23(a91,f4(a91),x5611),f4(a91))
% 2.58/2.53 [562]E(f20(a92,f4(a92),x5621),f4(a92))
% 2.58/2.53 [563]E(f12(f95(a11,x5631),f95(a7,x5631)),x5631)
% 2.58/2.53 [564]P72(f95(f31(a90,x5641),x5641))
% 2.58/2.53 [565]P72(f95(f31(a91,x5651),x5651))
% 2.58/2.53 [566]P72(f95(f31(a92,x5661),x5661))
% 2.58/2.53 [590]P72(f95(f31(a90,f4(a90)),f36(a91,x5901)))
% 2.58/2.53 [604]P72(f95(f31(a90,f95(a11,x6041)),f37(a94,x6041)))
% 2.58/2.53 [650]P72(f95(f31(a90,f19(a90,f95(a7,x6501))),f37(a94,x6501)))
% 2.58/2.53 [651]P72(f95(f31(a90,f19(a90,f95(a11,x6511))),f37(a94,x6511)))
% 2.58/2.53 [653]P72(f95(f31(a90,f95(a7,f18(f5(a90),x6531))),f5(a90)))
% 2.58/2.53 [654]P72(f95(f31(a90,f95(a11,f18(f5(a90),x6541))),f5(a90)))
% 2.58/2.53 [684]P72(f95(f31(a90,f19(a90,f95(a7,f18(f5(a90),x6841)))),f5(a90)))
% 2.58/2.53 [685]P72(f95(f31(a90,f19(a90,f95(a11,f18(f5(a90),x6851)))),f5(a90)))
% 2.58/2.53 [719]~E(f95(f95(f25(a91),x7191),f5(a91)),x7191)
% 2.58/2.53 [725]~E(f95(f95(f25(a91),x7251),f5(a91)),f4(a91))
% 2.58/2.53 [727]~P72(f95(f32(a91,x7271),x7271))
% 2.58/2.53 [730]~P72(f95(f32(a91,x7301),f4(a91)))
% 2.58/2.53 [732]~P72(f95(f32(a90,f36(a91,x7321)),f4(a90)))
% 2.58/2.53 [550]E(f95(f95(f24(a90),f5(a90)),x5501),x5501)
% 2.58/2.53 [551]E(f95(f95(f24(a91),f5(a91)),x5511),x5511)
% 2.58/2.53 [552]E(f95(f95(f24(a92),f5(a92)),x5521),x5521)
% 2.58/2.53 [553]E(f95(f95(f25(a91),f4(a91)),x5531),x5531)
% 2.58/2.53 [554]E(f95(f95(f25(a92),f4(a92)),x5541),x5541)
% 2.58/2.53 [557]E(f95(f95(f24(a91),f4(a91)),x5571),f4(a91))
% 2.58/2.53 [572]P72(f95(f31(a91,f4(a91)),x5721))
% 2.58/2.53 [586]E(f31(a91,f95(f95(f25(a91),x5861),f5(a91))),f32(a91,x5861))
% 2.58/2.53 [588]E(f28(f95(f95(f25(a91),f4(a91)),f5(a91)),x5881),x5881)
% 2.58/2.53 [594]P72(f95(f31(a90,x5941),f36(a91,f27(x5941))))
% 2.58/2.53 [597]E(f20(a91,x5971,f95(f95(f25(a91),f4(a91)),f5(a91))),x5971)
% 2.58/2.53 [602]E(f95(f95(f25(a90),f36(a91,x6021)),f5(a90)),f36(a91,f95(f95(f25(a91),x6021),f5(a91))))
% 2.58/2.53 [617]P72(f95(f32(a91,x6171),f95(f95(f25(a91),x6171),f5(a91))))
% 2.58/2.53 [621]P72(f95(f32(a91,f4(a91)),f95(f95(f25(a91),x6211),f5(a91))))
% 2.58/2.53 [648]P72(f95(f32(a90,f4(a90)),f95(f95(f25(a90),f5(a90)),f19(a90,x6481))))
% 2.58/2.53 [669]P72(f95(f32(a90,x6691),f95(f95(f25(a90),f36(a91,f26(x6691))),f5(a90))))
% 2.58/2.53 [670]P72(f95(f32(a90,f23(a90,x6701,f5(a90))),f36(a91,f26(x6701))))
% 2.58/2.53 [613]P72(f95(f31(a91,x6131),f95(f95(f24(a91),x6131),x6131)))
% 2.58/2.53 [633]E(f95(f95(f33(a91),f95(f95(f25(a91),f4(a91)),f5(a91))),x6331),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.53 [635]P72(f95(f31(a90,f37(a94,f95(a124,x6351))),a125))
% 2.58/2.53 [665]P72(f95(f32(a90,f4(a90)),f36(a91,f95(f95(f25(a91),x6651),f5(a91)))))
% 2.58/2.53 [677]P72(f95(f31(a90,f37(a90,f95(a7,x6771))),f95(f95(f24(a90),f37(a94,x6771)),a55)))
% 2.58/2.53 [678]P72(f95(f31(a90,f37(a90,f95(a7,x6781))),f95(f95(f24(a90),f37(a94,x6781)),a54)))
% 2.58/2.53 [679]P72(f95(f31(a90,f37(a90,f95(a7,x6791))),f95(f95(f24(a90),f37(a94,x6791)),a64)))
% 2.58/2.53 [680]P72(f95(f31(a90,f37(a90,f95(a11,x6801))),f95(f95(f24(a90),f37(a94,x6801)),a61)))
% 2.58/2.54 [681]P72(f95(f31(a90,f37(a90,f95(a11,x6811))),f95(f95(f24(a90),f37(a94,x6811)),a63)))
% 2.58/2.54 [682]P72(f95(f31(a90,f37(a90,f95(a11,x6821))),f95(f95(f24(a90),f37(a94,x6821)),a65)))
% 2.58/2.54 [736]~P72(f95(f31(a91,f95(f95(f25(a91),x7361),f5(a91))),x7361))
% 2.58/2.54 [737]~P72(f95(f32(a90,f95(f95(f25(a90),f19(a90,x7371)),f5(a90))),x7371))
% 2.58/2.54 [649]E(f37(a94,f12(f95(a11,f18(f5(a90),x6491)),f95(a7,f18(f5(a90),x6491)))),f5(a90))
% 2.58/2.54 [673]P72(f95(f31(a91,x6731),f95(f95(f24(a91),x6731),f95(f95(f24(a91),x6731),x6731))))
% 2.58/2.54 [695]E(f95(f95(f25(a90),f95(f95(f24(a90),f95(a11,f18(f5(a90),x6951))),f95(a11,f18(f5(a90),x6951)))),f95(f95(f24(a90),f95(a7,f18(f5(a90),x6951))),f95(a7,f18(f5(a90),x6951)))),f5(a90))
% 2.58/2.54 [733]~E(f95(f95(f25(a92),f95(f95(f25(a92),f5(a92)),x7331)),x7331),f4(a92))
% 2.58/2.54 [539]E(f14(f12(x5391,x5392)),f4(a91))
% 2.58/2.54 [540]E(f95(a7,f12(x5401,x5402)),x5402)
% 2.58/2.54 [541]E(f95(a11,f12(x5411,x5412)),x5411)
% 2.58/2.54 [542]E(f29(a94,f12(x5421,x5422)),f4(a91))
% 2.58/2.54 [548]E(f37(a94,f18(x5481,x5482)),f19(a90,x5481))
% 2.58/2.54 [605]E(f23(a90,f95(a7,x6051),f95(a7,x6052)),f95(a7,f23(a94,x6051,x6052)))
% 2.58/2.54 [606]E(f23(a90,f95(a11,x6061),f95(a11,x6062)),f95(a11,f23(a94,x6061,x6062)))
% 2.58/2.54 [700]P72(f95(f31(a90,f23(a90,f37(a94,f95(f95(f25(a94),x7001),x7002)),f37(a94,x7001))),f37(a94,x7002)))
% 2.58/2.54 [573]E(f95(f95(f24(a90),x5731),x5732),f95(f95(f24(a90),x5732),x5731))
% 2.58/2.54 [574]E(f95(f95(f24(a91),x5741),x5742),f95(f95(f24(a91),x5742),x5741))
% 2.58/2.54 [575]E(f95(f95(f24(a92),x5751),x5752),f95(f95(f24(a92),x5752),x5751))
% 2.58/2.54 [576]E(f95(f95(f25(a91),x5761),x5762),f95(f95(f25(a91),x5762),x5761))
% 2.58/2.54 [577]E(f95(f95(f25(a92),x5771),x5772),f95(f95(f25(a92),x5772),x5771))
% 2.58/2.54 [629]E(f23(a91,x6291,f95(f95(f25(a91),x6292),f5(a91))),f23(a91,f23(a91,x6291,f5(a91)),x6292))
% 2.58/2.54 [662]P72(f95(f31(a91,f23(a91,x6621,x6622)),x6621))
% 2.58/2.54 [663]P72(f95(f31(a91,f20(a91,x6631,x6632)),x6631))
% 2.58/2.54 [664]E(f12(f95(f95(f25(a90),f95(a11,x6641)),f95(a11,x6642)),f95(f95(f25(a90),f95(a7,x6641)),f95(a7,x6642))),f95(f95(f25(a94),x6641),x6642))
% 2.58/2.54 [676]P72(f95(f32(a91,f23(a91,x6761,x6762)),f95(f95(f25(a91),x6761),f5(a91))))
% 2.58/2.54 [687]P72(f95(f32(a91,x6871),f95(f95(f25(a91),f95(f95(f25(a91),x6872),x6871)),f5(a91))))
% 2.58/2.54 [688]P72(f95(f32(a91,x6881),f95(f95(f25(a91),f95(f95(f25(a91),x6881),x6882)),f5(a91))))
% 2.58/2.54 [696]P72(f95(f31(a90,f37(a94,x6961)),f95(f95(f25(a90),f37(a94,f95(f95(f25(a94),x6961),x6962))),f37(a94,x6962))))
% 2.58/2.54 [591]E(f23(a91,f95(f95(f25(a91),x5911),x5912),x5912),x5911)
% 2.58/2.54 [592]E(f23(a91,f95(f95(f25(a91),x5921),x5922),x5921),x5922)
% 2.58/2.54 [593]E(f23(a91,x5931,f95(f95(f25(a91),x5931),x5932)),f4(a91))
% 2.58/2.54 [596]E(f95(f95(f24(a94),f6(x5961)),f6(x5962)),f6(f95(f95(f25(a94),x5961),x5962)))
% 2.58/2.54 [598]E(f95(f95(f24(a90),x5981),f95(a7,f18(f5(a90),x5982))),f95(a7,f18(x5981,x5982)))
% 2.58/2.54 [599]E(f95(f95(f24(a90),x5991),f95(a11,f18(f5(a90),x5992))),f95(a11,f18(x5991,x5992)))
% 2.58/2.54 [601]E(f95(f95(f33(a90),f36(a91,x6011)),x6012),f36(a91,f95(f95(f33(a91),x6011),x6012)))
% 2.58/2.54 [607]E(f95(f95(f25(a90),f95(a7,x6071)),f95(a7,x6072)),f95(a7,f95(f95(f25(a94),x6071),x6072)))
% 2.58/2.54 [608]E(f95(f95(f25(a90),f95(a11,x6081)),f95(a11,x6082)),f95(a11,f95(f95(f25(a94),x6081),x6082)))
% 2.58/2.54 [609]E(f95(f95(f24(a90),f36(a91,x6091)),f36(a91,x6092)),f36(a91,f95(f95(f24(a91),x6091),x6092)))
% 2.58/2.54 [610]E(f95(f95(f25(a90),f36(a91,x6101)),f36(a91,x6102)),f36(a91,f95(f95(f25(a91),x6101),x6102)))
% 2.58/2.54 [611]E(f95(f95(f24(a94),f18(f5(a90),x6111)),f18(f5(a90),x6112)),f18(f5(a90),f95(f95(f25(a90),x6111),x6112)))
% 2.58/2.54 [614]P72(f95(f31(a91,x6141),f95(f95(f25(a91),x6142),x6141)))
% 2.58/2.54 [615]P72(f95(f31(a91,x6151),f95(f95(f25(a91),x6151),x6152)))
% 2.58/2.54 [620]E(f95(f95(f24(a91),x6201),f95(f95(f25(a91),x6202),f5(a91))),f95(f95(f25(a91),x6201),f95(f95(f24(a91),x6201),x6202)))
% 2.58/2.54 [624]E(f38(a90,f95(f95(f24(a90),x6241),x6242),f95(f95(f24(a90),x6241),x6241)),f38(a90,x6242,x6241))
% 2.58/2.54 [628]E(f18(f5(a90),f95(f95(f24(a90),f36(a91,x6281)),x6282)),f95(f95(f33(a94),f18(f5(a90),x6282)),x6281))
% 2.58/2.54 [643]E(f95(f95(f24(a91),f95(f95(f25(a91),x6431),f5(a91))),x6432),f95(f95(f25(a91),x6432),f95(f95(f24(a91),x6431),x6432)))
% 2.58/2.54 [644]E(f95(f95(f25(a91),f95(f95(f25(a91),x6441),f5(a91))),x6442),f95(f95(f25(a91),x6441),f95(f95(f25(a91),x6442),f5(a91))))
% 2.58/2.54 [655]P72(f95(f31(a92,f4(a92)),f95(f95(f33(a92),f19(a92,x6551)),x6552)))
% 2.58/2.54 [659]E(f95(f95(f25(a91),f95(f95(f25(a91),x6591),f5(a91))),x6592),f95(f95(f25(a91),f95(f95(f25(a91),x6591),x6592)),f5(a91)))
% 2.58/2.54 [672]E(f23(a90,f95(f95(f24(a90),f95(a11,x6721)),f95(a11,x6722)),f95(f95(f24(a90),f95(a7,x6721)),f95(a7,x6722))),f95(a11,f95(f95(f24(a94),x6721),x6722)))
% 2.58/2.54 [683]E(f95(f95(f25(a90),f95(f95(f24(a90),f95(a11,x6831)),f95(a7,x6832))),f95(f95(f24(a90),f95(a7,x6831)),f95(a11,x6832))),f95(a7,f95(f95(f24(a94),x6831),x6832)))
% 2.58/2.54 [705]E(f12(f23(a90,f95(f95(f24(a90),f95(a11,x7051)),f95(a11,x7052)),f95(f95(f24(a90),f95(a7,x7051)),f95(a7,x7052))),f95(f95(f25(a90),f95(f95(f24(a90),f95(a11,x7051)),f95(a7,x7052))),f95(f95(f24(a90),f95(a7,x7051)),f95(a11,x7052)))),f95(f95(f24(a94),x7051),x7052))
% 2.58/2.54 [674]E(f95(a7,f18(f5(a90),f95(f95(f24(a90),f36(a91,x6741)),x6742))),f95(a7,f95(f95(f33(a94),f18(f5(a90),x6742)),x6741)))
% 2.58/2.54 [675]E(f95(a11,f18(f5(a90),f95(f95(f24(a90),f36(a91,x6751)),x6752))),f95(a11,f95(f95(f33(a94),f18(f5(a90),x6752)),x6751)))
% 2.58/2.54 [691]E(f23(a90,f95(f95(f24(a90),f95(a11,f18(f5(a90),x6911))),f95(a11,f18(f5(a90),x6912))),f95(f95(f24(a90),f95(a7,f18(f5(a90),x6911))),f95(a7,f18(f5(a90),x6912)))),f95(a11,f18(f5(a90),f95(f95(f25(a90),x6911),x6912))))
% 2.58/2.54 [692]E(f23(a90,f95(f95(f24(a90),f95(a7,f18(f5(a90),x6921))),f95(a11,f18(f5(a90),x6922))),f95(f95(f24(a90),f95(a11,f18(f5(a90),x6921))),f95(a7,f18(f5(a90),x6922)))),f95(a7,f18(f5(a90),f23(a90,x6921,x6922))))
% 2.58/2.54 [693]E(f23(a90,f95(f95(f24(a90),f95(a11,f18(f5(a90),x6931))),f95(a7,f18(f5(a90),x6932))),f95(f95(f24(a90),f95(a7,f18(f5(a90),x6931))),f95(a11,f18(f5(a90),x6932)))),f95(a7,f18(f5(a90),f23(a90,x6932,x6931))))
% 2.58/2.54 [697]E(f95(f95(f25(a90),f95(f95(f24(a90),f95(a7,f18(f5(a90),x6971))),f95(a11,f18(f5(a90),x6972)))),f95(f95(f24(a90),f95(a11,f18(f5(a90),x6971))),f95(a7,f18(f5(a90),x6972)))),f95(a7,f18(f5(a90),f95(f95(f25(a90),x6971),x6972))))
% 2.58/2.54 [698]E(f95(f95(f25(a90),f95(f95(f24(a90),f95(a11,f18(f5(a90),x6981))),f95(a11,f18(f5(a90),x6982)))),f95(f95(f24(a90),f95(a7,f18(f5(a90),x6981))),f95(a7,f18(f5(a90),x6982)))),f95(a11,f18(f5(a90),f23(a90,x6982,x6981))))
% 2.58/2.54 [699]E(f95(f95(f25(a90),f95(f95(f24(a90),f95(a11,f18(f5(a90),x6991))),f95(a11,f18(f5(a90),x6992)))),f95(f95(f24(a90),f95(a7,f18(f5(a90),x6991))),f95(a7,f18(f5(a90),x6992)))),f95(a11,f18(f5(a90),f23(a90,x6991,x6992))))
% 2.58/2.54 [707]P72(f95(f31(a90,f37(a94,f23(a94,x7071,x7072))),f95(f95(f25(a90),f19(a90,f23(a90,f95(a11,x7071),f95(a11,x7072)))),f19(a90,f23(a90,f95(a7,x7071),f95(a7,x7072))))))
% 2.58/2.54 [734]~P72(f95(f32(a91,f95(f95(f25(a91),x7341),x7342)),x7342))
% 2.58/2.54 [735]~P72(f95(f32(a91,f95(f95(f25(a91),x7351),x7352)),x7351))
% 2.58/2.54 [690]E(f95(f95(f24(a94),f18(f5(a90),x6901)),f18(f5(a90),f95(f95(f24(a90),f36(a91,x6902)),x6901))),f18(f5(a90),f95(f95(f24(a90),f36(a91,f95(f95(f25(a91),x6902),f5(a91)))),x6901)))
% 2.58/2.54 [630]E(f23(a91,f23(a91,x6301,x6302),x6303),f23(a91,f23(a91,x6301,x6303),x6302))
% 2.58/2.54 [671]E(f23(a91,f23(a91,f95(f95(f25(a91),x6711),f5(a91)),x6712),f95(f95(f25(a91),x6713),f5(a91))),f23(a91,f23(a91,x6711,x6712),x6713))
% 2.58/2.54 [618]E(f95(f95(f25(a91),x6181),f95(f95(f25(a91),x6182),x6183)),f95(f95(f25(a91),x6182),f95(f95(f25(a91),x6181),x6183)))
% 2.58/2.54 [619]E(f95(f95(f25(a92),x6191),f95(f95(f25(a92),x6192),x6193)),f95(f95(f25(a92),x6192),f95(f95(f25(a92),x6191),x6193)))
% 2.58/2.54 [622]E(f23(a91,f95(f95(f25(a91),x6221),x6222),f95(f95(f25(a91),x6223),x6222)),f23(a91,x6221,x6223))
% 2.58/2.54 [623]E(f23(a91,f95(f95(f25(a91),x6231),x6232),f95(f95(f25(a91),x6231),x6233)),f23(a91,x6232,x6233))
% 2.58/2.54 [626]E(f23(a91,x6261,f95(f95(f25(a91),x6262),x6263)),f23(a91,f23(a91,x6261,x6262),x6263))
% 2.58/2.54 [627]E(f20(a91,x6271,f95(f95(f24(a91),x6272),x6273)),f20(a91,f20(a91,x6271,x6272),x6273))
% 2.58/2.54 [645]E(f23(a91,f95(f95(f24(a91),x6451),x6452),f95(f95(f24(a91),x6451),x6453)),f95(f95(f24(a91),x6451),f23(a91,x6452,x6453)))
% 2.58/2.54 [646]E(f23(a92,f95(f95(f24(a92),x6461),x6462),f95(f95(f24(a92),x6461),x6463)),f95(f95(f24(a92),x6461),f23(a92,x6462,x6463)))
% 2.58/2.54 [647]E(f18(f95(f95(f33(a90),x6471),x6472),f95(f95(f24(a90),f36(a91,x6472)),x6473)),f95(f95(f33(a94),f18(x6471,x6473)),x6472))
% 2.58/2.54 [656]E(f95(f95(f25(a91),f95(f95(f24(a91),x6561),x6562)),f95(f95(f24(a91),x6561),x6563)),f95(f95(f24(a91),x6561),f95(f95(f25(a91),x6562),x6563)))
% 2.58/2.54 [657]E(f95(f95(f25(a92),f95(f95(f24(a92),x6571),x6572)),f95(f95(f24(a92),x6571),x6573)),f95(f95(f24(a92),x6571),f95(f95(f25(a92),x6572),x6573)))
% 2.58/2.54 [658]E(f95(f95(f24(a92),f95(f95(f33(a92),x6581),x6582)),f95(f95(f33(a92),x6581),x6583)),f95(f95(f33(a92),x6581),f95(f95(f25(a91),x6582),x6583)))
% 2.58/2.54 [660]E(f23(a91,f95(f95(f24(a91),x6601),x6602),f95(f95(f24(a91),x6603),x6602)),f95(f95(f24(a91),f23(a91,x6601,x6603)),x6602))
% 2.58/2.54 [661]E(f23(a92,f95(f95(f24(a92),x6611),x6612),f95(f95(f24(a92),x6613),x6612)),f95(f95(f24(a92),f23(a92,x6611,x6613)),x6612))
% 2.58/2.54 [636]E(f95(f95(f24(a90),f95(f95(f24(a90),x6361),x6362)),x6363),f95(f95(f24(a90),x6361),f95(f95(f24(a90),x6362),x6363)))
% 2.58/2.54 [637]E(f95(f95(f24(a91),f95(f95(f24(a91),x6371),x6372)),x6373),f95(f95(f24(a91),x6371),f95(f95(f24(a91),x6372),x6373)))
% 2.58/2.54 [638]E(f95(f95(f24(a92),f95(f95(f24(a92),x6381),x6382)),x6383),f95(f95(f24(a92),x6381),f95(f95(f24(a92),x6382),x6383)))
% 2.58/2.54 [639]E(f95(f95(f33(a92),f95(f95(f33(a92),x6391),x6392)),x6393),f95(f95(f33(a92),x6391),f95(f95(f24(a91),x6392),x6393)))
% 2.58/2.54 [640]E(f95(f95(f25(a91),f95(f95(f25(a91),x6401),x6402)),x6403),f95(f95(f25(a91),x6401),f95(f95(f25(a91),x6402),x6403)))
% 2.58/2.54 [641]E(f95(f95(f25(a92),f95(f95(f25(a92),x6411),x6412)),x6413),f95(f95(f25(a92),x6411),f95(f95(f25(a92),x6412),x6413)))
% 2.58/2.54 [666]E(f95(f95(f25(a90),f95(f95(f24(a90),x6661),x6662)),f95(f95(f24(a90),x6663),x6662)),f95(f95(f24(a90),f95(f95(f25(a90),x6661),x6663)),x6662))
% 2.58/2.54 [667]E(f95(f95(f25(a91),f95(f95(f24(a91),x6671),x6672)),f95(f95(f24(a91),x6673),x6672)),f95(f95(f24(a91),f95(f95(f25(a91),x6671),x6673)),x6672))
% 2.58/2.54 [668]E(f95(f95(f25(a92),f95(f95(f24(a92),x6681),x6682)),f95(f95(f24(a92),x6683),x6682)),f95(f95(f24(a92),f95(f95(f25(a92),x6681),x6683)),x6682))
% 2.58/2.54 [584]E(f15(x5841,x5842,f12(x5843,x5844)),f95(f95(x5842,x5843),x5844))
% 2.58/2.54 [585]E(f16(x5851,x5852,f12(x5853,x5854)),f95(f95(x5852,x5853),x5854))
% 2.58/2.54 [587]E(f95(f8(x5871,x5872,x5873),x5874),x5873)
% 2.58/2.54 [616]E(f95(f95(f34(x6161,x6162,x6163),x6164),f4(a91)),x6162)
% 2.58/2.54 [634]E(f12(f23(a90,x6341,x6342),f23(a90,x6343,x6344)),f23(a94,f12(x6341,x6343),f12(x6342,x6344)))
% 2.58/2.54 [631]E(f18(f95(f95(f24(a90),x6311),x6312),f95(f95(f25(a90),x6313),x6314)),f95(f95(f24(a94),f18(x6311,x6313)),f18(x6312,x6314)))
% 2.58/2.54 [632]E(f12(f95(f95(f25(a90),x6321),x6322),f95(f95(f25(a90),x6323),x6324)),f95(f95(f25(a94),f12(x6321,x6323)),f12(x6322,x6324)))
% 2.58/2.54 [689]E(f12(f23(a90,f95(f95(f24(a90),x6891),x6892),f95(f95(f24(a90),x6893),x6894)),f95(f95(f25(a90),f95(f95(f24(a90),x6891),x6894)),f95(f95(f24(a90),x6893),x6892))),f95(f95(f24(a94),f12(x6891,x6893)),f12(x6892,x6894)))
% 2.58/2.54 [694]E(f95(f95(f25(a91),f95(f95(f24(a91),x6941),x6942)),f95(f95(f25(a91),f95(f95(f24(a91),x6943),x6942)),x6944)),f95(f95(f25(a91),f95(f95(f24(a91),f95(f95(f25(a91),x6941),x6943)),x6942)),x6944))
% 2.58/2.54 [686]E(f95(f95(f34(x6861,x6862,x6863),x6864),f95(f95(f25(a91),x6865),f5(a91))),f95(f95(x6863,x6864),f95(f95(f34(x6861,x6862,x6863),x6864),x6865)))
% 2.58/2.54 [701]E(f95(f9(x7011,x7012,x7013,x7014,x7015),x7016),f95(x7014,f95(x7015,x7016)))
% 2.58/2.54 [703]E(f95(f21(x7031,x7032,x7033,x7034,x7035),x7036),f95(x7034,f95(x7035,x7036)))
% 2.58/2.54 [704]E(f95(f10(x7041,x7042,x7043,x7044,x7045),x7046),f95(f95(x7044,x7046),x7045))
% 2.58/2.54 [706]E(f95(f21(x7061,x7062,x7063,f8(x7062,x7061,x7064),x7065),x7066),x7064)
% 2.58/2.54 [710]E(f21(x7101,x7102,x7103,x7104,f21(x7105,x7101,x7103,x7106,x7107)),f21(x7105,x7102,x7103,f21(x7101,x7102,x7105,x7104,x7106),x7107))
% 2.58/2.54 [738]~P47(x7381)+P6(f122(x7381))
% 2.58/2.54 [739]~P47(x7391)+P7(f122(x7391))
% 2.58/2.54 [740]~P47(x7401)+P8(f122(x7401))
% 2.58/2.54 [741]~P47(x7411)+P34(f122(x7411))
% 2.58/2.54 [742]~P9(x7421)+P9(f122(x7421))
% 2.58/2.54 [743]~P43(x7431)+P10(f122(x7431))
% 2.58/2.54 [744]~P47(x7441)+P41(f122(x7441))
% 2.58/2.54 [745]~P47(x7451)+P51(f122(x7451))
% 2.58/2.54 [746]~P47(x7461)+P52(f122(x7461))
% 2.58/2.54 [747]~P47(x7471)+P60(f122(x7471))
% 2.58/2.54 [748]~P47(x7481)+P62(f122(x7481))
% 2.58/2.54 [749]~P47(x7491)+P61(f122(x7491))
% 2.58/2.54 [750]~P50(x7501)+P53(f122(x7501))
% 2.58/2.54 [751]~P50(x7511)+P64(f122(x7511))
% 2.58/2.54 [752]~P43(x7521)+P54(f122(x7521))
% 2.58/2.54 [753]~P42(x7531)+P42(f122(x7531))
% 2.58/2.54 [754]~P43(x7541)+P43(f122(x7541))
% 2.58/2.54 [755]~P47(x7551)+P47(f122(x7551))
% 2.58/2.54 [756]~P47(x7561)+P55(f122(x7561))
% 2.58/2.54 [757]~P47(x7571)+P48(f122(x7571))
% 2.58/2.54 [758]~P47(x7581)+P56(f122(x7581))
% 2.58/2.54 [759]~P42(x7591)+P16(f122(x7591))
% 2.58/2.54 [760]~P42(x7601)+P68(f122(x7601))
% 2.58/2.54 [761]~P42(x7611)+P17(f122(x7611))
% 2.58/2.54 [762]~P42(x7621)+P22(f122(x7621))
% 2.58/2.54 [763]~P47(x7631)+P57(f122(x7631))
% 2.58/2.54 [764]~P50(x7641)+P65(f122(x7641))
% 2.58/2.54 [765]~P42(x7651)+P38(f122(x7651))
% 2.58/2.54 [766]~P43(x7661)+P69(f122(x7661))
% 2.58/2.54 [767]~P21(x7671)+P11(f122(x7671))
% 2.58/2.54 [768]~P20(x7681)+P18(f122(x7681))
% 2.58/2.54 [769]~P20(x7691)+P19(f122(x7691))
% 2.58/2.54 [770]~P43(x7701)+P44(f122(x7701))
% 2.58/2.54 [771]~P43(x7711)+P70(f122(x7711))
% 2.58/2.54 [772]~P50(x7721)+P71(f122(x7721))
% 2.58/2.54 [773]~P47(x7731)+P27(f122(x7731))
% 2.58/2.54 [774]~P47(x7741)+P31(f122(x7741))
% 2.58/2.54 [775]~P47(x7751)+P28(f122(x7751))
% 2.58/2.54 [776]~P21(x7761)+P21(f122(x7761))
% 2.58/2.54 [777]~P21(x7771)+P23(f122(x7771))
% 2.58/2.54 [778]~P47(x7781)+P24(f122(x7781))
% 2.58/2.54 [779]~P47(x7791)+P32(f122(x7791))
% 2.58/2.54 [780]~P47(x7801)+P58(f122(x7801))
% 2.58/2.54 [781]~P47(x7811)+P59(f122(x7811))
% 2.58/2.54 [782]~P47(x7821)+P29(f122(x7821))
% 2.58/2.54 [783]~P12(x7831)+P26(f122(x7831))
% 2.58/2.54 [784]~P12(x7841)+P12(f122(x7841))
% 2.58/2.54 [785]~P12(x7851)+P25(f122(x7851))
% 2.58/2.54 [786]~P46(x7861)+P66(f122(x7861))
% 2.58/2.54 [787]~P45(x7871)+P67(f122(x7871))
% 2.58/2.54 [788]~P45(x7881)+P45(f122(x7881))
% 2.58/2.54 [789]~P14(x7891)+P13(f122(x7891))
% 2.58/2.54 [790]~P47(x7901)+P30(f122(x7901))
% 2.58/2.54 [791]~P47(x7911)+P63(f122(x7911))
% 2.58/2.54 [792]~P50(x7921)+P50(f122(x7921))
% 2.58/2.54 [793]~P20(x7931)+P20(f122(x7931))
% 2.58/2.54 [794]~P46(x7941)+P46(f122(x7941))
% 2.58/2.54 [796]~P68(x7961)+~E(f5(x7961),f4(x7961))
% 2.58/2.54 [797]~E(x7971,f4(a91))+E(f36(a91,x7971),f4(a90))
% 2.58/2.54 [801]E(x8011,f4(a91))+~E(f36(a91,x8011),f4(a90))
% 2.58/2.54 [832]E(x8321,f4(a92))+E(f20(a92,x8321,x8321),f5(a92))
% 2.58/2.54 [804]~P35(x8041)+E(f37(x8041,f4(x8041)),f4(a90))
% 2.58/2.54 [805]~P39(x8051)+E(f37(x8051,f5(x8051)),f5(a90))
% 2.58/2.54 [810]~P30(x8101)+E(f19(x8101,f4(x8101)),f4(x8101))
% 2.58/2.54 [811]~P47(x8111)+E(f19(x8111,f5(x8111)),f5(x8111))
% 2.58/2.54 [881]~P38(x8811)+E(f34(x8811,f5(x8811),f24(x8811)),f33(x8811))
% 2.58/2.54 [923]~P37(x9231)+P72(f95(f31(a90,f4(a90)),f96(x9231)))
% 2.58/2.54 [924]~P37(x9241)+P72(f95(f32(a90,f4(a90)),f56(x9241)))
% 2.58/2.54 [928]P1(x9281)+P72(f95(f32(a91,f39(x9281)),f52(x9281)))
% 2.58/2.54 [941]~P57(x9411)+P72(f95(f31(x9411,f4(x9411)),f5(x9411)))
% 2.58/2.54 [942]~P57(x9421)+P72(f95(f32(x9421,f4(x9421)),f5(x9421)))
% 2.58/2.54 [946]E(x9461,f4(a91))+~P72(f95(f31(a91,x9461),f4(a91)))
% 2.58/2.54 [948]E(f26(x9481),f4(a91))+~P72(f95(f31(a90,x9481),f4(a90)))
% 2.58/2.54 [949]E(f27(x9491),f4(a91))+~P72(f95(f31(a90,x9491),f4(a90)))
% 2.58/2.54 [1027]~E(x10271,f4(a91))+P72(f95(f31(a90,f36(a91,x10271)),f4(a90)))
% 2.58/2.54 [1028]~E(x10281,f4(a92))+P72(f95(f32(a92,f19(a92,x10281)),f5(a92)))
% 2.58/2.54 [1043]~P57(x10431)+~P72(f95(f31(x10431,f5(x10431)),f4(x10431)))
% 2.58/2.54 [1044]~P57(x10441)+~P72(f95(f32(x10441,f5(x10441)),f4(x10441)))
% 2.58/2.54 [1100]~P72(f95(f31(a90,x11001),f5(a90)))+P72(f95(f31(a91,f27(x11001)),f5(a91)))
% 2.58/2.54 [1118]~P72(f95(f31(a91,f27(x11181)),f5(a91)))+P72(f95(f31(a90,x11181),f5(a90)))
% 2.58/2.54 [1157]E(x11571,f4(a91))+~P72(f95(f31(a90,f36(a91,x11571)),f4(a90)))
% 2.58/2.54 [1158]E(x11581,f4(a92))+~P72(f95(f32(a92,f19(a92,x11581)),f5(a92)))
% 2.58/2.54 [1891]~P72(f95(f32(a92,x18911),f4(a92)))+P72(f95(f32(a92,f95(f95(f25(a92),f95(f95(f25(a92),f5(a92)),x18911)),x18911)),f4(a92)))
% 2.58/2.54 [1917]P72(f95(f32(a92,x19171),f4(a92)))+~P72(f95(f32(a92,f95(f95(f25(a92),f95(f95(f25(a92),f5(a92)),x19171)),x19171)),f4(a92)))
% 2.58/2.54 [902]E(x9021,f4(a91))+P72(f95(f32(a91,f4(a91)),x9021))
% 2.58/2.54 [930]~E(f95(a11,f18(f5(a90),x9301)),f5(a90))+E(f95(a7,f18(f5(a90),x9301)),f4(a90))
% 2.58/2.54 [985]E(f28(x9851,f5(a90)),f5(a90))+~P72(f95(f32(a91,f4(a91)),x9851))
% 2.58/2.54 [1064]E(f95(f95(f25(a91),f80(x10641)),f5(a91)),x10641)+~P72(f95(f32(a91,f4(a91)),x10641))
% 2.58/2.54 [1093]~P72(f95(f32(a92,f4(a92)),x10931))+P72(f95(f31(a92,f5(a92)),x10931))
% 2.58/2.54 [1094]P72(f95(f32(a92,f4(a92)),x10941))+~P72(f95(f31(a92,f5(a92)),x10941))
% 2.58/2.54 [1102]~P72(f95(f32(a90,f4(a90)),x11021))+P72(f95(f32(a90,f35(x11021)),x11021))
% 2.58/2.54 [1103]P72(f95(f31(a90,f4(a90)),f35(x11031)))+~P72(f95(f31(a90,f5(a90)),x11031))
% 2.58/2.54 [1104]P72(f95(f31(a91,f5(a91)),f26(x11041)))+~P72(f95(f31(a90,f5(a90)),x11041))
% 2.58/2.54 [1105]P72(f95(f32(a90,f4(a90)),f35(x11051)))+~P72(f95(f32(a90,f5(a90)),x11051))
% 2.58/2.54 [1112]~P72(f95(f31(a91,f5(a91)),f26(x11121)))+P72(f95(f31(a90,f5(a90)),x11121))
% 2.58/2.54 [1152]P72(f95(f32(a90,f4(a90)),f36(a91,x11521)))+~P72(f95(f32(a91,f4(a91)),x11521))
% 2.58/2.54 [1166]~P72(f95(f31(a90,f4(a90)),x11661))+P72(f95(f32(a90,x11661),f36(a91,f111(x11661))))
% 2.58/2.54 [1174]~P72(f95(f32(a90,f4(a90)),f36(a91,x11741)))+P72(f95(f32(a91,f4(a91)),x11741))
% 2.58/2.54 [1176]E(f26(f95(f95(f25(a90),x11761),f5(a90))),f95(f95(f25(a91),f26(x11761)),f5(a91)))+~P72(f95(f31(a90,f4(a90)),x11761))
% 2.58/2.54 [1177]E(f27(f95(f95(f25(a90),x11771),f5(a90))),f95(f95(f25(a91),f27(x11771)),f5(a91)))+~P72(f95(f31(a90,f4(a90)),x11771))
% 2.58/2.54 [1278]~P57(x12781)+P72(f95(f32(x12781,f4(x12781)),f95(f95(f25(x12781),f5(x12781)),f5(x12781))))
% 2.58/2.54 [1292]E(f95(f95(f25(a91),f23(a91,x12921,f5(a91))),f5(a91)),x12921)+~P72(f95(f32(a91,f4(a91)),x12921))
% 2.58/2.54 [1357]E(x13571,f4(a91))+~P72(f95(f32(a91,x13571),f95(f95(f25(a91),f4(a91)),f5(a91))))
% 2.58/2.54 [1367]P1(x13671)+~P72(f95(f32(a91,f95(x13671,f39(x13671))),f95(x13671,f52(x13671))))
% 2.58/2.54 [1628]E(f95(f95(f25(a91),f23(a91,x16281,f95(f95(f25(a91),f4(a91)),f5(a91)))),f5(a91)),x16281)+~P72(f95(f32(a91,f4(a91)),x16281))
% 2.58/2.54 [1024]~E(f95(a7,f18(f5(a90),x10241)),f4(a90))+E(f19(a90,f95(a11,f18(f5(a90),x10241))),f5(a90))
% 2.58/2.54 [1149]E(x11491,f4(a90))+P72(f95(f32(a90,f4(a90)),f95(f95(f24(a90),x11491),x11491)))
% 2.58/2.54 [1232]~P72(f95(f31(a90,f4(a90)),x12321))+P72(f95(f31(a90,f36(a91,f26(x12321))),x12321))
% 2.58/2.54 [1233]~P72(f95(f31(a90,f4(a90)),x12331))+P72(f95(f31(a90,f36(a91,f97(x12331))),x12331))
% 2.58/2.54 [1327]~E(x13271,f4(a90))+~P72(f95(f32(a90,f4(a90)),f95(f95(f24(a90),x13271),x13271)))
% 2.58/2.54 [1331]~P72(f95(f31(a92,f4(a92)),x13311))+P72(f95(f32(a92,f4(a92)),f95(f95(f25(a92),f5(a92)),x13311)))
% 2.58/2.54 [1569]~P72(f95(f31(a90,f4(a90)),x15691))+P72(f95(f32(a90,x15691),f36(a91,f95(f95(f25(a91),f97(x15691)),f5(a91)))))
% 2.58/2.54 [1793]P1(x17931)+~P72(f95(f32(a91,f95(x17931,f83(x17931))),f95(x17931,f95(f95(f25(a91),f83(x17931)),f5(a91)))))
% 2.58/2.54 [1040]E(x10401,f4(a90))+E(f95(a11,f18(f5(a90),f13(f12(f4(a90),x10401)))),f4(a90))
% 2.58/2.54 [1197]~P72(f95(f32(a90,x11971),f4(a90)))+E(f95(a11,f18(f5(a90),f13(f12(f4(a90),x11971)))),f4(a90))
% 2.58/2.54 [1207]E(f95(a11,f18(f5(a90),f13(f12(f4(a90),x12071)))),f4(a90))+~P72(f95(f32(a90,f4(a90)),x12071))
% 2.58/2.54 [1806]~P72(f95(f31(a90,f4(a90)),x18061))+P72(f95(f31(a90,f36(a91,f23(a91,f111(x18061),f5(a91)))),x18061))
% 2.58/2.54 [1754]~P72(f95(f31(a90,f4(a90)),x17541))+P72(f95(f31(a90,f35(f95(f95(f25(a90),f5(a90)),x17541))),x17541))
% 2.58/2.54 [799]E(x7991,f4(a90))+~E(f12(x7991,x7992),a17)
% 2.58/2.54 [800]E(x8001,f5(a90))+~E(f12(x8002,x8001),a17)
% 2.58/2.54 [806]E(x8061,f4(a90))+~E(f12(x8062,x8061),f4(a94))
% 2.58/2.54 [807]E(x8071,f4(a90))+~E(f12(x8072,x8071),f5(a94))
% 2.58/2.54 [808]E(x8081,f4(a90))+~E(f12(x8081,x8082),f4(a94))
% 2.58/2.54 [809]E(x8091,f5(a90))+~E(f12(x8091,x8092),f5(a94))
% 2.58/2.54 [814]~P6(x8142)+P6(f123(x8141,x8142))
% 2.58/2.54 [815]~P7(x8152)+P7(f123(x8151,x8152))
% 2.58/2.54 [816]~P34(x8162)+P34(f123(x8161,x8162))
% 2.58/2.54 [817]~P26(x8172)+P26(f123(x8171,x8172))
% 2.58/2.54 [820]E(x8201,x8202)+~E(f36(a91,x8201),f36(a91,x8202))
% 2.58/2.54 [840]~E(x8402,f4(a92))+E(f20(a92,x8401,x8402),f4(a92))
% 2.58/2.54 [843]~P25(x8431)+E(f23(x8431,x8432,x8432),f4(x8431))
% 2.58/2.54 [833]~P35(x8331)+E(f19(a90,f37(x8331,x8332)),f37(x8331,x8332))
% 2.58/2.54 [839]~P30(x8391)+E(f19(x8391,f19(x8391,x8392)),f19(x8391,x8392))
% 2.58/2.54 [841]~P42(x8411)+E(f95(f95(f33(x8411),x8412),f5(a91)),x8412)
% 2.58/2.54 [842]~P22(x8421)+E(f95(f95(f33(x8421),x8422),f5(a91)),x8422)
% 2.58/2.54 [844]~P42(x8441)+E(f95(f95(f24(x8441),x8442),f5(x8441)),x8442)
% 2.58/2.54 [845]~P17(x8451)+E(f95(f95(f24(x8451),x8452),f5(x8451)),x8452)
% 2.58/2.54 [846]~P22(x8461)+E(f95(f95(f24(x8461),x8462),f5(x8461)),x8462)
% 2.58/2.54 [847]~P42(x8471)+E(f95(f95(f25(x8471),x8472),f4(x8471)),x8472)
% 2.58/2.54 [848]~P21(x8481)+E(f95(f95(f25(x8481),x8482),f4(x8481)),x8482)
% 2.58/2.54 [849]~P23(x8491)+E(f95(f95(f25(x8491),x8492),f4(x8491)),x8492)
% 2.58/2.54 [850]~P42(x8501)+E(f95(f95(f33(x8501),x8502),f4(a91)),f5(x8501))
% 2.58/2.54 [851]~P38(x8511)+E(f95(f95(f33(x8511),x8512),f4(a91)),f5(x8511))
% 2.58/2.54 [852]~P25(x8521)+E(f23(x8521,x8522,f4(x8521)),x8522)
% 2.58/2.54 [853]~P13(x8531)+E(f20(x8531,x8532,f5(x8531)),x8532)
% 2.58/2.54 [859]~P37(x8591)+E(f95(f95(f24(x8591),x8592),f4(x8591)),f4(x8591))
% 2.58/2.54 [860]~P54(x8601)+E(f95(f95(f24(x8601),x8602),f4(x8601)),f4(x8601))
% 2.58/2.54 [861]~P42(x8611)+E(f95(f95(f24(x8611),x8612),f4(x8611)),f4(x8611))
% 2.58/2.54 [863]~P13(x8631)+E(f20(x8631,x8632,f4(x8631)),f4(x8631))
% 2.58/2.54 [864]~P13(x8641)+E(f20(x8641,f4(x8641),x8642),f4(x8641))
% 2.58/2.54 [882]~E(x8821,x8822)+P72(f95(f31(a90,x8821),x8822))
% 2.58/2.54 [885]~E(x8851,x8852)+P72(f95(f31(a91,x8851),x8852))
% 2.58/2.54 [900]~P6(x9001)+P72(f95(f31(x9001,x9002),x9002))
% 2.58/2.54 [903]E(f30(x9031,x9032),f4(a92))+P72(f95(f31(a92,x9032),x9031))
% 2.58/2.54 [932]~E(x9321,x9322)+~P72(f95(f32(a90,x9321),x9322))
% 2.58/2.54 [937]~E(x9371,x9372)+~P72(f95(f32(a91,x9371),x9372))
% 2.58/2.54 [938]~E(x9381,x9382)+~P72(f95(f32(a92,x9381),x9382))
% 2.58/2.54 [940]~E(x9401,f4(a91))+~P72(f95(f32(a91,x9402),x9401))
% 2.58/2.54 [943]E(x9431,x9432)+~E(f95(x9431,f40(x9432,x9431)),f95(x9432,f40(x9432,x9431)))
% 2.58/2.54 [947]~P1(x9472)+P72(f95(f31(a91,x9471),f95(x9472,x9471)))
% 2.58/2.54 [950]~P6(x9501)+~P72(f95(f32(x9501,x9502),x9502))
% 2.58/2.54 [958]~P30(x9581)+P72(f95(f31(x9581,x9582),f19(x9581,x9582)))
% 2.58/2.54 [962]~P35(x9621)+P72(f95(f31(a90,f4(a90)),f37(x9621,x9622)))
% 2.58/2.54 [963]~P37(x9632)+P72(f95(f31(a90,f4(a90)),f99(x9631,x9632)))
% 2.58/2.54 [964]~P37(x9642)+P72(f95(f31(a90,f4(a90)),f110(x9641,x9642)))
% 2.58/2.54 [965]~P37(x9652)+P72(f95(f32(a90,f4(a90)),f57(x9651,x9652)))
% 2.58/2.54 [966]~P37(x9662)+P72(f95(f32(a90,f4(a90)),f58(x9661,x9662)))
% 2.58/2.54 [975]P72(f95(f31(a90,x9752),x9751))+P72(f95(f31(a90,x9751),x9752))
% 2.58/2.54 [976]P72(f95(f31(a91,x9762),x9761))+P72(f95(f31(a91,x9761),x9762))
% 2.58/2.54 [977]P72(f95(f31(a92,x9772),x9771))+P72(f95(f31(a92,x9771),x9772))
% 2.58/2.54 [988]~E(f23(a91,x9881,x9882),f4(a91))+P72(f95(f31(a91,x9881),x9882))
% 2.58/2.54 [990]~P30(x9901)+P72(f95(f31(x9901,f4(x9901)),f19(x9901,x9902)))
% 2.58/2.54 [1021]E(f23(a91,x10211,x10212),f4(a91))+~P72(f95(f31(a91,x10211),x10212))
% 2.58/2.54 [1022]E(f20(a91,x10221,x10222),f4(a91))+~P72(f95(f32(a91,x10221),x10222))
% 2.58/2.54 [1035]E(f23(a92,x10351,x10352),f30(x10351,x10352))+~P72(f95(f31(a92,x10352),x10351))
% 2.58/2.54 [1041]E(f95(f95(f25(a91),x10411),f100(x10412,x10411)),x10412)+~P72(f95(f31(a91,x10411),x10412))
% 2.58/2.54 [1042]E(f95(f95(f25(a91),x10421),f103(x10422,x10421)),x10422)+~P72(f95(f31(a91,x10421),x10422))
% 2.58/2.54 [1046]~P72(f95(f32(a90,x10461),x10462))+P72(f95(f31(a90,x10461),x10462))
% 2.58/2.54 [1051]~P72(f95(f32(a91,x10511),x10512))+P72(f95(f31(a91,x10511),x10512))
% 2.58/2.54 [1052]~P72(f95(f32(a92,x10521),x10522))+P72(f95(f31(a92,x10521),x10522))
% 2.58/2.54 [1092]E(f95(f95(f25(a91),x10921),f23(a91,x10922,x10921)),x10922)+P72(f95(f32(a91,x10922),x10921))
% 2.58/2.54 [1097]~P72(f95(f31(a90,x10971),x10972))+P72(f95(f31(a91,f26(x10971)),f26(x10972)))
% 2.58/2.54 [1098]~P72(f95(f31(a90,x10981),x10982))+P72(f95(f31(a91,f27(x10981)),f27(x10982)))
% 2.58/2.54 [1146]E(f95(f95(f25(a91),x11461),f23(a91,x11462,x11461)),x11462)+~P72(f95(f31(a91,x11461),x11462))
% 2.58/2.54 [1159]E(f23(a91,x11591,f23(a91,x11591,x11592)),x11592)+~P72(f95(f31(a91,x11592),x11591))
% 2.58/2.54 [1175]~P35(x11751)+~P72(f95(f32(a90,f37(x11751,x11752)),f4(a90)))
% 2.58/2.54 [1200]~P30(x12001)+~P72(f95(f32(x12001,f19(x12001,x12002)),f4(x12001)))
% 2.58/2.54 [1210]~P72(f95(f31(a91,x12101),x12102))+P72(f95(f31(a90,f36(a91,x12101)),f36(a91,x12102)))
% 2.58/2.54 [1211]~P72(f95(f32(a91,x12111),x12112))+P72(f95(f32(a90,f36(a91,x12111)),f36(a91,x12112)))
% 2.58/2.54 [1214]E(f23(a90,f36(a91,x12141),f36(a91,x12142)),f36(a91,f23(a91,x12141,x12142)))+~P72(f95(f31(a91,x12142),x12141))
% 2.58/2.54 [1294]P72(f95(f31(a91,x12941),x12942))+~P72(f95(f31(a90,f36(a91,x12941)),f36(a91,x12942)))
% 2.58/2.54 [1295]P72(f95(f32(a91,x12951),x12952))+~P72(f95(f32(a90,f36(a91,x12951)),f36(a91,x12952)))
% 2.58/2.54 [1301]P72(f95(f32(a91,f4(a91)),f23(a91,x13011,x13012)))+~P72(f95(f32(a91,x13012),x13011))
% 2.58/2.54 [1350]E(f95(f95(f25(a91),f95(f95(f25(a91),x13501),f105(x13502,x13501))),f5(a91)),x13502)+~P72(f95(f32(a91,x13501),x13502))
% 2.58/2.54 [1433]~P72(f95(f32(a91,f4(a91)),f23(a91,x14332,x14331)))+P72(f95(f32(a91,x14331),x14332))
% 2.58/2.54 [1486]~P72(f95(f31(a90,x14861),x14862))+P72(f95(f31(a90,f23(a90,x14861,x14862)),f4(a90)))
% 2.58/2.54 [1487]~P72(f95(f32(a92,x14871),x14872))+P72(f95(f32(a92,f23(a92,x14871,x14872)),f4(a92)))
% 2.58/2.54 [1599]~P41(x15991)+~P72(f95(f32(x15991,f95(f95(f24(x15991),x15992),x15992)),f4(x15991)))
% 2.58/2.54 [1644]P72(f95(f31(a90,x16441),x16442))+~P72(f95(f31(a90,f23(a90,x16441,x16442)),f4(a90)))
% 2.58/2.54 [1645]P72(f95(f32(a92,x16451),x16452))+~P72(f95(f32(a92,f23(a92,x16451,x16452)),f4(a92)))
% 2.58/2.54 [1722]~P72(f95(f32(a91,x17221),x17222))+P72(f95(f31(a90,f95(f95(f25(a90),f36(a91,x17221)),f5(a90))),f36(a91,x17222)))
% 2.58/2.54 [1844]P72(f95(f32(a91,x18441),x18442))+~P72(f95(f31(a90,f95(f95(f25(a90),f36(a91,x18441)),f5(a90))),f36(a91,x18442)))
% 2.58/2.54 [827]~E(x8271,f4(a91))+E(f95(f95(f25(a91),x8271),x8272),x8272)
% 2.58/2.54 [828]~E(x8282,f4(a91))+E(f95(f95(f24(a91),x8281),x8282),f4(a91))
% 2.58/2.54 [830]~E(x8301,f4(a91))+E(f95(f95(f24(a91),x8301),x8302),f4(a91))
% 2.58/2.54 [831]~E(x8312,f4(a91))+E(f95(f95(f33(a91),x8311),x8312),f5(a91))
% 2.58/2.54 [835]~P33(x8351)+E(f95(f95(f24(x8351),x8352),x8352),x8352)
% 2.58/2.54 [869]~P42(x8691)+E(f95(f95(f24(x8691),f5(x8691)),x8692),x8692)
% 2.58/2.54 [870]~P17(x8701)+E(f95(f95(f24(x8701),f5(x8701)),x8702),x8702)
% 2.58/2.54 [871]~P22(x8711)+E(f95(f95(f24(x8711),f5(x8711)),x8712),x8712)
% 2.58/2.54 [872]~P42(x8721)+E(f95(f95(f25(x8721),f4(x8721)),x8722),x8722)
% 2.58/2.54 [873]~P21(x8731)+E(f95(f95(f25(x8731),f4(x8731)),x8732),x8732)
% 2.58/2.54 [874]~P23(x8741)+E(f95(f95(f25(x8741),f4(x8741)),x8742),x8742)
% 2.58/2.54 [876]~P37(x8761)+E(f95(f95(f24(x8761),f4(x8761)),x8762),f4(x8761))
% 2.58/2.54 [877]~P54(x8771)+E(f95(f95(f24(x8771),f4(x8771)),x8772),f4(x8771))
% 2.58/2.54 [878]~P42(x8781)+E(f95(f95(f24(x8781),f4(x8781)),x8782),f4(x8781))
% 2.58/2.54 [879]~P22(x8791)+E(f95(f95(f33(x8791),f5(x8791)),x8792),f5(x8791))
% 2.58/2.54 [880]E(x8801,f4(a91))+~E(f95(f95(f25(a91),x8802),x8801),x8802)
% 2.58/2.54 [888]E(x8881,f4(a91))+~E(f95(f95(f25(a91),x8882),x8881),f4(a91))
% 2.58/2.54 [889]E(x8891,f4(a91))+~E(f95(f95(f25(a91),x8891),x8892),f4(a91))
% 2.58/2.54 [890]E(x8901,f5(a91))+~E(f95(f95(f24(a91),x8902),x8901),f5(a91))
% 2.58/2.54 [891]E(x8911,f5(a91))+~E(f95(f95(f24(a91),x8911),x8912),f5(a91))
% 2.58/2.54 [897]~P12(x8971)+E(f23(f122(x8971),x8972,f4(f122(x8971))),x8972)
% 2.58/2.54 [918]~P21(x9181)+E(f95(f95(f25(f122(x9181)),x9182),f4(f122(x9181))),x9182)
% 2.58/2.54 [922]~E(x9222,f4(a91))+E(f95(f95(f33(a91),x9221),x9222),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [927]~P43(x9271)+E(f95(f95(f24(f122(x9271)),x9272),f4(f122(x9271))),f4(f122(x9271)))
% 2.58/2.54 [993]~E(x9931,f95(f95(f25(a91),x9932),f5(a91)))+P72(f95(f32(a91,f4(a91)),x9931))
% 2.58/2.54 [1036]~P47(x10361)+E(f95(f95(f24(x10361),f19(x10361,x10362)),f19(x10361,x10362)),f95(f95(f24(x10361),x10362),x10362))
% 2.58/2.54 [1037]~E(x10371,f95(f95(f25(a91),f4(a91)),f5(a91)))+E(f95(f95(f33(a91),x10371),x10372),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1068]E(f28(x10681,f19(a90,x10682)),f19(a90,f28(x10681,x10682)))+~P72(f95(f32(a91,f4(a91)),x10681))
% 2.58/2.54 [1069]E(x10691,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f24(a91),x10692),x10691),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1070]E(x10701,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f24(a91),x10701),x10702),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1147]~E(x11471,x11472)+P72(f95(f32(a91,x11471),f95(f95(f25(a91),x11472),f5(a91))))
% 2.58/2.54 [1148]~E(x11481,x11482)+P72(f95(f32(a92,x11481),f95(f95(f25(a92),x11482),f5(a92))))
% 2.58/2.54 [1154]~E(x11541,f4(a91))+P72(f95(f32(a91,x11541),f95(f95(f25(a91),x11542),f5(a91))))
% 2.58/2.54 [1162]P72(f95(f32(a90,f4(a90)),f107(x11621,x11622)))+~P72(f95(f32(a90,f4(a90)),x11622))
% 2.58/2.54 [1171]~P72(f95(f31(a90,x11711),f36(a91,x11712)))+P72(f95(f31(a91,f27(x11711)),x11712))
% 2.58/2.54 [1198]~P57(x11981)+P72(f95(f32(x11981,x11982),f95(f95(f25(x11981),x11982),f5(x11981))))
% 2.58/2.54 [1213]E(f95(f95(f33(a90),f107(x12131,x12132)),f95(f95(f25(a91),x12131),f5(a91))),x12132)+~P72(f95(f32(a90,f4(a90)),x12132))
% 2.58/2.54 [1215]E(f26(f95(f95(f25(a90),x12151),f36(a91,x12152))),f95(f95(f25(a91),f26(x12151)),x12152))+~P72(f95(f31(a90,f4(a90)),x12151))
% 2.58/2.54 [1216]E(f27(f95(f95(f25(a90),x12161),f36(a91,x12162))),f95(f95(f25(a91),f27(x12161)),x12162))+~P72(f95(f31(a90,f4(a90)),x12161))
% 2.58/2.54 [1220]P72(f95(f32(a91,x12201),x12202))+P72(f95(f32(a91,x12202),f95(f95(f25(a91),x12201),f5(a91))))
% 2.58/2.54 [1231]P72(f95(f31(a91,x12311),f26(x12312)))+~P72(f95(f31(a90,f36(a91,x12311)),x12312))
% 2.58/2.54 [1238]E(f95(f95(f25(a91),f23(a91,x12381,x12382)),x12382),x12381)+~P72(f95(f31(a91,x12382),x12381))
% 2.58/2.54 [1267]~P72(f95(f31(a91,x12671),x12672))+P72(f95(f32(a91,x12671),f95(f95(f25(a91),x12672),f5(a91))))
% 2.58/2.54 [1270]~P72(f95(f31(a92,x12701),x12702))+P72(f95(f32(a92,x12701),f95(f95(f25(a92),x12702),f5(a92))))
% 2.58/2.54 [1271]~P72(f95(f32(a92,x12711),x12712))+P72(f95(f32(a92,x12711),f95(f95(f25(a92),x12712),f5(a92))))
% 2.58/2.54 [1300]~P72(f95(f32(a92,x13001),x13002))+P72(f95(f31(a92,x13001),f23(a92,x13002,f5(a92))))
% 2.58/2.54 [1363]E(f26(f23(a90,x13631,f36(a91,x13632))),f23(a91,f26(x13631),x13632))+~P72(f95(f31(a90,f36(a91,x13632)),x13631))
% 2.58/2.54 [1364]E(f27(f23(a90,x13641,f36(a91,x13642))),f23(a91,f27(x13641),x13642))+~P72(f95(f31(a90,f36(a91,x13642)),x13641))
% 2.58/2.54 [1382]P72(f95(f31(a91,x13821),x13822))+~P72(f95(f32(a91,x13821),f95(f95(f25(a91),x13822),f5(a91))))
% 2.58/2.54 [1383]P72(f95(f31(a92,x13831),x13832))+~P72(f95(f32(a92,x13831),f95(f95(f25(a92),x13832),f5(a92))))
% 2.58/2.54 [1432]P72(f95(f32(a92,x14321),x14322))+~P72(f95(f31(a92,x14321),f23(a92,x14322,f5(a92))))
% 2.58/2.54 [1434]~P72(f95(f32(a91,x14341),x14342))+~P72(f95(f32(a91,x14342),f95(f95(f25(a91),x14341),f5(a91))))
% 2.58/2.54 [1454]~P67(x14541)+E(f95(f95(f24(x14541),f95(f95(f25(x14541),x14542),f5(x14541))),f23(x14541,x14542,f5(x14541))),f23(x14541,f95(f95(f24(x14541),x14542),x14542),f5(x14541)))
% 2.58/2.54 [1528]~P72(f95(f31(a91,x15281),x15282))+P72(f95(f32(a90,f36(a91,x15281)),f95(f95(f25(a90),f36(a91,x15282)),f5(a90))))
% 2.58/2.54 [1688]P72(f95(f31(a91,x16881),x16882))+~P72(f95(f32(a90,f36(a91,x16881)),f95(f95(f25(a90),f36(a91,x16882)),f5(a90))))
% 2.58/2.54 [1762]P72(f95(f31(a91,x17621),x17622))+~P72(f95(f31(a91,f95(f95(f25(a91),x17621),f5(a91))),f95(f95(f25(a91),x17622),f5(a91))))
% 2.58/2.54 [1764]P72(f95(f32(a91,x17641),x17642))+~P72(f95(f32(a91,f95(f95(f25(a91),x17641),f5(a91))),f95(f95(f25(a91),x17642),f5(a91))))
% 2.58/2.54 [1774]E(x17741,f4(a91))+E(f95(f95(f25(a91),f95(f95(f25(a91),f23(a91,x17741,f5(a91))),x17742)),f5(a91)),f95(f95(f25(a91),x17741),x17742))
% 2.58/2.54 [929]~P21(x9291)+E(f95(f95(f25(f122(x9291)),f4(f122(x9291))),x9292),x9292)
% 2.58/2.54 [945]~P43(x9451)+E(f95(f95(f24(f122(x9451)),f4(f122(x9451))),x9452),f4(f122(x9451)))
% 2.58/2.54 [1029]E(f19(a92,x10291),f5(a92))+~E(f19(a92,f95(f95(f24(a92),x10291),x10292)),f5(a92))
% 2.58/2.54 [1030]~E(f36(a91,f26(x10301)),x10301)+E(f26(f95(f95(f33(a90),x10301),x10302)),f95(f95(f33(a91),f26(x10301)),x10302))
% 2.58/2.54 [1156]~E(x11562,f4(a91))+P72(f95(f32(a91,f4(a91)),f95(f95(f33(a91),x11561),x11562)))
% 2.58/2.54 [1163]E(f20(a91,f95(f95(f24(a91),x11631),x11632),x11632),x11631)+~P72(f95(f32(a91,f4(a91)),x11632))
% 2.58/2.54 [1164]E(f20(a91,f95(f95(f24(a91),x11641),x11642),x11641),x11642)+~P72(f95(f32(a91,f4(a91)),x11641))
% 2.58/2.54 [1199]~P41(x11991)+P72(f95(f31(x11991,f4(x11991)),f95(f95(f24(x11991),x11992),x11992)))
% 2.58/2.54 [1209]E(f95(f95(f24(a90),f36(a91,x12091)),f35(x12092)),f35(f95(f95(f33(a90),x12092),x12091)))+~P72(f95(f32(a90,f4(a90)),x12092))
% 2.58/2.54 [1273]~P42(x12731)+E(f95(f95(f25(x12731),x12732),x12732),f95(f95(f24(x12731),f95(f95(f25(x12731),f5(x12731)),f5(x12731))),x12732))
% 2.58/2.54 [1282]E(x12821,f4(a91))+E(f95(f95(f24(a91),x12822),f95(f95(f33(a91),x12822),f23(a91,x12821,f5(a91)))),f95(f95(f33(a91),x12822),x12821))
% 2.58/2.54 [1285]~P72(f95(f31(a92,f4(a92)),x12851))+P72(f95(f31(a92,f4(a92)),f95(f95(f33(a92),x12851),x12852)))
% 2.58/2.54 [1287]~P72(f95(f32(a91,f4(a91)),x12871))+P72(f95(f32(a91,f4(a91)),f95(f95(f33(a91),x12871),x12872)))
% 2.58/2.54 [1355]E(x13551,f4(a92))+P72(f95(f32(a92,f4(a92)),f95(f95(f33(a92),f19(a92,x13551)),x13552)))
% 2.58/2.54 [1356]~E(x13562,f4(a91))+P72(f95(f32(a92,f4(a92)),f95(f95(f33(a92),f19(a92,x13561)),x13562)))
% 2.58/2.54 [1390]E(x13901,f4(a90))+~E(f95(f95(f25(a90),f95(f95(f24(a90),x13902),x13902)),f95(f95(f24(a90),x13901),x13901)),f4(a90))
% 2.58/2.54 [1391]E(x13911,f4(a90))+~E(f95(f95(f25(a90),f95(f95(f24(a90),x13911),x13911)),f95(f95(f24(a90),x13912),x13912)),f4(a90))
% 2.58/2.54 [1395]P72(f95(f32(a91,f4(a91)),x13951))+~P72(f95(f32(a91,f4(a91)),f95(f95(f24(a91),x13952),x13951)))
% 2.58/2.54 [1396]P72(f95(f32(a91,f4(a91)),x13961))+~P72(f95(f32(a91,f4(a91)),f95(f95(f24(a91),x13961),x13962)))
% 2.58/2.54 [1425]E(f28(f95(f95(f25(a91),x14251),f5(a91)),f95(f95(f33(a90),x14252),f95(f95(f25(a91),x14251),f5(a91)))),x14252)+~P72(f95(f32(a90,f4(a90)),x14252))
% 2.58/2.54 [1428]P72(f95(f31(a91,x14281),x14282))+P72(f95(f31(a91,f95(f95(f25(a91),x14282),f5(a91))),x14281))
% 2.58/2.54 [1464]~P72(f95(f32(a91,x14641),x14642))+P72(f95(f31(a91,f95(f95(f25(a91),x14641),f5(a91))),x14642))
% 2.58/2.54 [1466]~P72(f95(f32(a92,x14661),x14662))+P72(f95(f31(a92,f95(f95(f25(a92),x14661),f5(a92))),x14662))
% 2.58/2.54 [1496]~P1(x14961)+P72(f95(f32(a91,f95(x14961,x14962)),f95(x14961,f95(f95(f25(a91),x14962),f5(a91)))))
% 2.58/2.54 [1604]P72(f95(f32(a91,x16041),x16042))+~P72(f95(f31(a91,f95(f95(f25(a91),x16041),f5(a91))),x16042))
% 2.58/2.54 [1606]P72(f95(f32(a92,x16061),x16062))+~P72(f95(f31(a92,f95(f95(f25(a92),x16061),f5(a92))),x16062))
% 2.58/2.54 [1637]~P72(f95(f31(a91,x16371),x16372))+~P72(f95(f31(a91,f95(f95(f25(a91),x16372),f5(a91))),x16371))
% 2.58/2.54 [1724]P72(f95(f32(a90,x17241),f36(a91,x17242)))+~P72(f95(f31(a91,f95(f95(f25(a91),f26(x17241)),f5(a91))),x17242))
% 2.58/2.54 [1846]~P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18461))+P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),f95(f95(f33(a91),x18461),x18462)))
% 2.58/2.54 [1863]P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18631))+~P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),f95(f95(f24(a91),x18632),x18631)))
% 2.58/2.54 [1864]P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18641))+~P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),f95(f95(f24(a91),x18641),x18642)))
% 2.58/2.54 [1499]E(x14991,f4(a91))+E(f95(f95(f25(a91),x14992),f95(f95(f24(a91),f23(a91,x14991,f5(a91))),x14992)),f95(f95(f24(a91),x14991),x14992))
% 2.58/2.54 [1723]~P72(f95(f32(a90,f4(a90)),x17232))+P72(f95(f32(a90,x17231),f95(f95(f24(a90),f36(a91,f72(x17232,x17231))),x17232)))
% 2.58/2.54 [1839]~P72(f95(f32(a91,f4(a91)),x18391))+P72(f95(f32(a91,f23(a91,x18391,f95(f95(f25(a91),x18392),f5(a91)))),x18391))
% 2.58/2.54 [1933]~P72(f95(f31(a90,f4(a90)),x19332))+P72(f95(f31(a90,f95(f95(f25(a90),f95(f95(f24(a90),f36(a91,x19331)),x19332)),f5(a90))),f95(f95(f33(a90),f95(f95(f25(a90),x19332),f5(a90))),x19331)))
% 2.58/2.54 [1115]~P35(x11151)+E(f37(x11151,f23(x11151,x11152,x11153)),f37(x11151,f23(x11151,x11153,x11152)))
% 2.58/2.54 [1116]~P30(x11161)+E(f19(x11161,f23(x11161,x11162,x11163)),f19(x11161,f23(x11161,x11163,x11162)))
% 2.58/2.54 [1203]~P73(x12031,x12033,x12032)+P72(f95(x12031,f20(a92,x12032,x12033)))
% 2.58/2.54 [1328]P73(x13281,x13282,x13283)+~P72(f95(x13281,f20(a92,x13283,x13282)))
% 2.58/2.54 [1337]~E(x13372,f95(f95(f25(a91),f95(f95(f25(a91),x13371),x13373)),f5(a91)))+P72(f95(f32(a91,x13371),x13372))
% 2.58/2.54 [1613]~P72(f95(f31(a91,x16133),x16132))+P72(f95(f31(a91,f23(a91,x16131,x16132)),f23(a91,x16131,x16133)))
% 2.58/2.54 [1614]~P72(f95(f31(a91,x16141),x16143))+P72(f95(f31(a91,f23(a91,x16141,x16142)),f23(a91,x16143,x16142)))
% 2.58/2.54 [1615]~P72(f95(f31(a91,x16151),x16153))+P72(f95(f31(a91,f20(a91,x16151,x16152)),f20(a91,x16153,x16152)))
% 2.58/2.54 [1934]~P41(x19341)+~P72(f95(f32(x19341,f95(f95(f25(x19341),f95(f95(f24(x19341),x19342),x19342)),f95(f95(f24(x19341),x19343),x19343))),f4(x19341)))
% 2.58/2.54 [910]~E(x9102,f4(a91))+E(f95(f95(f24(a91),x9101),x9102),f95(f95(f24(a91),x9103),x9102))
% 2.58/2.54 [912]~E(x9121,f4(a91))+E(f95(f95(f24(a91),x9121),x9122),f95(f95(f24(a91),x9121),x9123))
% 2.58/2.54 [925]~P42(x9251)+E(f95(f95(f24(x9251),x9252),x9253),f95(f95(f24(x9251),x9253),x9252))
% 2.58/2.54 [926]~P42(x9261)+E(f95(f95(f25(x9261),x9262),x9263),f95(f95(f25(x9261),x9263),x9262))
% 2.58/2.54 [960]E(x9601,x9602)+~E(f95(f95(f25(a91),x9603),x9601),f95(f95(f25(a91),x9603),x9602))
% 2.58/2.54 [961]E(x9611,x9612)+~E(f95(f95(f25(a91),x9611),x9613),f95(f95(f25(a91),x9612),x9613))
% 2.58/2.54 [968]~E(x9682,f95(f95(f25(a91),x9681),x9683))+P72(f95(f31(a91,x9681),x9682))
% 2.58/2.54 [1153]~P25(x11531)+E(f95(f95(f25(x11531),f23(x11531,x11532,x11533)),x11533),x11532)
% 2.58/2.54 [1293]~P30(x12931)+E(f19(x12931,f95(f95(f25(x12931),f19(x12931,x12932)),f19(x12931,x12933))),f95(f95(f25(x12931),f19(x12931,x12932)),f19(x12931,x12933)))
% 2.58/2.54 [1481]~P72(f95(f32(a91,x14811),x14813))+P72(f95(f32(a91,f23(a91,x14811,x14812)),x14813))
% 2.58/2.54 [1683]E(f23(a91,f95(f95(f25(a91),x16831),x16832),f95(f95(f25(a91),x16833),f5(a91))),f23(a91,x16831,f95(f95(f25(a91),f23(a91,x16833,x16832)),f5(a91))))+~P72(f95(f31(a91,x16832),x16833))
% 2.58/2.54 [1837]~P35(x18371)+P72(f95(f31(a90,f23(a90,f37(x18371,x18372),f37(x18371,x18373))),f37(x18371,f23(x18371,x18372,x18373))))
% 2.58/2.54 [1840]~P30(x18401)+P72(f95(f31(x18401,f23(x18401,f19(x18401,x18402),f19(x18401,x18403))),f19(x18401,f23(x18401,x18403,x18402))))
% 2.58/2.54 [1841]~P30(x18411)+P72(f95(f31(x18411,f23(x18411,f19(x18411,x18412),f19(x18411,x18413))),f19(x18411,f23(x18411,x18412,x18413))))
% 2.58/2.54 [1847]~P37(x18471)+P72(f95(f31(a90,f37(x18471,f95(f95(f24(x18471),x18472),x18473))),f95(f95(f24(a90),f37(x18471,x18473)),f99(x18472,x18471))))
% 2.58/2.54 [1848]~P37(x18481)+P72(f95(f31(a90,f37(x18481,f95(f95(f24(x18481),x18482),x18483))),f95(f95(f24(a90),f37(x18481,x18483)),f42(x18482,x18481))))
% 2.58/2.54 [1849]~P37(x18491)+P72(f95(f31(a90,f37(x18491,f95(f95(f24(x18491),x18492),x18493))),f95(f95(f24(a90),f37(x18491,x18493)),f58(x18492,x18491))))
% 2.58/2.54 [1850]~P37(x18501)+P72(f95(f31(a90,f37(x18501,f95(f95(f24(x18501),x18502),x18503))),f95(f95(f24(a90),f37(x18501,x18502)),f37(x18501,x18503))))
% 2.58/2.54 [1851]~P37(x18511)+P72(f95(f31(a90,f37(x18511,f95(f95(f24(x18511),x18512),x18513))),f95(f95(f24(a90),f37(x18511,x18512)),f110(x18513,x18511))))
% 2.58/2.54 [1852]~P37(x18521)+P72(f95(f31(a90,f37(x18521,f95(f95(f24(x18521),x18522),x18523))),f95(f95(f24(a90),f37(x18521,x18522)),f44(x18523,x18521))))
% 2.58/2.54 [1853]~P37(x18531)+P72(f95(f31(a90,f37(x18531,f95(f95(f24(x18531),x18532),x18533))),f95(f95(f24(a90),f37(x18531,x18532)),f57(x18533,x18531))))
% 2.58/2.54 [1854]~P35(x18541)+P72(f95(f31(a90,f37(x18541,f95(f95(f25(x18541),x18542),x18543))),f95(f95(f25(a90),f37(x18541,x18542)),f37(x18541,x18543))))
% 2.58/2.54 [1855]~P30(x18551)+P72(f95(f31(x18551,f19(x18551,f95(f95(f25(x18551),x18552),x18553))),f95(f95(f25(x18551),f19(x18551,x18552)),f19(x18551,x18553))))
% 2.58/2.54 [1856]~P35(x18561)+P72(f95(f31(a90,f37(x18561,f23(x18561,x18562,x18563))),f95(f95(f25(a90),f37(x18561,x18562)),f37(x18561,x18563))))
% 2.58/2.54 [1860]~P30(x18601)+P72(f95(f31(x18601,f19(x18601,f23(x18601,x18602,x18603))),f95(f95(f25(x18601),f19(x18601,x18602)),f19(x18601,x18603))))
% 2.58/2.54 [1899]~P35(x18991)+P72(f95(f31(a90,f19(a90,f23(a90,f37(x18991,x18992),f37(x18991,x18993)))),f37(x18991,f23(x18991,x18992,x18993))))
% 2.58/2.54 [1900]~P30(x19001)+P72(f95(f31(x19001,f19(x19001,f23(x19001,f19(x19001,x19002),f19(x19001,x19003)))),f19(x19001,f23(x19001,x19002,x19003))))
% 2.58/2.54 [1911]~P37(x19111)+P72(f95(f31(a90,f37(x19111,f95(f95(f24(x19111),x19112),x19113))),f95(f95(f24(a90),f95(f95(f24(a90),f37(x19111,x19112)),f37(x19111,x19113))),f96(x19111))))
% 2.58/2.54 [1912]~P37(x19121)+P72(f95(f31(a90,f37(x19121,f95(f95(f24(x19121),x19122),x19123))),f95(f95(f24(a90),f95(f95(f24(a90),f37(x19121,x19122)),f37(x19121,x19123))),f43(x19121))))
% 2.58/2.54 [1913]~P37(x19131)+P72(f95(f31(a90,f37(x19131,f95(f95(f24(x19131),x19132),x19133))),f95(f95(f24(a90),f95(f95(f24(a90),f37(x19131,x19132)),f37(x19131,x19133))),f56(x19131))))
% 2.58/2.54 [989]~P25(x9891)+E(f23(x9891,f95(f95(f25(x9891),x9892),x9893),x9893),x9892)
% 2.58/2.54 [1066]~P33(x10661)+E(f95(f95(f24(x10661),x10662),f95(f95(f24(x10661),x10662),x10663)),f95(f95(f24(x10661),x10662),x10663))
% 2.58/2.54 [1091]~P36(x10911)+E(f37(x10911,f95(f95(f33(x10911),x10912),x10913)),f95(f95(f33(a90),f37(x10911,x10912)),x10913))
% 2.58/2.54 [1095]~P47(x10951)+E(f19(x10951,f95(f95(f33(x10951),x10952),x10953)),f95(f95(f33(x10951),f19(x10951,x10952)),x10953))
% 2.58/2.54 [1107]~E(x11071,f4(a91))+E(f20(a91,f95(f95(f24(a91),x11071),x11072),f95(f95(f24(a91),x11071),x11073)),f4(a91))
% 2.58/2.54 [1113]~P36(x11131)+E(f95(f95(f24(a90),f37(x11131,x11132)),f37(x11131,x11133)),f37(x11131,f95(f95(f24(x11131),x11132),x11133)))
% 2.58/2.54 [1120]~P47(x11201)+E(f95(f95(f24(x11201),f19(x11201,x11202)),f19(x11201,x11203)),f19(x11201,f95(f95(f24(x11201),x11202),x11203)))
% 2.58/2.54 [1170]E(x11701,f4(a91))+E(f20(a91,f95(f95(f24(a91),x11701),x11702),f95(f95(f24(a91),x11701),x11703)),f20(a91,x11702,x11703))
% 2.58/2.54 [1184]~P42(x11841)+E(f95(f95(f24(x11841),x11842),f95(f95(f33(x11841),x11842),x11843)),f95(f95(f33(x11841),x11842),f95(f95(f25(a91),x11843),f5(a91))))
% 2.58/2.54 [1185]~P42(x11851)+E(f95(f95(f33(x11851),x11852),f95(f95(f25(a91),x11853),f5(a91))),f95(f95(f24(x11851),x11852),f95(f95(f33(x11851),x11852),x11853)))
% 2.58/2.54 [1186]~P38(x11861)+E(f95(f95(f33(x11861),x11862),f95(f95(f25(a91),x11863),f5(a91))),f95(f95(f24(x11861),x11862),f95(f95(f33(x11861),x11862),x11863)))
% 2.58/2.54 [1217]E(f28(x12171,f95(f95(f33(a90),x12172),x12173)),f95(f95(f33(a90),f28(x12171,x12172)),x12173))+~P72(f95(f32(a91,f4(a91)),x12171))
% 2.58/2.54 [1236]E(f95(f95(f24(a90),f28(x12361,x12362)),f28(x12361,x12363)),f28(x12361,f95(f95(f24(a90),x12362),x12363)))+~P72(f95(f32(a91,f4(a91)),x12361))
% 2.58/2.54 [1242]~P72(f95(f31(a91,x12421),x12423))+P72(f95(f31(a91,x12421),f95(f95(f25(a91),x12422),x12423)))
% 2.58/2.54 [1244]~P72(f95(f31(a91,x12441),x12442))+P72(f95(f31(a91,x12441),f95(f95(f25(a91),x12442),x12443)))
% 2.58/2.54 [1246]~P72(f95(f32(a91,x12461),x12463))+P72(f95(f32(a91,x12461),f95(f95(f25(a91),x12462),x12463)))
% 2.58/2.54 [1248]~P72(f95(f32(a91,x12481),x12482))+P72(f95(f32(a91,x12481),f95(f95(f25(a91),x12482),x12483)))
% 2.58/2.54 [1299]~P72(f95(f31(a91,x12993),x12992))+E(f23(a91,f95(f95(f25(a91),x12991),x12992),x12993),f95(f95(f25(a91),x12991),f23(a91,x12992,x12993)))
% 2.58/2.54 [1322]~P72(f95(f31(a91,x13222),x13223))+E(f23(a91,f95(f95(f25(a91),x13221),x13222),x13223),f23(a91,x13221,f23(a91,x13223,x13222)))
% 2.58/2.54 [1324]E(f20(a91,f95(f95(f24(a91),x13241),x13242),f95(f95(f24(a91),x13241),x13243)),f20(a91,x13242,x13243))+~P72(f95(f32(a91,f4(a91)),x13241))
% 2.58/2.54 [1338]E(f20(a92,x13381,f95(f95(f24(a92),x13382),x13383)),f20(a92,f20(a92,x13381,x13382),x13383))+~P72(f95(f32(a92,f4(a92)),x13383))
% 2.58/2.54 [1341]~P42(x13411)+E(f95(f95(f25(x13411),x13412),f95(f95(f24(x13411),x13413),x13412)),f95(f95(f24(x13411),f95(f95(f25(x13411),x13413),f5(x13411))),x13412))
% 2.58/2.54 [1407]~P72(f95(f31(a91,x14073),x14071))+E(f23(a91,f95(f95(f25(a91),x14071),x14072),x14073),f95(f95(f25(a91),f23(a91,x14071,x14073)),x14072))
% 2.58/2.54 [1415]~P47(x14151)+P72(f95(f31(x14151,f4(x14151)),f95(f95(f33(x14151),f19(x14151,x14152)),x14153)))
% 2.58/2.54 [1548]P72(f95(f32(a91,f4(a91)),x15481))+P72(f95(f31(a91,f95(f95(f24(a91),x15482),x15481)),f95(f95(f24(a91),x15483),x15481)))
% 2.58/2.54 [1549]P72(f95(f32(a91,f4(a91)),x15491))+P72(f95(f31(a91,f95(f95(f24(a91),x15491),x15492)),f95(f95(f24(a91),x15491),x15493)))
% 2.58/2.54 [1558]~P72(f95(f31(a90,x15582),x15583))+P72(f95(f31(a90,f95(f95(f25(a90),x15581),x15582)),f95(f95(f25(a90),x15581),x15583)))
% 2.58/2.54 [1560]~P72(f95(f31(a91,x15602),x15603))+P72(f95(f31(a91,f95(f95(f24(a91),x15601),x15602)),f95(f95(f24(a91),x15601),x15603)))
% 2.58/2.54 [1562]~P72(f95(f31(a91,x15621),x15623))+P72(f95(f31(a91,f95(f95(f24(a91),x15621),x15622)),f95(f95(f24(a91),x15623),x15622)))
% 2.58/2.54 [1563]~P72(f95(f31(a91,x15632),x15633))+P72(f95(f31(a91,f95(f95(f25(a91),x15631),x15632)),f95(f95(f25(a91),x15631),x15633)))
% 2.58/2.54 [1564]~P72(f95(f31(a91,x15641),x15643))+P72(f95(f31(a91,f95(f95(f25(a91),x15641),x15642)),f95(f95(f25(a91),x15643),x15642)))
% 2.58/2.54 [1565]~P72(f95(f31(a92,x15652),x15653))+P72(f95(f31(a92,f95(f95(f25(a92),x15651),x15652)),f95(f95(f25(a92),x15651),x15653)))
% 2.58/2.54 [1566]~P72(f95(f32(a91,x15662),x15663))+P72(f95(f32(a91,f95(f95(f25(a91),x15661),x15662)),f95(f95(f25(a91),x15661),x15663)))
% 2.58/2.54 [1567]~P72(f95(f32(a91,x15671),x15673))+P72(f95(f32(a91,f95(f95(f25(a91),x15671),x15672)),f95(f95(f25(a91),x15673),x15672)))
% 2.58/2.54 [1568]~P72(f95(f32(a92,x15681),x15683))+P72(f95(f32(a92,f95(f95(f25(a92),x15681),x15682)),f95(f95(f25(a92),x15683),x15682)))
% 2.58/2.54 [1573]E(x15731,x15732)+~E(f95(f95(f24(a91),f95(f95(f25(a91),x15733),f5(a91))),x15731),f95(f95(f24(a91),f95(f95(f25(a91),x15733),f5(a91))),x15732))
% 2.58/2.54 [1674]P72(f95(f31(a91,f23(a91,x16741,x16742)),x16743))+~P72(f95(f31(a91,x16741),f95(f95(f25(a91),x16743),x16742)))
% 2.58/2.54 [1684]~P72(f95(f31(a91,x16842),x16841))+E(f23(a91,f95(f95(f25(a91),x16841),f5(a91)),f95(f95(f25(a91),x16842),x16843)),f23(a91,f95(f95(f25(a91),f23(a91,x16841,x16842)),f5(a91)),x16843))
% 2.58/2.54 [1746]~P72(f95(f31(a91,f23(a91,x17461,x17463)),x17462))+P72(f95(f31(a91,x17461),f95(f95(f25(a91),x17462),x17463)))
% 2.58/2.54 [1747]P72(f95(f31(a91,x17471),x17472))+~P72(f95(f31(a91,f95(f95(f25(a91),x17473),x17471)),f95(f95(f25(a91),x17473),x17472)))
% 2.58/2.54 [1748]P72(f95(f32(a91,x17481),x17482))+~P72(f95(f32(a91,f95(f95(f25(a91),x17483),x17481)),f95(f95(f25(a91),x17483),x17482)))
% 2.58/2.54 [1749]P72(f95(f32(a91,x17491),x17492))+~P72(f95(f32(a91,f95(f95(f24(a91),x17493),x17491)),f95(f95(f24(a91),x17493),x17492)))
% 2.58/2.54 [1750]P72(f95(f32(a91,x17501),x17502))+~P72(f95(f32(a91,f95(f95(f24(a91),x17501),x17503)),f95(f95(f24(a91),x17502),x17503)))
% 2.58/2.54 [1752]P72(f95(f32(a91,f4(a91)),x17521))+~P72(f95(f32(a91,f95(f95(f24(a91),x17522),x17521)),f95(f95(f24(a91),x17523),x17521)))
% 2.58/2.54 [1753]P72(f95(f32(a91,f4(a91)),x17531))+~P72(f95(f32(a91,f95(f95(f24(a91),x17531),x17532)),f95(f95(f24(a91),x17531),x17533)))
% 2.58/2.54 [1838]~P39(x18381)+P72(f95(f31(a90,f37(x18381,f95(f95(f33(x18381),x18382),x18383))),f95(f95(f33(a90),f37(x18381,x18382)),x18383)))
% 2.58/2.54 [1903]~P45(x19031)+E(f23(x19031,f95(f95(f33(x19031),x19032),f95(f95(f25(a91),f95(f95(f25(a91),f4(a91)),f5(a91))),f5(a91))),f95(f95(f33(x19031),x19033),f95(f95(f25(a91),f95(f95(f25(a91),f4(a91)),f5(a91))),f5(a91)))),f95(f95(f24(x19031),f23(x19031,x19032,x19033)),f95(f95(f25(x19031),x19032),x19033)))
% 2.58/2.54 [1296]~P42(x12961)+E(f95(f95(f24(x12961),f95(f95(f33(x12961),x12962),x12963)),x12962),f95(f95(f33(x12961),x12962),f95(f95(f25(a91),x12963),f5(a91))))
% 2.58/2.54 [1297]~P22(x12971)+E(f95(f95(f33(x12971),x12972),f95(f95(f25(a91),x12973),f5(a91))),f95(f95(f24(x12971),f95(f95(f33(x12971),x12972),x12973)),x12972))
% 2.58/2.54 [1308]~P22(x13081)+E(f95(f95(f24(x13081),f95(f95(f33(x13081),x13082),x13083)),x13082),f95(f95(f24(x13081),x13082),f95(f95(f33(x13081),x13082),x13083)))
% 2.58/2.54 [1436]~P42(x14361)+E(f95(f95(f25(x14361),f95(f95(f24(x14361),x14362),x14363)),x14363),f95(f95(f24(x14361),f95(f95(f25(x14361),x14362),f5(x14361))),x14363))
% 2.58/2.54 [1579]P72(f95(f31(a91,x15791),x15792))+~P72(f95(f31(a91,f95(f95(f25(a91),x15793),x15791)),x15792))
% 2.58/2.54 [1580]P72(f95(f31(a91,x15801),x15802))+~P72(f95(f31(a91,f95(f95(f25(a91),x15801),x15803)),x15802))
% 2.58/2.54 [1581]P72(f95(f32(a91,x15811),x15812))+~P72(f95(f32(a91,f95(f95(f25(a91),x15811),x15813)),x15812))
% 2.58/2.54 [1582]~P72(f95(f31(a91,x15823),x15822))+P72(f95(f31(a91,x15821),f23(a91,f95(f95(f25(a91),x15822),x15821),x15823)))
% 2.58/2.54 [1663]~P72(f95(f32(a91,x16631),f23(a91,x16633,x16632)))+P72(f95(f32(a91,f95(f95(f25(a91),x16631),x16632)),x16633))
% 2.58/2.54 [1704]P72(f95(f32(a91,x17041),f23(a91,x17042,x17043)))+~P72(f95(f32(a91,f95(f95(f25(a91),x17041),x17043)),x17042))
% 2.58/2.54 [1834]~P35(x18341)+P72(f95(f31(a90,f23(a90,f37(x18341,x18342),f37(x18341,x18343))),f37(x18341,f95(f95(f25(x18341),x18342),x18343))))
% 2.58/2.54 [1857]~P41(x18571)+P72(f95(f31(x18571,f4(x18571)),f95(f95(f25(x18571),f95(f95(f24(x18571),x18572),x18572)),f95(f95(f24(x18571),x18573),x18573))))
% 2.58/2.54 [1908]~P72(f95(f32(a91,x19082),x19083))+P72(f95(f32(a91,f95(f95(f24(a91),f95(f95(f25(a91),x19081),f5(a91))),x19082)),f95(f95(f24(a91),f95(f95(f25(a91),x19081),f5(a91))),x19083)))
% 2.58/2.54 [1937]P72(f95(f31(a91,x19371),x19372))+~P72(f95(f31(a91,f95(f95(f24(a91),f95(f95(f25(a91),x19373),f5(a91))),x19371)),f95(f95(f24(a91),f95(f95(f25(a91),x19373),f5(a91))),x19372)))
% 2.58/2.54 [1966]~P72(f95(f32(a92,f4(a92)),x19663))+P72(f95(f32(a92,x19661),f95(f95(f25(a92),x19662),f95(f95(f24(a92),f95(f95(f25(a92),f19(a92,f23(a92,x19662,x19661))),f5(a92))),x19663))))
% 2.58/2.54 [1970]~P72(f95(f32(a92,f4(a92)),x19703))+P72(f95(f32(a92,f23(a92,x19701,f95(f95(f24(a92),f95(f95(f25(a92),f19(a92,f23(a92,x19701,x19702))),f5(a92))),x19703))),x19702))
% 2.58/2.54 [825]E(x8251,x8252)+~E(f12(x8253,x8251),f12(x8254,x8252))
% 2.58/2.54 [826]E(x8261,x8262)+~E(f12(x8261,x8263),f12(x8262,x8264))
% 2.58/2.54 [1195]~P42(x11951)+E(f95(f95(f24(x11951),x11952),f95(f95(f24(x11951),x11953),x11954)),f95(f95(f24(x11951),x11953),f95(f95(f24(x11951),x11952),x11954)))
% 2.58/2.54 [1196]~P42(x11961)+E(f95(f95(f25(x11961),x11962),f95(f95(f25(x11961),x11963),x11964)),f95(f95(f25(x11961),x11963),f95(f95(f25(x11961),x11962),x11964)))
% 2.58/2.54 [1201]~P49(x12011)+E(f38(x12011,f95(f95(f24(x12011),x12012),x12013),x12014),f95(f95(f24(x12011),x12012),f38(x12011,x12013,x12014)))
% 2.58/2.54 [1326]~P37(x13261)+E(f23(x13261,f95(f95(f24(x13261),x13262),x13263),f95(f95(f24(x13261),x13262),x13264)),f95(f95(f24(x13261),x13262),f23(x13261,x13263,x13264)))
% 2.58/2.54 [1393]~P22(x13931)+E(f95(f95(f24(x13931),f95(f95(f33(x13931),x13932),x13933)),f95(f95(f33(x13931),x13932),x13934)),f95(f95(f33(x13931),x13932),f95(f95(f25(a91),x13933),x13934)))
% 2.58/2.54 [1394]~P42(x13941)+E(f95(f95(f24(x13941),f95(f95(f33(x13941),x13942),x13943)),f95(f95(f33(x13941),x13942),x13944)),f95(f95(f33(x13941),x13942),f95(f95(f25(a91),x13943),x13944)))
% 2.58/2.54 [1411]~P37(x14111)+E(f95(f95(f25(x14111),f95(f95(f24(x14111),x14112),x14113)),f95(f95(f24(x14111),x14112),x14114)),f95(f95(f24(x14111),x14112),f95(f95(f25(x14111),x14113),x14114)))
% 2.58/2.54 [1412]~P42(x14121)+E(f95(f95(f25(x14121),f95(f95(f24(x14121),x14122),x14123)),f95(f95(f24(x14121),x14122),x14124)),f95(f95(f24(x14121),x14122),f95(f95(f25(x14121),x14123),x14124)))
% 2.58/2.54 [1423]~P37(x14231)+E(f23(x14231,f95(f95(f24(x14231),x14232),x14233),f95(f95(f24(x14231),x14234),x14233)),f95(f95(f24(x14231),f23(x14231,x14232,x14234)),x14233))
% 2.58/2.54 [1424]~P15(x14241)+E(f38(x14241,f95(f95(f33(x14241),x14242),x14243),f95(f95(f33(x14241),x14244),x14243)),f95(f95(f33(x14241),f38(x14241,x14242,x14244)),x14243))
% 2.58/2.54 [1281]~P14(x12811)+E(f20(f122(x12811),x12812,f95(f95(f24(f122(x12811)),x12813),x12814)),f20(f122(x12811),f20(f122(x12811),x12812,x12813),x12814))
% 2.58/2.54 [1283]~P42(x12831)+E(f95(f95(f33(x12831),f95(f95(f33(x12831),x12832),x12833)),x12834),f95(f95(f33(x12831),x12832),f95(f95(f24(a91),x12833),x12834)))
% 2.58/2.54 [1284]~P22(x12841)+E(f95(f95(f33(x12841),f95(f95(f33(x12841),x12842),x12843)),x12844),f95(f95(f33(x12841),x12842),f95(f95(f24(a91),x12843),x12844)))
% 2.58/2.54 [1306]~P10(x13061)+E(f95(f95(f24(x13061),f95(f95(f24(x13061),x13062),x13063)),x13064),f95(f95(f24(x13061),x13062),f95(f95(f24(x13061),x13063),x13064)))
% 2.58/2.54 [1307]~P42(x13071)+E(f95(f95(f24(x13071),f95(f95(f24(x13071),x13072),x13073)),x13074),f95(f95(f24(x13071),x13072),f95(f95(f24(x13071),x13073),x13074)))
% 2.58/2.54 [1309]~P42(x13091)+E(f95(f95(f25(x13091),f95(f95(f25(x13091),x13092),x13093)),x13094),f95(f95(f25(x13091),x13092),f95(f95(f25(x13091),x13093),x13094)))
% 2.58/2.54 [1310]~P11(x13101)+E(f95(f95(f25(x13101),f95(f95(f25(x13101),x13102),x13103)),x13104),f95(f95(f25(x13101),x13102),f95(f95(f25(x13101),x13103),x13104)))
% 2.58/2.54 [1408]~P42(x14081)+E(f95(f95(f24(x14081),f95(f95(f24(x14081),x14082),x14083)),x14084),f95(f95(f24(x14081),f95(f95(f24(x14081),x14082),x14084)),x14083))
% 2.58/2.54 [1409]~P42(x14091)+E(f95(f95(f25(x14091),f95(f95(f25(x14091),x14092),x14093)),x14094),f95(f95(f25(x14091),f95(f95(f25(x14091),x14092),x14094)),x14093))
% 2.58/2.54 [1490]~P37(x14901)+E(f95(f95(f25(x14901),f95(f95(f24(x14901),x14902),x14903)),f95(f95(f24(x14901),x14904),x14903)),f95(f95(f24(x14901),f95(f95(f25(x14901),x14902),x14904)),x14903))
% 2.58/2.54 [1492]~P44(x14921)+E(f95(f95(f25(x14921),f95(f95(f24(x14921),x14922),x14923)),f95(f95(f24(x14921),x14924),x14923)),f95(f95(f24(x14921),f95(f95(f25(x14921),x14922),x14924)),x14923))
% 2.58/2.54 [1493]~P42(x14931)+E(f95(f95(f24(x14931),f95(f95(f33(x14931),x14932),x14933)),f95(f95(f33(x14931),x14934),x14933)),f95(f95(f33(x14931),f95(f95(f24(x14931),x14932),x14934)),x14933))
% 2.58/2.54 [1494]~P17(x14941)+E(f95(f95(f24(x14941),f95(f95(f33(x14941),x14942),x14943)),f95(f95(f33(x14941),x14944),x14943)),f95(f95(f33(x14941),f95(f95(f24(x14941),x14942),x14944)),x14943))
% 2.58/2.54 [1495]~P42(x14951)+E(f95(f95(f25(x14951),f95(f95(f24(x14951),x14952),x14953)),f95(f95(f24(x14951),x14954),x14953)),f95(f95(f24(x14951),f95(f95(f25(x14951),x14952),x14954)),x14953))
% 2.58/2.54 [1682]~P43(x16821)+E(f95(f95(f25(f122(x16821)),f95(f95(f24(f122(x16821)),x16822),x16823)),f95(f95(f24(f122(x16821)),x16824),x16823)),f95(f95(f24(f122(x16821)),f95(f95(f25(f122(x16821)),x16822),x16824)),x16823))
% 2.58/2.54 [1168]~P26(x11682)+E(f95(f23(f123(x11681,x11682),x11683,x11684),x11685),f23(x11682,f95(x11683,x11685),f95(x11684,x11685)))
% 2.58/2.54 [1506]~P12(x15061)+E(f23(x15061,f95(f95(f25(x15061),x15062),x15063),f95(f95(f25(x15061),x15064),x15065)),f95(f95(f25(x15061),f23(x15061,x15062,x15064)),f23(x15061,x15063,x15065)))
% 2.58/2.54 [1553]~P42(x15531)+E(f95(f95(f24(x15531),f95(f95(f24(x15531),x15532),x15533)),f95(f95(f24(x15531),x15534),x15535)),f95(f95(f24(x15531),f95(f95(f24(x15531),x15532),x15534)),f95(f95(f24(x15531),x15533),x15535)))
% 2.58/2.54 [1554]~P42(x15541)+E(f95(f95(f25(x15541),f95(f95(f25(x15541),x15542),x15543)),f95(f95(f25(x15541),x15544),x15545)),f95(f95(f25(x15541),f95(f95(f25(x15541),x15542),x15544)),f95(f95(f25(x15541),x15543),x15545)))
% 2.58/2.54 [1845]~P66(x18451)+E(f95(f95(f25(x18451),f95(f95(f24(x18451),x18452),f23(x18451,x18453,x18454))),f95(f95(f24(x18451),f23(x18451,x18452,x18455)),x18454)),f23(x18451,f95(f95(f24(x18451),x18452),x18453),f95(f95(f24(x18451),x18455),x18454)))
% 2.58/2.54 [1945]~P35(x19451)+P72(f95(f31(a90,f37(x19451,f23(x19451,f95(f95(f25(x19451),x19452),x19453),f95(f95(f25(x19451),x19454),x19455)))),f95(f95(f25(a90),f37(x19451,f23(x19451,x19452,x19454))),f37(x19451,f23(x19451,x19453,x19455)))))
% 2.58/2.54 [1946]~P30(x19461)+P72(f95(f31(x19461,f19(x19461,f23(x19461,f95(f95(f25(x19461),x19462),x19463),f95(f95(f25(x19461),x19464),x19465)))),f95(f95(f25(x19461),f19(x19461,f23(x19461,x19462,x19464))),f19(x19461,f23(x19461,x19463,x19465)))))
% 2.58/2.54 [1950]~P37(x19501)+E(f95(f95(f25(x19501),f95(f95(f25(x19501),f95(f95(f24(x19501),f23(x19501,x19502,x19503)),f23(x19501,x19504,x19505))),f95(f95(f24(x19501),f23(x19501,x19502,x19503)),x19505))),f95(f95(f24(x19501),x19503),f23(x19501,x19504,x19505))),f23(x19501,f95(f95(f24(x19501),x19502),x19504),f95(f95(f24(x19501),x19503),x19505)))
% 2.58/2.54 [1914]~P72(f95(f31(a91,x19141),x19144))+E(f23(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19141),x19142)),x19143),f95(f95(f25(a91),f95(f95(f24(a91),x19144),x19142)),x19145)),f23(a91,x19143,f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19144,x19141)),x19142)),x19145)))
% 2.58/2.54 [1915]~P72(f95(f31(a91,x19154),x19151))+E(f23(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19151),x19152)),x19153),f95(f95(f25(a91),f95(f95(f24(a91),x19154),x19152)),x19155)),f23(a91,f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19151,x19154)),x19152)),x19153),x19155))
% 2.58/2.54 [1874]~P70(x18741)+E(f95(f95(f25(x18741),f95(f95(f24(x18741),x18742),x18743)),f95(f95(f25(x18741),f95(f95(f24(x18741),x18744),x18743)),x18745)),f95(f95(f25(x18741),f95(f95(f24(x18741),f95(f95(f25(x18741),x18742),x18744)),x18743)),x18745))
% 2.58/2.54 [1886]~E(f21(x18865,x18866,x18867,x18861,x18862),x18864)+E(f95(x18861,f95(x18862,x18863)),f95(x18864,x18863))
% 2.58/2.54 [1923]~E(f21(x19236,x19237,x19238,x19231,x19232),f21(x19239,x19237,x19238,x19234,x19235))+E(f95(x19231,f95(x19232,x19233)),f95(x19234,f95(x19235,x19233)))
% 2.58/2.54 [1943]~E(f95(x19434,f95(x19435,x19436)),f95(x19439,f95(x194310,x194311)))+E(f95(f21(x19431,x19432,x19433,x19434,x19435),x19436),f95(f21(x19437,x19432,x19438,x19439,x194310),x194311))
% 2.58/2.54 [974]~E(x9741,f5(a90))+E(f35(x9741),f4(a90))+~P72(f95(f32(a90,f4(a90)),x9741))
% 2.58/2.54 [979]~E(f35(x9791),f4(a90))+E(x9791,f5(a90))+~P72(f95(f32(a90,f4(a90)),x9791))
% 2.58/2.54 [1187]P2(a90,f95(f33(a90),x11871))+~P72(f95(f31(a90,x11871),f5(a90)))+~P72(f95(f31(a90,f4(a90)),x11871))
% 2.58/2.54 [1188]P4(a90,f95(f33(a90),x11881))+~P72(f95(f31(a90,x11881),f5(a90)))+~P72(f95(f31(a90,f4(a90)),x11881))
% 2.58/2.54 [1240]~P72(f95(f32(a90,x12401),f5(a90)))+P72(f95(f32(a90,f35(x12401)),f4(a90)))+~P72(f95(f32(a90,f4(a90)),x12401))
% 2.58/2.54 [1258]~P72(f95(f31(a90,f4(a90)),f35(x12581)))+~P72(f95(f32(a90,f4(a90)),x12581))+P72(f95(f31(a90,f5(a90)),x12581))
% 2.58/2.54 [1260]~P72(f95(f32(a90,f4(a90)),f35(x12601)))+~P72(f95(f32(a90,f4(a90)),x12601))+P72(f95(f32(a90,f5(a90)),x12601))
% 2.58/2.54 [1272]~P72(f95(f32(a90,f35(x12721)),f4(a90)))+P72(f95(f32(a90,x12721),f5(a90)))+~P72(f95(f32(a90,f4(a90)),x12721))
% 2.58/2.54 [1873]E(x18731,f4(a91))+E(x18731,f95(f95(f25(a91),f4(a91)),f5(a91)))+~P72(f95(f32(a91,x18731),f95(f95(f25(a91),f95(f95(f25(a91),f4(a91)),f5(a91))),f5(a91))))
% 2.58/2.54 [822]~P34(x8221)+~P3(x8221,x8222)+P2(x8221,x8222)
% 2.58/2.54 [823]~P34(x8231)+~P5(x8231,x8232)+P2(x8231,x8232)
% 2.58/2.54 [798]~E(x7982,f5(a90))+~E(x7981,f4(a90))+E(f12(x7981,x7982),a17)
% 2.58/2.54 [802]~E(x8022,f4(a90))+~E(x8021,f4(a90))+E(f12(x8021,x8022),f4(a94))
% 2.58/2.54 [803]~E(x8032,f4(a90))+~E(x8031,f5(a90))+E(f12(x8031,x8032),f5(a94))
% 2.58/2.54 [812]~P35(x8121)+~E(x8122,f4(x8121))+E(f37(x8121,x8122),f4(a90))
% 2.58/2.54 [813]~P30(x8131)+~E(x8132,f4(x8131))+E(f19(x8131,x8132),f4(x8131))
% 2.58/2.54 [818]~P35(x8182)+E(x8181,f4(x8182))+~E(f37(x8182,x8181),f4(a90))
% 2.58/2.54 [819]~P30(x8192)+~E(f19(x8192,x8191),f4(x8192))+E(x8191,f4(x8192))
% 2.58/2.54 [862]~P13(x8622)+E(f20(x8622,x8621,x8621),f5(x8622))+E(x8621,f4(x8622))
% 2.58/2.54 [893]E(x8931,x8932)+~E(f95(a7,x8931),f95(a7,x8932))+~E(f95(a11,x8931),f95(a11,x8932))
% 2.58/2.54 [1025]E(x10251,x10252)+~E(f23(a91,x10252,x10251),f4(a91))+~E(f23(a91,x10251,x10252),f4(a91))
% 2.58/2.54 [821]~P9(x8211)+E(f22(x8211,x8212),f4(a91))+~E(x8212,f4(f122(x8211)))
% 2.58/2.54 [824]~P9(x8242)+~E(f22(x8242,x8241),f4(a91))+E(x8241,f4(f122(x8242)))
% 2.58/2.54 [978]~P35(x9782)+E(x9781,f4(x9782))+P72(f95(f32(a90,f4(a90)),f37(x9782,x9781)))
% 2.58/2.54 [981]E(x9811,x9812)+P72(f95(f32(a91,x9812),x9811))+P72(f95(f32(a91,x9811),x9812))
% 2.58/2.54 [982]E(x9821,x9822)+P72(f95(f32(a92,x9822),x9821))+P72(f95(f32(a92,x9821),x9822))
% 2.58/2.54 [996]~P35(x9962)+~P4(x9962,x9961)+P72(f95(f32(a90,f4(a90)),f59(x9961,x9962)))
% 2.58/2.54 [997]~P35(x9972)+~P4(x9972,x9971)+P72(f95(f32(a90,f4(a90)),f66(x9971,x9972)))
% 2.58/2.54 [1000]~P30(x10002)+E(x10001,f4(x10002))+P72(f95(f32(x10002,f4(x10002)),f19(x10002,x10001)))
% 2.58/2.54 [1058]E(x10581,x10582)+P72(f95(f32(a90,x10581),x10582))+~P72(f95(f31(a90,x10581),x10582))
% 2.58/2.54 [1061]E(x10611,x10612)+P72(f95(f32(a91,x10611),x10612))+~P72(f95(f31(a91,x10611),x10612))
% 2.58/2.54 [1062]E(x10621,x10622)+P72(f95(f32(a92,x10621),x10622))+~P72(f95(f31(a92,x10621),x10622))
% 2.58/2.54 [1065]~P35(x10651)+~E(x10652,f4(x10651))+P72(f95(f31(a90,f37(x10651,x10652)),f4(a90)))
% 2.58/2.54 [1067]~P30(x10671)+~E(x10672,f4(x10671))+P72(f95(f31(x10671,f19(x10671,x10672)),f4(x10671)))
% 2.58/2.54 [1099]~P35(x10992)+~E(x10991,f4(x10992))+~P72(f95(f32(a90,f4(a90)),f37(x10992,x10991)))
% 2.58/2.54 [1108]E(x11081,x11082)+~P72(f95(f31(a90,x11082),x11081))+~P72(f95(f31(a90,x11081),x11082))
% 2.58/2.54 [1109]E(x11091,x11092)+~P72(f95(f31(a91,x11092),x11091))+~P72(f95(f31(a91,x11091),x11092))
% 2.58/2.54 [1110]E(x11101,x11102)+~P72(f95(f31(a92,x11102),x11101))+~P72(f95(f31(a92,x11101),x11102))
% 2.58/2.54 [1121]~P34(x11211)+P3(x11211,x11212)+P72(f95(f31(a91,f67(x11212,x11211)),f82(x11212,x11211)))
% 2.58/2.54 [1122]~P34(x11221)+P5(x11221,x11222)+P72(f95(f31(a91,f120(x11222,x11221)),f121(x11222,x11221)))
% 2.58/2.54 [1123]~P34(x11231)+P2(x11231,x11232)+P72(f95(f31(a91,f41(x11232,x11231)),f45(x11232,x11231)))
% 2.58/2.54 [1124]~P34(x11241)+P2(x11241,x11242)+P72(f95(f31(a91,f46(x11242,x11241)),f47(x11242,x11241)))
% 2.58/2.54 [1125]~P34(x11251)+P2(x11251,x11252)+P72(f95(f31(a91,f48(x11252,x11251)),f49(x11252,x11251)))
% 2.58/2.54 [1126]~P34(x11261)+P2(x11261,x11262)+P72(f95(f31(a91,f50(x11262,x11261)),f51(x11262,x11261)))
% 2.58/2.54 [1130]~P30(x11302)+~E(x11301,f4(x11302))+~P72(f95(f32(x11302,f4(x11302)),f19(x11302,x11301)))
% 2.58/2.54 [1181]~P35(x11812)+E(x11811,f4(x11812))+~P72(f95(f31(a90,f37(x11812,x11811)),f4(a90)))
% 2.58/2.54 [1183]E(f20(a92,x11831,x11832),f4(a92))+~P72(f95(f32(a92,x11832),x11831))+~P72(f95(f31(a92,x11831),f4(a92)))
% 2.58/2.54 [1202]~P30(x12022)+E(x12021,f4(x12022))+~P72(f95(f31(x12022,f19(x12022,x12021)),f4(x12022)))
% 2.58/2.54 [1446]P72(f95(f31(a90,f4(a90)),f38(a90,x14461,x14462)))+~P72(f95(f31(a90,x14461),f4(a90)))+~P72(f95(f31(a90,x14462),f4(a90)))
% 2.58/2.54 [1447]P72(f95(f31(a92,f4(a92)),f20(a92,x14471,x14472)))+~P72(f95(f31(a92,x14471),f4(a92)))+~P72(f95(f32(a92,x14472),f4(a92)))
% 2.58/2.54 [1524]~P24(x15241)+~P72(f95(f31(x15241,x15242),f4(x15241)))+P72(f95(f31(x15241,f95(f95(f25(x15241),x15242),x15242)),f4(x15241)))
% 2.58/2.54 [1525]~P47(x15251)+~P72(f95(f32(x15251,x15252),f4(x15251)))+P72(f95(f32(x15251,f95(f95(f25(x15251),x15252),x15252)),f4(x15251)))
% 2.58/2.54 [1526]~P24(x15261)+~P72(f95(f32(x15261,x15262),f4(x15261)))+P72(f95(f32(x15261,f95(f95(f25(x15261),x15262),x15262)),f4(x15261)))
% 2.58/2.54 [1530]~P72(f95(f31(a92,f4(a92)),f20(a92,x15301,x15302)))+P72(f95(f31(a92,x15301),f4(a92)))+~P72(f95(f32(a92,x15302),f4(a92)))
% 2.58/2.54 [1671]~P24(x16711)+~P72(f95(f31(x16711,f95(f95(f25(x16711),x16712),x16712)),f4(x16711)))+P72(f95(f31(x16711,x16712),f4(x16711)))
% 2.58/2.54 [1672]~P47(x16721)+~P72(f95(f32(x16721,f95(f95(f25(x16721),x16722),x16722)),f4(x16721)))+P72(f95(f32(x16721,x16722),f4(x16721)))
% 2.58/2.54 [1673]~P24(x16731)+~P72(f95(f32(x16731,f95(f95(f25(x16731),x16732),x16732)),f4(x16731)))+P72(f95(f32(x16731,x16732),f4(x16731)))
% 2.58/2.54 [1947]E(x19471,f4(a91))+E(x19472,f4(a94))+P72(f95(f32(a90,f37(a94,f95(f95(f25(a94),f5(a94)),f95(f95(f24(a94),x19472),f95(f95(f33(a94),f106(x19471,x19472)),x19471))))),f5(a90)))
% 2.58/2.54 [837]~E(x8372,f5(a91))+~E(x8371,f5(a91))+E(f95(f95(f24(a91),x8371),x8372),f5(a91))
% 2.58/2.54 [838]~E(x8382,f4(a91))+~E(x8381,f4(a91))+E(f95(f95(f25(a91),x8381),x8382),f4(a91))
% 2.58/2.54 [868]~P24(x8681)+~E(x8682,f4(x8681))+E(f95(f95(f25(x8681),x8682),x8682),f4(x8681))
% 2.58/2.54 [894]E(x8941,f5(a91))+E(x8942,f4(a91))+~E(f95(f95(f24(a91),x8942),x8941),x8942)
% 2.58/2.54 [895]E(x8951,f4(a91))+E(x8952,f4(a91))+~E(f95(f95(f24(a91),x8952),x8951),f4(a91))
% 2.58/2.54 [915]~P24(x9152)+E(x9151,f4(x9152))+~E(f95(f95(f25(x9152),x9151),x9151),f4(x9152))
% 2.58/2.54 [986]~E(x9862,f4(a90))+E(f28(x9861,x9862),f4(a90))+~P72(f95(f32(a91,f4(a91)),x9861))
% 2.58/2.54 [987]~E(x9872,f5(a90))+E(f28(x9871,x9872),f5(a90))+~P72(f95(f32(a91,f4(a91)),x9871))
% 2.58/2.54 [991]E(x9911,f4(a91))+E(x9912,f4(a91))+~E(f95(f95(f25(a91),x9912),x9911),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [992]E(x9921,f4(a91))+E(x9922,f4(a91))+~E(f95(f95(f25(a91),f4(a91)),f5(a91)),f95(f95(f25(a91),x9922),x9921))
% 2.58/2.54 [994]E(x9941,f4(a90))+~E(f28(x9942,x9941),f4(a90))+~P72(f95(f32(a91,f4(a91)),x9942))
% 2.58/2.54 [995]E(x9951,f5(a90))+~E(f28(x9952,x9951),f5(a90))+~P72(f95(f32(a91,f4(a91)),x9952))
% 2.58/2.54 [1026]~P38(x10261)+~P69(x10261)+E(f95(f95(f33(x10261),f4(x10261)),f95(f95(f25(a91),x10262),f5(a91))),f4(x10261))
% 2.58/2.54 [1038]~P30(x10381)+E(f19(x10381,x10382),x10382)+~P72(f95(f31(x10381,f4(x10381)),x10382))
% 2.58/2.54 [1039]~P30(x10391)+E(f19(x10391,x10392),x10392)+~P72(f95(f32(x10391,f4(x10391)),x10392))
% 2.58/2.54 [1053]~E(x10532,f4(a91))+~E(x10531,f95(f95(f25(a91),f4(a91)),f5(a91)))+E(f95(f95(f25(a91),x10531),x10532),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1054]~E(x10541,f4(a91))+~E(x10542,f95(f95(f25(a91),f4(a91)),f5(a91)))+E(f95(f95(f25(a91),x10541),x10542),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1055]~E(x10552,f4(a91))+~E(x10551,f95(f95(f25(a91),f4(a91)),f5(a91)))+E(f95(f95(f25(a91),f4(a91)),f5(a91)),f95(f95(f25(a91),x10551),x10552))
% 2.58/2.54 [1056]~E(x10561,f4(a91))+~E(x10562,f95(f95(f25(a91),f4(a91)),f5(a91)))+E(f95(f95(f25(a91),f4(a91)),f5(a91)),f95(f95(f25(a91),x10561),x10562))
% 2.58/2.54 [1075]E(x10751,f5(a92))+~E(f95(f95(f24(a92),x10752),x10751),f5(a92))+~P72(f95(f32(a92,f4(a92)),x10752))
% 2.58/2.54 [1076]E(x10761,f5(a92))+~E(f95(f95(f24(a92),x10761),x10762),f5(a92))+~P72(f95(f32(a92,f4(a92)),x10761))
% 2.58/2.54 [1077]E(x10771,f4(a91))+E(x10772,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f33(a91),x10772),x10771),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1078]E(x10781,f4(a91))+E(x10781,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f25(a91),x10782),x10781),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1079]E(x10791,f4(a91))+E(x10791,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f25(a91),x10791),x10792),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1080]E(x10801,f4(a91))+E(x10801,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f25(a91),f4(a91)),f5(a91)),f95(f95(f25(a91),x10802),x10801))
% 2.58/2.54 [1081]E(x10811,f4(a91))+E(x10811,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f25(a91),f4(a91)),f5(a91)),f95(f95(f25(a91),x10811),x10812))
% 2.58/2.54 [1129]~P72(f95(x11291,x11292))+P72(f95(x11291,f4(a91)))+P72(f95(f32(a91,f104(x11292,x11291)),x11292))
% 2.58/2.54 [1150]E(x11501,f95(f95(f25(a91),f4(a91)),f5(a91)))+E(x11502,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f25(a91),x11501),x11502),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1151]E(x11511,f95(f95(f25(a91),f4(a91)),f5(a91)))+E(x11512,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(f95(f95(f25(a91),f4(a91)),f5(a91)),f95(f95(f25(a91),x11511),x11512))
% 2.58/2.54 [1161]~E(x11612,f95(f95(f25(a91),f4(a91)),f5(a91)))+~E(x11611,f95(f95(f25(a91),f4(a91)),f5(a91)))+E(f95(f95(f24(a91),x11611),x11612),f95(f95(f25(a91),f4(a91)),f5(a91)))
% 2.58/2.54 [1191]E(f20(a92,x11911,x11912),f4(a92))+~P72(f95(f32(a92,x11911),x11912))+~P72(f95(f31(a92,f4(a92)),x11911))
% 2.58/2.54 [1249]E(f95(f95(f33(a90),f28(x12491,x12492)),x12491),x12492)+~P72(f95(f31(a90,f4(a90)),x12492))+~P72(f95(f32(a91,f4(a91)),x12491))
% 2.58/2.54 [1250]E(f95(f95(f33(a90),f28(x12501,x12502)),x12501),x12502)+~P72(f95(f32(a90,f4(a90)),x12502))+~P72(f95(f32(a91,f4(a91)),x12501))
% 2.58/2.54 [1251]E(f95(f95(f33(a90),f101(x12511,x12512)),x12512),x12511)+~P72(f95(f32(a90,f4(a90)),x12511))+~P72(f95(f32(a91,f4(a91)),x12512))
% 2.58/2.54 [1252]E(f95(f95(f33(a90),f102(x12521,x12522)),x12522),x12521)+~P72(f95(f32(a90,f4(a90)),x12521))+~P72(f95(f32(a91,f4(a91)),x12522))
% 2.58/2.54 [1312]P72(f95(f31(a90,f4(a90)),f28(x13121,x13122)))+~P72(f95(f31(a90,f4(a90)),x13122))+~P72(f95(f32(a91,f4(a91)),x13121))
% 2.58/2.54 [1313]P72(f95(f31(a90,f4(a90)),f28(x13131,x13132)))+~P72(f95(f32(a90,f4(a90)),x13132))+~P72(f95(f32(a91,f4(a91)),x13131))
% 2.58/2.54 [1314]P72(f95(f31(a90,f5(a90)),f28(x13141,x13142)))+~P72(f95(f32(a91,f4(a91)),x13141))+~P72(f95(f31(a90,f5(a90)),x13142))
% 2.58/2.54 [1315]P72(f95(f31(a92,f4(a92)),f30(x13151,x13152)))+~P72(f95(f31(a92,f4(a92)),x13151))+~P72(f95(f31(a92,f4(a92)),x13152))
% 2.58/2.54 [1317]P72(f95(f32(a90,f4(a90)),f28(x13171,x13172)))+~P72(f95(f32(a90,f4(a90)),x13172))+~P72(f95(f32(a91,f4(a91)),x13171))
% 2.58/2.54 [1318]P72(f95(f32(a90,f4(a90)),f101(x13181,x13182)))+~P72(f95(f32(a90,f4(a90)),x13181))+~P72(f95(f32(a91,f4(a91)),x13182))
% 2.58/2.54 [1319]P72(f95(f32(a90,f4(a90)),f102(x13191,x13192)))+~P72(f95(f32(a90,f4(a90)),x13191))+~P72(f95(f32(a91,f4(a91)),x13192))
% 2.58/2.54 [1320]P72(f95(f32(a90,f5(a90)),f28(x13201,x13202)))+~P72(f95(f32(a91,f4(a91)),x13201))+~P72(f95(f32(a90,f5(a90)),x13202))
% 2.58/2.54 [1321]P72(f95(f31(a90,x13211),f36(a91,x13212)))+~P72(f95(f31(a90,f4(a90)),x13211))+~P72(f95(f31(a91,f27(x13211)),x13212))
% 2.58/2.54 [1330]~P72(f95(f32(a90,x13301),f36(a91,x13302)))+~P72(f95(f31(a90,f4(a90)),x13301))+P72(f95(f32(a91,f26(x13301)),x13302))
% 2.58/2.54 [1343]~P72(f95(f31(a91,x13431),f26(x13432)))+~P72(f95(f31(a90,f4(a90)),x13432))+P72(f95(f31(a90,f36(a91,x13431)),x13432))
% 2.58/2.54 [1344]~P72(f95(f31(a90,f4(a90)),f28(x13442,x13441)))+P72(f95(f31(a90,f4(a90)),x13441))+~P72(f95(f32(a91,f4(a91)),x13442))
% 2.58/2.54 [1345]~P72(f95(f31(a90,f5(a90)),f28(x13452,x13451)))+~P72(f95(f32(a91,f4(a91)),x13452))+P72(f95(f31(a90,f5(a90)),x13451))
% 2.58/2.54 [1346]~P72(f95(f32(a90,f4(a90)),f28(x13462,x13461)))+P72(f95(f32(a90,f4(a90)),x13461))+~P72(f95(f32(a91,f4(a91)),x13462))
% 2.58/2.54 [1347]~P72(f95(f32(a90,f5(a90)),f28(x13472,x13471)))+~P72(f95(f32(a91,f4(a91)),x13472))+P72(f95(f32(a90,f5(a90)),x13471))
% 2.58/2.54 [1351]~P72(f95(f31(a90,x13512),f4(a90)))+P72(f95(f31(a90,f28(x13511,x13512)),f4(a90)))+~P72(f95(f32(a91,f4(a91)),x13511))
% 2.58/2.54 [1352]~P72(f95(f31(a90,x13522),f5(a90)))+P72(f95(f31(a90,f28(x13521,x13522)),f5(a90)))+~P72(f95(f32(a91,f4(a91)),x13521))
% 2.58/2.54 [1353]~P72(f95(f32(a90,x13532),f4(a90)))+P72(f95(f32(a90,f28(x13531,x13532)),f4(a90)))+~P72(f95(f32(a91,f4(a91)),x13531))
% 2.58/2.54 [1354]~P72(f95(f32(a90,x13542),f5(a90)))+P72(f95(f32(a90,f28(x13541,x13542)),f5(a90)))+~P72(f95(f32(a91,f4(a91)),x13541))
% 2.58/2.54 [1379]E(f26(f38(a90,x13791,f36(a91,x13792))),f20(a91,f26(x13791),x13792))+~P72(f95(f32(a91,f4(a91)),x13792))+~P72(f95(f31(a90,f5(a90)),x13791))
% 2.58/2.54 [1387]E(x13871,x13872)+P72(f95(f32(a91,x13871),x13872))+~P72(f95(f32(a91,x13871),f95(f95(f25(a91),x13872),f5(a91))))
% 2.58/2.54 [1388]E(x13881,x13882)+P72(f95(f32(a92,x13881),x13882))+~P72(f95(f32(a92,x13881),f95(f95(f25(a92),x13882),f5(a92))))
% 2.58/2.54 [1399]~P72(f95(f31(a90,f28(x13992,x13991)),f4(a90)))+P72(f95(f31(a90,x13991),f4(a90)))+~P72(f95(f32(a91,f4(a91)),x13992))
% 2.58/2.54 [1400]~P72(f95(f31(a90,f28(x14002,x14001)),f5(a90)))+P72(f95(f31(a90,x14001),f5(a90)))+~P72(f95(f32(a91,f4(a91)),x14002))
% 2.58/2.54 [1401]~P72(f95(f32(a90,f28(x14012,x14011)),f4(a90)))+P72(f95(f32(a90,x14011),f4(a90)))+~P72(f95(f32(a91,f4(a91)),x14012))
% 2.58/2.54 [1402]~P72(f95(f32(a90,f28(x14022,x14021)),f5(a90)))+P72(f95(f32(a90,x14021),f5(a90)))+~P72(f95(f32(a91,f4(a91)),x14022))
% 2.58/2.54 [1405]~P72(f95(x14051,x14052))+P72(f95(x14051,f4(a91)))+P72(f95(x14051,f95(f95(f25(a91),f104(x14052,x14051)),f5(a91))))
% 2.58/2.54 [1416]E(x14161,f4(a91))+E(f95(f95(f25(a91),f81(x14162,x14161)),f5(a91)),x14161)+~P72(f95(f32(a91,x14161),f95(f95(f25(a91),x14162),f5(a91))))
% 2.58/2.54 [1435]E(x14351,x14352)+~P72(f95(f31(a91,x14352),x14351))+~P72(f95(f32(a91,x14351),f95(f95(f25(a91),x14352),f5(a91))))
% 2.58/2.54 [1442]E(x14421,f95(f95(f25(a91),x14422),f5(a91)))+P72(f95(f31(a91,x14421),x14422))+~P72(f95(f31(a91,x14421),f95(f95(f25(a91),x14422),f5(a91))))
% 2.58/2.54 [1445]P72(f95(f32(a92,f4(a92)),f20(a92,x14451,x14452)))+~P72(f95(f31(a92,x14452),x14451))+~P72(f95(f32(a92,f4(a92)),x14452))
% 2.58/2.54 [1450]P72(f95(f31(a90,f4(a90)),f38(a90,x14501,x14502)))+~P72(f95(f31(a90,x14502),f4(a90)))+~P72(f95(f31(a90,f4(a90)),x14502))
% 2.58/2.54 [1451]P72(f95(f31(a90,f4(a90)),f38(a90,x14511,x14512)))+~P72(f95(f31(a90,x14511),f4(a90)))+~P72(f95(f31(a90,f4(a90)),x14511))
% 2.58/2.54 [1455]P72(f95(f31(a90,f4(a90)),f38(a90,x14551,x14552)))+~P72(f95(f31(a90,f4(a90)),x14552))+~P72(f95(f31(a90,f4(a90)),x14551))
% 2.58/2.54 [1456]P72(f95(f31(a92,f4(a92)),f20(a92,x14561,x14562)))+~P72(f95(f31(a92,f4(a92)),x14562))+~P72(f95(f31(a92,f4(a92)),x14561))
% 2.58/2.54 [1457]P72(f95(f31(a92,f4(a92)),f20(a92,x14571,x14572)))+~P72(f95(f31(a92,f4(a92)),x14571))+~P72(f95(f32(a92,f4(a92)),x14572))
% 2.58/2.54 [1480]E(x14801,f4(a91))+P72(f95(f32(a91,f81(x14802,x14801)),x14802))+~P72(f95(f32(a91,x14801),f95(f95(f25(a91),x14802),f5(a91))))
% 2.58/2.54 [1504]~P72(f95(f31(a90,f4(a90)),f38(a90,x15042,x15041)))+P72(f95(f31(a90,x15041),f4(a90)))+P72(f95(f31(a90,f4(a90)),x15042))
% 2.58/2.54 [1505]~P72(f95(f31(a90,f4(a90)),f38(a90,x15051,x15052)))+P72(f95(f31(a90,x15051),f4(a90)))+P72(f95(f31(a90,f4(a90)),x15052))
% 2.58/2.54 [1534]~P72(f95(f32(a92,f4(a92)),f20(a92,x15342,x15341)))+P72(f95(f31(a92,x15341),x15342))+~P72(f95(f32(a92,f4(a92)),x15341))
% 2.58/2.54 [1535]~P72(f95(f32(a92,f4(a92)),f20(a92,x15352,x15351)))+P72(f95(f31(a92,x15351),x15352))+~P72(f95(f31(a92,f4(a92)),x15352))
% 2.58/2.54 [1536]~P72(f95(f31(a92,f4(a92)),f20(a92,x15361,x15362)))+P72(f95(f31(a92,f4(a92)),x15361))+~P72(f95(f32(a92,f4(a92)),x15362))
% 2.58/2.54 [1537]~P72(f95(f32(a92,f4(a92)),f20(a92,x15372,x15371)))+P72(f95(f32(a92,f4(a92)),x15371))+~P72(f95(f31(a92,f4(a92)),x15372))
% 2.58/2.54 [1583]~P72(f95(f31(a92,x15831),f4(a92)))+P72(f95(f31(a92,f20(a92,x15831,x15832)),f4(a92)))+~P72(f95(f32(a92,f4(a92)),x15832))
% 2.58/2.54 [1584]~P72(f95(f32(a92,x15842),f4(a92)))+P72(f95(f31(a92,f20(a92,x15841,x15842)),f4(a92)))+~P72(f95(f31(a92,f4(a92)),x15841))
% 2.58/2.54 [1585]~P72(f95(f32(a92,x15852),f4(a92)))+P72(f95(f32(a92,f20(a92,x15851,x15852)),f4(a92)))+~P72(f95(f32(a92,f4(a92)),x15851))
% 2.58/2.54 [1587]~P72(f95(f32(a92,x15871),f4(a92)))+P72(f95(f32(a92,f20(a92,x15871,x15872)),f4(a92)))+~P72(f95(f32(a92,f4(a92)),x15872))
% 2.58/2.54 [1588]~P72(f95(f32(a91,f4(a91)),x15881))+~P72(f95(f32(a91,f4(a91)),x15882))+P72(f95(f32(a91,f23(a91,x15881,x15882)),x15881))
% 2.58/2.54 [1589]~P72(f95(f32(a91,f4(a91)),x15891))+P72(f95(f32(a91,f20(a91,x15891,x15892)),x15891))+~P72(f95(f32(a91,f5(a91)),x15892))
% 2.58/2.54 [1590]~P72(f95(f32(a92,f4(a92)),x15901))+P72(f95(f32(a92,f20(a92,x15901,x15902)),x15901))+~P72(f95(f32(a92,f5(a92)),x15902))
% 2.58/2.54 [1664]~P34(x16641)+P3(x16641,x16642)+~P72(f95(f31(x16641,f95(x16642,f82(x16642,x16641))),f95(x16642,f67(x16642,x16641))))
% 2.58/2.54 [1665]~P34(x16651)+P5(x16651,x16652)+~P72(f95(f31(x16651,f95(x16652,f120(x16652,x16651))),f95(x16652,f121(x16652,x16651))))
% 2.58/2.54 [1666]~P34(x16661)+P2(x16661,x16662)+~P72(f95(f31(x16661,f95(x16662,f41(x16662,x16661))),f95(x16662,f45(x16662,x16661))))
% 2.58/2.54 [1667]~P34(x16671)+P2(x16671,x16672)+~P72(f95(f31(x16671,f95(x16672,f47(x16672,x16671))),f95(x16672,f46(x16672,x16671))))
% 2.58/2.54 [1668]~P34(x16681)+P2(x16681,x16682)+~P72(f95(f31(x16681,f95(x16682,f48(x16682,x16681))),f95(x16682,f49(x16682,x16681))))
% 2.58/2.54 [1669]~P34(x16691)+P2(x16691,x16692)+~P72(f95(f31(x16691,f95(x16692,f51(x16692,x16691))),f95(x16692,f50(x16692,x16691))))
% 2.58/2.54 [1692]E(f95(f95(f25(a91),f20(a91,f23(a91,x16921,x16922),x16922)),f5(a91)),f20(a91,x16921,x16922))+P72(f95(f32(a91,x16921),x16922))+~P72(f95(f32(a91,f4(a91)),x16922))
% 2.58/2.54 [1705]E(f26(x17051),x17052)+~P72(f95(f31(a90,f36(a91,x17052)),x17051))+~P72(f95(f32(a90,x17051),f95(f95(f25(a90),f36(a91,x17052)),f5(a90))))
% 2.58/2.54 [1716]E(f95(f95(f25(a91),f20(a91,f23(a91,x17161,x17162),x17162)),f5(a91)),f20(a91,x17161,x17162))+~P72(f95(f31(a91,x17162),x17161))+~P72(f95(f32(a91,f4(a91)),x17162))
% 2.58/2.54 [1725]~P72(f95(f32(a92,x17252),f4(a92)))+~P72(f95(f32(a92,f20(a92,x17251,x17252)),f4(a92)))+P72(f95(f32(a92,f4(a92)),x17251))
% 2.58/2.54 [1741]P72(f95(f32(a92,x17411),f4(a92)))+~P72(f95(f32(a92,f20(a92,x17411,x17412)),f4(a92)))+~P72(f95(f32(a92,f4(a92)),x17412))
% 2.58/2.54 [1745]E(f27(x17451),f95(f95(f25(a91),x17452),f5(a91)))+~P72(f95(f32(a90,f36(a91,x17452)),x17451))+~P72(f95(f31(a90,x17451),f95(f95(f25(a90),f36(a91,x17452)),f5(a90))))
% 2.58/2.54 [1909]~P34(x19091)+P2(x19091,x19092)+~P72(f95(f31(x19091,f95(x19092,f95(f95(f25(a91),f85(x19092,x19091)),f5(a91)))),f95(x19092,f85(x19092,x19091))))
% 2.58/2.54 [1208]~E(x12082,f4(a90))+~E(x12081,f4(a90))+E(f95(f95(f25(a90),f95(f95(f24(a90),x12081),x12081)),f95(f95(f24(a90),x12082),x12082)),f4(a90))
% 2.58/2.54 [1256]E(f28(x12561,f95(f95(f33(a90),x12562),x12561)),x12562)+~P72(f95(f31(a90,f4(a90)),x12562))+~P72(f95(f32(a91,f4(a91)),x12561))
% 2.58/2.54 [1332]E(f95(f95(f25(a90),f35(x13321)),f35(x13322)),f35(f95(f95(f24(a90),x13321),x13322)))+~P72(f95(f32(a90,f4(a90)),x13322))+~P72(f95(f32(a90,f4(a90)),x13321))
% 2.58/2.54 [1370]~P24(x13701)+~P72(f95(f31(x13701,f4(x13701)),x13702))+P72(f95(f31(x13701,f4(x13701)),f95(f95(f25(x13701),x13702),x13702)))
% 2.58/2.54 [1373]~P24(x13731)+~P72(f95(f32(x13731,f4(x13731)),x13732))+P72(f95(f32(x13731,f4(x13731)),f95(f95(f25(x13731),x13732),x13732)))
% 2.58/2.54 [1404]E(x14041,f4(a91))+P72(f95(f32(a91,f4(a91)),x14042))+~P72(f95(f32(a91,f4(a91)),f95(f95(f33(a91),x14042),x14041)))
% 2.58/2.54 [1437]~P72(f95(f31(a92,f4(a92)),x14371))+~P72(f95(f31(a92,f4(a92)),x14372))+P72(f95(f31(a92,f4(a92)),f95(f95(f24(a92),x14371),x14372)))
% 2.58/2.54 [1438]~P72(f95(f31(a92,f4(a92)),x14381))+~P72(f95(f31(a92,f4(a92)),x14382))+P72(f95(f31(a92,f4(a92)),f95(f95(f25(a92),x14381),x14382)))
% 2.58/2.54 [1439]~P72(f95(f32(a90,f4(a90)),x14392))+~P72(f95(f32(a90,f4(a90)),x14391))+P72(f95(f32(a90,f4(a90)),f95(f95(f24(a90),x14391),x14392)))
% 2.58/2.54 [1440]~P72(f95(f32(a91,f4(a91)),x14402))+~P72(f95(f32(a91,f4(a91)),x14401))+P72(f95(f32(a91,f4(a91)),f95(f95(f24(a91),x14401),x14402)))
% 2.58/2.54 [1477]P72(f95(f32(a91,f4(a91)),x14771))+P72(f95(f32(a91,f4(a91)),x14772))+~P72(f95(f32(a91,f4(a91)),f95(f95(f25(a91),x14772),x14771)))
% 2.58/2.54 [1478]~P24(x14781)+P72(f95(f31(x14781,f4(x14781)),x14782))+~P72(f95(f31(x14781,f4(x14781)),f95(f95(f25(x14781),x14782),x14782)))
% 2.58/2.54 [1479]~P24(x14791)+P72(f95(f32(x14791,f4(x14791)),x14792))+~P72(f95(f32(x14791,f4(x14791)),f95(f95(f25(x14791),x14792),x14792)))
% 2.58/2.54 [1503]E(f95(f95(f25(a91),x15031),f5(a91)),x15032)+~P72(f95(f32(a91,x15031),x15032))+P72(f95(f32(a91,f95(f95(f25(a91),x15031),f5(a91))),x15032))
% 2.58/2.54 [1551]E(x15511,f4(a91))+~E(x15512,f4(a92))+~P72(f95(f32(a92,f4(a92)),f95(f95(f33(a92),f19(a92,x15512)),x15511)))
% 2.58/2.54 [1597]E(f20(a92,f95(f95(f33(a92),x15971),x15972),x15971),f95(f95(f33(a92),x15971),f23(a91,x15972,f95(f95(f25(a91),f4(a91)),f5(a91)))))+~P72(f95(f32(a91,f4(a91)),x15972))+~P72(f95(f32(a92,f4(a92)),x15971))
% 2.58/2.54 [1875]~P72(f95(f32(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18751))+~P72(f95(f32(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18752))+P72(f95(f32(a91,x18751),f95(f95(f24(a91),x18752),x18751)))
% 2.58/2.54 [1876]~P72(f95(f32(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18761))+~P72(f95(f32(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18762))+P72(f95(f32(a91,x18761),f95(f95(f24(a91),x18761),x18762)))
% 2.58/2.54 [1887]~P34(x18871)+P2(x18871,x18872)+~P72(f95(f31(x18871,f95(x18872,f84(x18872,x18871))),f95(x18872,f95(f95(f25(a91),f84(x18872,x18871)),f5(a91)))))
% 2.58/2.54 [1896]~P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18961))+~P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18962))+P72(f95(f31(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),f95(f95(f24(a91),x18961),x18962)))
% 2.58/2.54 [1897]~P72(f95(f32(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18972))+~P72(f95(f32(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),x18971))+P72(f95(f32(a91,f95(f95(f25(a91),f4(a91)),f5(a91))),f95(f95(f24(a91),x18971),x18972)))
% 2.58/2.54 [1796]~P72(f95(f31(a90,f4(a90)),x17962))+~P72(f95(f31(a90,f4(a90)),x17961))+P72(f95(f31(a91,f95(f95(f24(a91),f26(x17961)),f26(x17962))),f26(f95(f95(f24(a90),x17961),x17962))))
% 2.58/2.54 [1882]~P72(f95(f31(a90,f4(a90)),x18821))+~P72(f95(f32(a90,f4(a90)),x18822))+P72(f95(f31(a90,f95(f95(f24(a90),f36(a91,f98(x18821,x18822))),x18822)),x18821))
% 2.58/2.54 [1925]~P72(f95(f31(a90,f4(a90)),x19251))+~P72(f95(f32(a90,f4(a90)),x19252))+P72(f95(f32(a90,x19251),f95(f95(f24(a90),f36(a91,f95(f95(f25(a91),f98(x19251,x19252)),f5(a91)))),x19252)))
% 2.58/2.54 [855]~E(x8552,x8553)+~P12(x8551)+E(f23(x8551,x8552,x8553),f4(x8551))
% 2.58/2.54 [856]~E(x8562,x8563)+~P25(x8561)+E(f23(x8561,x8562,x8563),f4(x8561))
% 2.58/2.54 [916]~P12(x9163)+E(x9161,x9162)+~E(f23(x9163,x9161,x9162),f4(x9163))
% 2.58/2.54 [917]~P25(x9173)+E(x9171,x9172)+~E(f23(x9173,x9171,x9172),f4(x9173))
% 2.58/2.54 [905]~E(x9052,x9053)+~P6(x9051)+P72(f95(f31(x9051,x9052),x9053))
% 2.58/2.54 [907]~E(x9072,x9073)+~P34(x9071)+P72(f95(f31(x9071,x9072),x9073))
% 2.58/2.54 [944]~P73(x9441,x9442,x9443)+~E(x9442,f4(a92))+P72(f95(x9441,f4(a92)))
% 2.58/2.54 [956]~E(x9561,x9562)+~P8(x9563)+~P72(f95(f32(x9563,x9561),x9562))
% 2.58/2.54 [957]~E(x9571,x9572)+~P34(x9573)+~P72(f95(f32(x9573,x9571),x9572))
% 2.58/2.54 [1002]~P8(x10021)+P72(f95(f31(x10021,x10023),x10022))+P72(f95(f31(x10021,x10022),x10023))
% 2.58/2.54 [1007]~P8(x10071)+P72(f95(f32(x10071,x10073),x10072))+P72(f95(f31(x10071,x10072),x10073))
% 2.58/2.54 [1072]~P6(x10721)+~P72(f95(f32(x10721,x10722),x10723))+P72(f95(f31(x10721,x10722),x10723))
% 2.58/2.54 [1074]~P34(x10741)+~P72(f95(f32(x10741,x10742),x10743))+P72(f95(f31(x10741,x10742),x10743))
% 2.58/2.54 [1106]~P15(x11061)+~P40(x11061)+E(f38(a90,f37(x11061,x11062),f37(x11061,x11063)),f37(x11061,f38(x11061,x11062,x11063)))
% 2.58/2.54 [1131]~P6(x11311)+~P72(f95(f32(x11311,x11313),x11312))+~P72(f95(f31(x11311,x11312),x11313))
% 2.58/2.54 [1135]~P6(x11351)+~P72(f95(f32(x11351,x11353),x11352))+~P72(f95(f32(x11351,x11352),x11353))
% 2.58/2.54 [1138]~P8(x11381)+~P72(f95(f32(x11381,x11383),x11382))+~P72(f95(f31(x11381,x11382),x11383))
% 2.58/2.54 [1139]~P8(x11391)+~P72(f95(f32(x11391,x11393),x11392))+~P72(f95(f32(x11391,x11392),x11393))
% 2.58/2.54 [1140]~P34(x11401)+~P72(f95(f32(x11401,x11403),x11402))+~P72(f95(f32(x11401,x11402),x11403))
% 2.58/2.54 [1180]~E(x11803,f4(a91))+P72(f95(x11801,f20(a91,x11802,x11803)))+~P72(f95(x11801,f4(a91)))
% 2.58/2.54 [1192]~P72(f95(f31(a90,x11921),x11923))+P72(f95(f31(a90,x11921),x11922))+~P72(f95(f31(a90,x11923),x11922))
% 2.58/2.54 [1193]~P72(f95(f31(a91,x11931),x11933))+P72(f95(f31(a91,x11931),x11932))+~P72(f95(f31(a91,x11933),x11932))
% 2.58/2.54 [1194]~P72(f95(f31(a92,x11941),x11943))+P72(f95(f31(a92,x11941),x11942))+~P72(f95(f31(a92,x11943),x11942))
% 2.58/2.54 [1235]~P1(x12351)+~P72(f95(f32(a91,x12352),x12353))+P72(f95(f32(a91,f95(x12351,x12352)),f95(x12351,x12353)))
% 2.58/2.54 [1303]~E(x13032,f4(a91))+~P72(f95(x13031,f20(a91,x13033,x13032)))+P72(f95(x13031,f4(a91)))
% 2.58/2.54 [1348]E(f95(f95(f25(a91),x13481),f108(x13481,x13482,x13483)),x13482)+P72(f95(x13483,f23(a91,x13482,x13481)))+~P72(f95(x13483,f4(a91)))
% 2.58/2.54 [1349]E(f95(f95(f25(a91),x13491),f109(x13491,x13492,x13493)),x13492)+P72(f95(x13493,f23(a91,x13492,x13491)))+~P72(f95(x13493,f4(a91)))
% 2.58/2.54 [1359]E(f95(f95(f25(a91),x13591),f108(x13591,x13592,x13593)),x13592)+P72(f95(x13593,f23(a91,x13592,x13591)))+P72(f95(f32(a91,x13592),x13591))
% 2.58/2.54 [1360]E(f95(f95(f25(a91),x13601),f109(x13601,x13602,x13603)),x13602)+P72(f95(x13603,f23(a91,x13602,x13601)))+P72(f95(f32(a91,x13602),x13601))
% 2.58/2.54 [1361]~P35(x13611)+~P4(x13611,x13612)+P72(f95(f31(a90,f37(x13611,f95(x13612,x13613))),f59(x13612,x13611)))
% 2.58/2.54 [1362]~P35(x13621)+~P4(x13621,x13622)+P72(f95(f31(a90,f37(x13621,f95(x13622,x13623))),f66(x13622,x13621)))
% 2.58/2.54 [1418]~P72(f95(x14181,f23(a91,x14182,x14183)))+~P72(f95(f32(a91,x14182),x14183))+P72(f95(x14181,f4(a91)))
% 2.58/2.54 [1444]E(f23(a91,f23(a91,x14441,x14442),f23(a91,x14443,x14442)),f23(a91,x14441,x14443))+~P72(f95(f31(a91,x14442),x14441))+~P72(f95(f31(a91,x14442),x14443))
% 2.58/2.54 [1488]E(x14881,f4(a91))+P72(f95(x14882,f115(x14881,x14883,x14882)))+~P72(f95(x14882,f20(a91,x14883,x14881)))
% 2.58/2.54 [1498]E(x14981,f4(a91))+~P72(f95(x14982,f116(x14981,x14983,x14982)))+P72(f95(x14982,f20(a91,x14983,x14981)))
% 2.58/2.54 [1520]P72(f95(x15201,f115(x15202,x15203,x15201)))+~P72(f95(x15201,f20(a91,x15203,x15202)))+P72(f95(x15201,f4(a91)))
% 2.58/2.54 [1522]~P29(x15221)+~P72(f95(f31(x15221,x15222),x15223))+P72(f95(f31(x15221,f23(x15221,x15222,x15223)),f4(x15221)))
% 2.58/2.54 [1523]~P29(x15231)+~P72(f95(f32(x15231,x15232),x15233))+P72(f95(f32(x15231,f23(x15231,x15232,x15233)),f4(x15231)))
% 2.58/2.54 [1531]~P72(f95(x15311,f108(x15313,x15312,x15311)))+P72(f95(x15311,f23(a91,x15312,x15313)))+~P72(f95(x15311,f4(a91)))
% 2.58/2.54 [1532]~P72(f95(x15321,f109(x15323,x15322,x15321)))+P72(f95(x15321,f23(a91,x15322,x15323)))+~P72(f95(x15321,f4(a91)))
% 2.58/2.54 [1533]~P72(f95(x15331,f116(x15333,x15332,x15331)))+P72(f95(x15331,f20(a91,x15332,x15333)))+~P72(f95(x15331,f4(a91)))
% 2.58/2.54 [1543]~P72(f95(x15433,f108(x15432,x15431,x15433)))+P72(f95(x15433,f23(a91,x15431,x15432)))+P72(f95(f32(a91,x15431),x15432))
% 2.58/2.54 [1544]~P72(f95(x15443,f109(x15442,x15441,x15443)))+P72(f95(x15443,f23(a91,x15441,x15442)))+P72(f95(f32(a91,x15441),x15442))
% 2.58/2.54 [1680]~P29(x16801)+~P72(f95(f31(x16801,f23(x16801,x16802,x16803)),f4(x16801)))+P72(f95(f31(x16801,x16802),x16803))
% 2.58/2.54 [1681]~P29(x16811)+~P72(f95(f32(x16811,f23(x16811,x16812,x16813)),f4(x16811)))+P72(f95(f32(x16811,x16812),x16813))
% 2.58/2.54 [1689]~P72(f95(f32(a91,x16893),x16892))+~P72(f95(f32(a91,x16893),x16891))+P72(f95(f32(a91,f23(a91,x16891,x16892)),f23(a91,x16891,x16893)))
% 2.58/2.54 [1690]~P72(f95(f31(a91,x16902),x16901))+~P72(f95(f32(a91,x16901),x16903))+P72(f95(f32(a91,f23(a91,x16901,x16902)),f23(a91,x16903,x16902)))
% 2.58/2.54 [1694]~P72(f95(f31(a92,x16943),x16941))+P72(f95(f31(a92,f20(a92,x16941,x16942)),f20(a92,x16943,x16942)))+~P72(f95(f32(a92,x16942),f4(a92)))
% 2.58/2.54 [1742]E(x17421,f4(a91))+E(f95(f95(f25(a91),f95(f95(f24(a91),x17421),f116(x17421,x17422,x17423))),f118(x17421,x17422,x17423)),x17422)+P72(f95(x17423,f20(a91,x17422,x17421)))
% 2.58/2.54 [1751]E(f95(f95(f25(a91),f95(f95(f24(a91),x17511),f116(x17511,x17512,x17513))),f118(x17511,x17512,x17513)),x17512)+P72(f95(x17513,f20(a91,x17512,x17511)))+~P72(f95(x17513,f4(a91)))
% 2.58/2.54 [1935]~P51(x19352)+E(x19351,f4(x19352))+~P72(f95(f31(x19352,f95(f95(f25(x19352),f95(f95(f24(x19352),x19353),x19353)),f95(f95(f24(x19352),x19351),x19351))),f4(x19352)))
% 2.58/2.54 [1936]~P51(x19362)+E(x19361,f4(x19362))+~P72(f95(f31(x19362,f95(f95(f25(x19362),f95(f95(f24(x19362),x19361),x19361)),f95(f95(f24(x19362),x19363),x19363))),f4(x19362)))
% 2.58/2.54 [854]~P71(x8541)+~E(x8543,f4(x8541))+E(f95(f95(f25(x8541),x8542),x8543),x8542)
% 2.58/2.54 [857]~P38(x8571)+~E(x8573,f4(a91))+E(f95(f95(f33(x8571),x8572),x8573),f5(x8571))
% 2.58/2.54 [866]~P64(x8661)+~E(x8663,f4(x8661))+E(f95(f95(f24(x8661),x8662),x8663),f4(x8661))
% 2.58/2.54 [867]~P64(x8671)+~E(x8672,f4(x8671))+E(f95(f95(f24(x8671),x8672),x8673),f4(x8671))
% 2.58/2.54 [908]~P71(x9082)+E(x9081,f4(x9082))+~E(f95(f95(f25(x9082),x9083),x9081),x9083)
% 2.58/2.54 [914]~P65(x9142)+E(x9141,f4(x9142))+~E(f95(f95(f33(x9142),x9141),x9143),f4(x9142))
% 2.58/2.54 [969]E(x9691,x9692)+E(x9693,f4(a90))+~E(f95(f95(f24(a90),x9693),x9691),f95(f95(f24(a90),x9693),x9692))
% 2.58/2.54 [971]E(x9711,x9712)+E(x9713,f4(a91))+~E(f95(f95(f24(a91),x9713),x9711),f95(f95(f24(a91),x9713),x9712))
% 2.58/2.54 [972]E(x9721,x9722)+E(x9723,f4(a90))+~E(f95(f95(f24(a90),x9721),x9723),f95(f95(f24(a90),x9722),x9723))
% 2.58/2.54 [973]E(x9731,x9732)+E(x9733,f4(a91))+~E(f95(f95(f24(a91),x9731),x9733),f95(f95(f24(a91),x9732),x9733))
% 2.58/2.54 [1033]E(x10331,x10332)+~E(f28(x10333,x10331),f28(x10333,x10332))+~P72(f95(f32(a91,f4(a91)),x10333))
% 2.58/2.54 [1114]E(f23(a91,x11141,x11142),x11143)+~E(x11141,f95(f95(f25(a91),x11143),x11142))+~P72(f95(f31(a91,x11142),x11141))
% 2.58/2.54 [1119]~E(f23(a91,x11191,x11193),x11192)+E(x11191,f95(f95(f25(a91),x11192),x11193))+~P72(f95(f31(a91,x11193),x11191))
% 2.58/2.54 [1169]E(x11691,x11692)+~E(f95(f95(f24(a91),x11693),x11691),f95(f95(f24(a91),x11693),x11692))+~P72(f95(f32(a91,f4(a91)),x11693))
% 2.58/2.54 [1234]E(f28(x12341,f28(x12342,x12343)),f28(x12342,f28(x12341,x12343)))+~P72(f95(f32(a91,f4(a91)),x12342))+~P72(f95(f32(a91,f4(a91)),x12341))
% 2.58/2.54 [1255]~P30(x12551)+P72(f95(f31(x12551,x12552),x12553))+~P72(f95(f31(x12551,f19(x12551,x12552)),x12553))
% 2.58/2.54 [1358]~E(x13581,f95(f95(f25(a91),x13583),f5(a91)))+~P72(f95(f32(a91,x13583),x13582))+P72(f95(f32(a91,x13581),f95(f95(f25(a91),x13582),f5(a91))))
% 2.58/2.54 [1376]~P72(f95(f31(a90,x13762),x13763))+P72(f95(f31(a90,f28(x13761,x13762)),f28(x13761,x13763)))+~P72(f95(f32(a91,f4(a91)),x13761))
% 2.58/2.54 [1378]~P72(f95(f32(a90,x13782),x13783))+P72(f95(f32(a90,f28(x13781,x13782)),f28(x13781,x13783)))+~P72(f95(f32(a91,f4(a91)),x13781))
% 2.58/2.54 [1460]~P72(f95(f31(a90,f28(x14603,x14601)),f28(x14603,x14602)))+P72(f95(f31(a90,x14601),x14602))+~P72(f95(f32(a91,f4(a91)),x14603))
% 2.58/2.54 [1461]~P72(f95(f32(a90,f28(x14613,x14611)),f28(x14613,x14612)))+P72(f95(f32(a90,x14611),x14612))+~P72(f95(f32(a91,f4(a91)),x14613))
% 2.58/2.54 [1571]E(x15711,f4(a91))+P72(f95(x15712,f20(a91,x15713,x15711)))+P72(f95(f32(a91,f118(x15711,x15713,x15712)),x15711))
% 2.58/2.54 [1600]P72(f95(x16001,f20(a91,x16002,x16003)))+~P72(f95(x16001,f4(a91)))+P72(f95(f32(a91,f118(x16003,x16002,x16001)),x16003))
% 2.58/2.54 [1616]E(x16161,f4(a90))+~P72(f95(f31(a90,x16162),f4(a90)))+~P72(f95(f31(a90,f19(a90,x16161)),f95(f95(f24(a90),x16162),f19(a90,x16163))))
% 2.58/2.54 [1697]~P72(f95(f31(a91,x16973),x16972))+P72(f95(f31(a91,f20(a91,x16971,x16972)),f20(a91,x16971,x16973)))+~P72(f95(f32(a91,f4(a91)),x16973))
% 2.58/2.54 [1698]~P72(f95(f31(a92,x16981),x16983))+P72(f95(f31(a92,f20(a92,x16981,x16982)),f20(a92,x16983,x16982)))+~P72(f95(f32(a92,f4(a92)),x16982))
% 2.58/2.54 [1944]~P35(x19441)+~P4(x19441,x19442)+P4(x19441,f9(a91,x19441,a91,x19442,f10(a91,a91,a91,f25(a91),x19443)))
% 2.58/2.54 [1958]~P35(x19581)+P4(x19581,x19582)+~P4(x19581,f9(a91,x19581,a91,x19582,f10(a91,a91,a91,f25(a91),x19583)))
% 2.58/2.54 [998]~P13(x9982)+E(x9981,f4(x9982))+E(f20(x9982,f95(f95(f24(x9982),x9983),x9981),x9981),x9983)
% 2.58/2.54 [999]~P13(x9992)+E(x9991,f4(x9992))+E(f20(x9992,f95(f95(f24(x9992),x9991),x9993),x9991),x9993)
% 2.58/2.54 [1280]~P47(x12801)+E(f19(x12801,f95(f95(f24(x12801),x12802),x12803)),f95(f95(f24(x12801),f19(x12801,x12802)),x12803))+~P72(f95(f31(x12801,f4(x12801)),x12803))
% 2.58/2.54 [1323]E(f28(f95(f95(f24(a91),x13231),x13232),x13233),f28(x13231,f28(x13232,x13233)))+~P72(f95(f32(a91,f4(a91)),x13232))+~P72(f95(f32(a91,f4(a91)),x13231))
% 2.58/2.54 [1336]~P38(x13362)+E(x13361,f4(a91))+E(f95(f95(f24(x13362),x13363),f95(f95(f33(x13362),x13363),f23(a91,x13361,f5(a91)))),f95(f95(f33(x13362),x13363),x13361))
% 2.58/2.54 [1339]~P13(x13392)+E(x13391,f4(x13392))+E(f20(x13392,f95(f95(f25(x13392),x13393),x13391),x13391),f95(f95(f25(x13392),f20(x13392,x13393,x13391)),f5(x13392)))
% 2.58/2.54 [1340]~P13(x13402)+E(x13401,f4(x13402))+E(f20(x13402,f95(f95(f25(x13402),x13401),x13403),x13401),f95(f95(f25(x13402),f20(x13402,x13403,x13401)),f5(x13402)))
% 2.58/2.54 [1369]~P57(x13691)+~P72(f95(f31(x13691,f4(x13691)),x13692))+P72(f95(f31(x13691,f4(x13691)),f95(f95(f33(x13691),x13692),x13693)))
% 2.58/2.54 [1371]~P57(x13711)+~P72(f95(f31(x13711,f5(x13711)),x13712))+P72(f95(f31(x13711,f5(x13711)),f95(f95(f33(x13711),x13712),x13713)))
% 2.58/2.54 [1372]~P57(x13721)+~P72(f95(f32(x13721,f4(x13721)),x13722))+P72(f95(f32(x13721,f4(x13721)),f95(f95(f33(x13721),x13722),x13723)))
% 2.58/2.54 [1467]~P51(x14672)+E(x14671,f4(x14672))+~E(f95(f95(f25(x14672),f95(f95(f24(x14672),x14673),x14673)),f95(f95(f24(x14672),x14671),x14671)),f4(x14672))
% 2.58/2.54 [1468]~P51(x14682)+E(x14681,f4(x14682))+~E(f95(f95(f25(x14682),f95(f95(f24(x14682),x14681),x14681)),f95(f95(f24(x14682),x14683),x14683)),f4(x14682))
% 2.58/2.54 [1546]~P72(f95(f32(a91,x15461),x15463))+~P72(f95(f32(a91,x15463),x15462))+P72(f95(f32(a91,f95(f95(f25(a91),x15461),f5(a91))),x15462))
% 2.58/2.54 [1646]~E(x16463,f20(a91,x16461,x16462))+~P72(f95(f32(a91,f4(a91)),x16462))+P72(f95(f32(a91,x16461),f95(f95(f24(a91),x16462),f95(f95(f25(a91),x16463),f5(a91)))))
% 2.58/2.54 [1648]~P57(x16481)+~P72(f95(f32(x16481,f5(x16481)),x16482))+P72(f95(f32(x16481,f5(x16481)),f95(f95(f33(x16481),x16482),f95(f95(f25(a91),x16483),f5(a91)))))
% 2.58/2.54 [1651]~P72(f95(f31(a90,x16512),x16513))+~P72(f95(f32(a90,f4(a90)),x16511))+P72(f95(f31(a90,f95(f95(f24(a90),x16511),x16512)),f95(f95(f24(a90),x16511),x16513)))
% 2.58/2.54 [1652]~P72(f95(f31(a90,x16521),x16523))+~P72(f95(f32(a90,f4(a90)),x16522))+P72(f95(f31(a90,f95(f95(f24(a90),x16521),x16522)),f95(f95(f24(a90),x16523),x16522)))
% 2.58/2.54 [1654]~P72(f95(f32(a90,x16541),x16543))+~P72(f95(f32(a90,f4(a90)),x16542))+P72(f95(f32(a90,f95(f95(f24(a90),x16541),x16542)),f95(f95(f24(a90),x16543),x16542)))
% 2.58/2.54 [1655]~P72(f95(f32(a90,x16552),x16553))+~P72(f95(f32(a90,f4(a90)),x16551))+P72(f95(f32(a90,f95(f95(f24(a90),x16551),x16552)),f95(f95(f24(a90),x16551),x16553)))
% 2.58/2.54 [1659]~P72(f95(f32(a91,x16591),x16593))+~P72(f95(f32(a91,f4(a91)),x16592))+P72(f95(f32(a91,f95(f95(f24(a91),x16591),x16592)),f95(f95(f24(a91),x16593),x16592)))
% 2.58/2.54 [1660]~P72(f95(f32(a91,x16602),x16603))+~P72(f95(f32(a91,f4(a91)),x16601))+P72(f95(f32(a91,f95(f95(f24(a91),x16601),x16602)),f95(f95(f24(a91),x16601),x16603)))
% 2.58/2.54 [1661]~P72(f95(f32(a92,x16612),x16613))+~P72(f95(f32(a92,f4(a92)),x16611))+P72(f95(f32(a92,f95(f95(f24(a92),x16611),x16612)),f95(f95(f24(a92),x16611),x16613)))
% 2.58/2.54 [1785]P72(f95(f31(a90,x17851),x17852))+~P72(f95(f32(a90,f4(a90)),x17853))+~P72(f95(f31(a90,f95(f95(f24(a90),x17853),x17851)),f95(f95(f24(a90),x17853),x17852)))
% 2.58/2.54 [1786]P72(f95(f31(a90,x17861),x17862))+~P72(f95(f32(a90,f4(a90)),x17863))+~P72(f95(f31(a90,f95(f95(f24(a90),x17861),x17863)),f95(f95(f24(a90),x17862),x17863)))
% 2.58/2.54 [1788]P72(f95(f31(a91,x17881),x17882))+~P72(f95(f32(a91,f4(a91)),x17883))+~P72(f95(f31(a91,f95(f95(f24(a91),x17883),x17881)),f95(f95(f24(a91),x17883),x17882)))
% 2.58/2.54 [1789]P72(f95(f31(a91,x17891),x17892))+~P72(f95(f32(a91,f4(a91)),x17893))+~P72(f95(f31(a91,f95(f95(f24(a91),x17891),x17893)),f95(f95(f24(a91),x17892),x17893)))
% 2.58/2.54 [1790]P72(f95(f32(a90,x17901),x17902))+~P72(f95(f32(a90,f4(a90)),x17903))+~P72(f95(f32(a90,f95(f95(f24(a90),x17901),x17903)),f95(f95(f24(a90),x17902),x17903)))
% 2.58/2.54 [1792]P72(f95(f32(a91,x17921),x17922))+~P72(f95(f32(a91,f4(a91)),x17923))+~P72(f95(f32(a91,f95(f95(f33(a91),x17923),x17921)),f95(f95(f33(a91),x17923),x17922)))
% 2.58/2.54 [1799]~P35(x17991)+~P4(x17991,x17992)+P72(f95(f31(a90,f37(x17991,f95(x17992,x17993))),f36(a91,f95(f95(f25(a91),f86(x17992,x17991)),f5(a91)))))
% 2.58/2.54 [1800]~P35(x18001)+~P4(x18001,x18002)+P72(f95(f32(a90,f37(x18001,f95(x18002,x18003))),f36(a91,f95(f95(f25(a91),f87(x18002,x18001)),f5(a91)))))
% 2.58/2.54 [1868]E(x18681,f4(a91))+~P72(f95(x18683,f20(a91,x18682,x18681)))+P72(f95(f31(a91,f95(f95(f24(a91),x18681),f115(x18681,x18682,x18683))),x18682))
% 2.58/2.54 [1869]~P72(f95(x18691,f20(a91,x18693,x18692)))+P72(f95(x18691,f4(a91)))+P72(f95(f31(a91,f95(f95(f24(a91),x18692),f115(x18692,x18693,x18691))),x18693))
% 2.58/2.54 [1902]E(x19021,f4(a91))+~P72(f95(x19023,f20(a91,x19022,x19021)))+P72(f95(f32(a91,x19022),f95(f95(f24(a91),x19021),f95(f95(f25(a91),f115(x19021,x19022,x19023)),f5(a91)))))
% 2.58/2.54 [1904]~P72(f95(x19041,f20(a91,x19042,x19043)))+P72(f95(x19041,f4(a91)))+P72(f95(f32(a91,x19042),f95(f95(f24(a91),x19043),f95(f95(f25(a91),f115(x19043,x19042,x19041)),f5(a91)))))
% 2.58/2.54 [1926]~P35(x19261)+P4(x19261,x19262)+~P72(f95(f31(a90,f37(x19261,f95(x19262,f88(x19262,x19261,x19263)))),f36(a91,f95(f95(f25(a91),x19263),f5(a91)))))
% 2.58/2.54 [1927]~P35(x19271)+P4(x19271,x19272)+~P72(f95(f32(a90,f37(x19271,f95(x19272,f89(x19272,x19271,x19273)))),f36(a91,f95(f95(f25(a91),x19273),f5(a91)))))
% 2.58/2.54 [1928]~P35(x19282)+P72(f95(f32(a90,f4(a90)),f73(x19281,x19282)))+~P72(f95(f31(a90,f37(x19282,f95(x19281,f74(x19281,x19282,x19283)))),f36(a91,f95(f95(f25(a91),x19283),f5(a91)))))
% 2.58/2.54 [1929]~P35(x19292)+P72(f95(f32(a90,f4(a90)),f75(x19291,x19292)))+~P72(f95(f32(a90,f37(x19292,f95(x19291,f76(x19291,x19292,x19293)))),f36(a91,f95(f95(f25(a91),x19293),f5(a91)))))
% 2.58/2.54 [1527]~E(x15272,f20(a91,x15273,x15271))+~P72(f95(f32(a91,f4(a91)),x15271))+P72(f95(f31(a91,f95(f95(f24(a91),x15271),x15272)),x15273))
% 2.58/2.54 [1675]~P22(x16751)+E(f95(f95(f24(x16751),f95(f95(f33(x16751),x16752),f23(a91,x16753,f5(a91)))),x16752),f95(f95(f33(x16751),x16752),x16753))+~P72(f95(f32(a91,f4(a91)),x16753))
% 2.58/2.54 [1676]~P57(x16761)+~P72(f95(f32(x16761,f5(x16761)),x16762))+P72(f95(f32(x16761,f5(x16761)),f95(f95(f24(x16761),x16762),f95(f95(f33(x16761),x16762),x16763))))
% 2.58/2.54 [1740]~P72(f95(f31(a91,x17402),x17403))+~P72(f95(f31(a91,x17401),f23(a91,x17403,x17402)))+P72(f95(f31(a91,f95(f95(f25(a91),x17401),x17402)),x17403))
% 2.58/2.54 [1760]~P72(f95(f31(a91,x17603),x17602))+P72(f95(f31(a91,x17601),f23(a91,x17602,x17603)))+~P72(f95(f31(a91,f95(f95(f25(a91),x17601),x17603)),x17602))
% 2.58/2.54 [1805]~P57(x18051)+~P72(f95(f32(x18051,f5(x18051)),x18052))+P72(f95(f32(x18051,f95(f95(f33(x18051),x18052),x18053)),f95(f95(f24(x18051),x18052),f95(f95(f33(x18051),x18052),x18053))))
% 2.58/2.54 [1858]~P51(x18582)+E(x18581,f4(x18582))+P72(f95(f32(x18582,f4(x18582)),f95(f95(f25(x18582),f95(f95(f24(x18582),x18583),x18583)),f95(f95(f24(x18582),x18581),x18581))))
% 2.58/2.54 [1859]~P51(x18592)+E(x18591,f4(x18592))+P72(f95(f32(x18592,f4(x18592)),f95(f95(f25(x18592),f95(f95(f24(x18592),x18591),x18591)),f95(f95(f24(x18592),x18593),x18593))))
% 2.58/2.54 [1758]~P35(x17581)+P4(x17581,x17582)+P72(f95(f31(a91,x17583),f68(x17584,x17582,x17583,x17581)))
% 2.58/2.54 [1009]~P18(x10093)+E(x10091,x10092)+~E(f95(f95(f25(x10093),x10094),x10091),f95(f95(f25(x10093),x10094),x10092))
% 2.58/2.54 [1010]~P19(x10103)+E(x10101,x10102)+~E(f95(f95(f25(x10103),x10104),x10101),f95(f95(f25(x10103),x10104),x10102))
% 2.58/2.54 [1012]~P18(x10123)+E(x10121,x10122)+~E(f95(f95(f25(x10123),x10121),x10124),f95(f95(f25(x10123),x10122),x10124))
% 2.58/2.54 [1218]~E(f95(f95(f25(a91),x12183),x12182),f95(f95(f25(a91),x12181),x12184))+~P72(f95(f32(a91,x12183),x12184))+P72(f95(f32(a91,x12181),x12182))
% 2.58/2.54 [1366]P72(f95(x13661,x13662))+~E(x13663,f95(f95(f25(a91),x13664),x13662))+~P72(f95(x13661,f23(a91,x13663,x13664)))
% 2.58/2.54 [1368]~P7(x13682)+~P72(f95(f32(f123(x13681,x13682),x13683),x13684))+P72(f95(f31(f123(x13681,x13682),x13683),x13684))
% 2.58/2.54 [1476]~P7(x14761)+~P72(f95(f32(f123(x14762,x14761),x14764),x14763))+~P72(f95(f31(f123(x14762,x14761),x14763),x14764))
% 2.58/2.54 [1955]~P7(x19552)+~P72(f95(f31(x19552,f95(x19553,f62(x19554,x19553,x19551,x19552))),f95(x19554,f62(x19554,x19553,x19551,x19552))))+P72(f95(f31(f123(x19551,x19552),x19553),x19554))
% 2.58/2.54 [1160]~P13(x11601)+~E(x11602,f4(x11601))+E(f20(x11601,f95(f95(f24(x11601),x11602),x11603),f95(f95(f24(x11601),x11602),x11604)),f4(x11601))
% 2.58/2.54 [1204]~P13(x12042)+E(x12041,f4(x12042))+E(f20(x12042,f95(f95(f24(x12042),x12043),x12041),f95(f95(f24(x12042),x12044),x12041)),f20(x12042,x12043,x12044))
% 2.58/2.54 [1206]~P13(x12062)+E(x12061,f4(x12062))+E(f20(x12062,f95(f95(f24(x12062),x12061),x12063),f95(f95(f24(x12062),x12061),x12064)),f20(x12062,x12063,x12064))
% 2.58/2.54 [1629]~P27(x16291)+~P72(f95(f31(x16291,x16293),x16294))+P72(f95(f31(x16291,f95(f95(f25(x16291),x16292),x16293)),f95(f95(f25(x16291),x16292),x16294)))
% 2.58/2.54 [1630]~P28(x16301)+~P72(f95(f31(x16301,x16303),x16304))+P72(f95(f31(x16301,f95(f95(f25(x16301),x16302),x16303)),f95(f95(f25(x16301),x16302),x16304)))
% 2.58/2.54 [1631]~P27(x16311)+~P72(f95(f31(x16311,x16312),x16314))+P72(f95(f31(x16311,f95(f95(f25(x16311),x16312),x16313)),f95(f95(f25(x16311),x16314),x16313)))
% 2.58/2.54 [1632]~P28(x16321)+~P72(f95(f31(x16321,x16322),x16324))+P72(f95(f31(x16321,f95(f95(f25(x16321),x16322),x16323)),f95(f95(f25(x16321),x16324),x16323)))
% 2.58/2.54 [1633]~P27(x16331)+~P72(f95(f32(x16331,x16333),x16334))+P72(f95(f32(x16331,f95(f95(f25(x16331),x16332),x16333)),f95(f95(f25(x16331),x16332),x16334)))
% 2.58/2.54 [1634]~P31(x16341)+~P72(f95(f32(x16341,x16343),x16344))+P72(f95(f32(x16341,f95(f95(f25(x16341),x16342),x16343)),f95(f95(f25(x16341),x16342),x16344)))
% 2.58/2.54 [1635]~P27(x16351)+~P72(f95(f32(x16351,x16352),x16354))+P72(f95(f32(x16351,f95(f95(f25(x16351),x16352),x16353)),f95(f95(f25(x16351),x16354),x16353)))
% 2.58/2.54 [1636]~P31(x16361)+~P72(f95(f32(x16361,x16362),x16364))+P72(f95(f32(x16361,f95(f95(f25(x16361),x16362),x16363)),f95(f95(f25(x16361),x16364),x16363)))
% 2.58/2.54 [1640]~P72(f95(f31(a91,x16402),x16404))+~P72(f95(f31(a91,x16401),x16403))+P72(f95(f31(a91,f95(f95(f24(a91),x16401),x16402)),f95(f95(f24(a91),x16403),x16404)))
% 2.58/2.54 [1641]~P72(f95(f31(a91,x16412),x16414))+~P72(f95(f31(a91,x16411),x16413))+P72(f95(f31(a91,f95(f95(f25(a91),x16411),x16412)),f95(f95(f25(a91),x16413),x16414)))
% 2.58/2.54 [1642]~P72(f95(f32(a91,x16422),x16424))+~P72(f95(f32(a91,x16421),x16423))+P72(f95(f32(a91,f95(f95(f25(a91),x16421),x16422)),f95(f95(f25(a91),x16423),x16424)))
% 2.58/2.54 [1643]~P72(f95(f31(a92,x16432),x16434))+~P72(f95(f32(a92,x16431),x16433))+P72(f95(f32(a92,f95(f95(f25(a92),x16431),x16432)),f95(f95(f25(a92),x16433),x16434)))
% 2.58/2.54 [1773]~P22(x17731)+E(f95(f95(f33(x17731),x17732),f23(a91,f95(f95(f25(a91),x17733),f5(a91)),x17734)),f95(f95(f24(x17731),f95(f95(f33(x17731),x17732),f23(a91,x17733,x17734))),x17732))+~P72(f95(f31(a91,x17734),x17733))
% 2.58/2.54 [1778]~P27(x17781)+P72(f95(f31(x17781,x17782),x17783))+~P72(f95(f31(x17781,f95(f95(f25(x17781),x17784),x17782)),f95(f95(f25(x17781),x17784),x17783)))
% 2.58/2.54 [1780]~P27(x17801)+P72(f95(f31(x17801,x17802),x17803))+~P72(f95(f31(x17801,f95(f95(f25(x17801),x17802),x17804)),f95(f95(f25(x17801),x17803),x17804)))
% 2.58/2.54 [1782]~P27(x17821)+P72(f95(f32(x17821,x17822),x17823))+~P72(f95(f32(x17821,f95(f95(f25(x17821),x17824),x17822)),f95(f95(f25(x17821),x17824),x17823)))
% 2.58/2.54 [1784]~P27(x17841)+P72(f95(f32(x17841,x17842),x17843))+~P72(f95(f32(x17841,f95(f95(f25(x17841),x17842),x17844)),f95(f95(f25(x17841),x17843),x17844)))
% 2.58/2.54 [1885]~P47(x18851)+~P72(f95(f32(x18851,f19(x18851,f23(x18851,x18852,x18853))),x18854))+P72(f95(f32(x18851,x18852),f95(f95(f25(x18851),x18853),x18854)))
% 2.58/2.54 [1890]~P47(x18901)+P72(f95(f32(x18901,f23(x18901,x18902,x18903)),x18904))+~P72(f95(f32(x18901,f19(x18901,f23(x18901,x18904,x18902))),x18903))
% 2.58/2.54 [1931]~P35(x19311)+P72(f95(f31(a90,f37(x19311,f95(x19312,x19313))),f73(x19312,x19311)))+~P72(f95(f31(a90,f37(x19311,f95(x19312,f74(x19312,x19311,x19314)))),f36(a91,f95(f95(f25(a91),x19314),f5(a91)))))
% 2.58/2.54 [1932]~P35(x19321)+P72(f95(f31(a90,f37(x19321,f95(x19322,x19323))),f75(x19322,x19321)))+~P72(f95(f32(a90,f37(x19321,f95(x19322,f76(x19322,x19321,x19324)))),f36(a91,f95(f95(f25(a91),x19324),f5(a91)))))
% 2.58/2.54 [1426]~P13(x14262)+E(x14261,f4(x14262))+E(f20(x14262,f95(f95(f25(x14262),x14263),f95(f95(f24(x14262),x14264),x14261)),x14261),f95(f95(f25(x14262),x14264),f20(x14262,x14263,x14261)))
% 2.58/2.54 [1427]~P13(x14272)+E(x14271,f4(x14272))+E(f20(x14272,f95(f95(f25(x14272),x14273),f95(f95(f24(x14272),x14271),x14274)),x14271),f95(f95(f25(x14272),x14274),f20(x14272,x14273,x14271)))
% 2.58/2.54 [1961]~P35(x19611)+P4(x19611,x19612)+~P72(f95(f31(a90,f37(x19611,f95(x19612,f68(x19613,x19612,x19614,x19611)))),x19613))
% 2.58/2.54 [1431]~P7(x14311)+P72(f95(f31(x14311,f95(x14312,x14313)),f95(x14314,x14313)))+~P72(f95(f31(f123(x14315,x14311),x14312),x14314))
% 2.58/2.54 [1556]~E(x15562,x15564)+~P71(x15561)+E(f95(f95(f25(x15561),f95(f95(f24(x15561),x15562),x15563)),f95(f95(f24(x15561),x15564),x15565)),f95(f95(f25(x15561),f95(f95(f24(x15561),x15562),x15565)),f95(f95(f24(x15561),x15564),x15563)))
% 2.58/2.54 [1878]~P72(f95(f31(a91,x18783),x18782))+E(x18781,f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x18782,x18783)),x18784)),x18785))+~E(f95(f95(f25(a91),f95(f95(f24(a91),x18783),x18784)),x18781),f95(f95(f25(a91),f95(f95(f24(a91),x18782),x18784)),x18785))
% 2.58/2.54 [1879]~P72(f95(f31(a91,x18792),x18791))+E(f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x18791,x18792)),x18793)),x18794),x18795)+~E(f95(f95(f25(a91),f95(f95(f24(a91),x18791),x18793)),x18794),f95(f95(f25(a91),f95(f95(f24(a91),x18792),x18793)),x18795))
% 2.58/2.54 [1892]~P72(f95(f31(a91,x18924),x18921))+~E(x18925,f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x18921,x18924)),x18922)),x18923))+E(f95(f95(f25(a91),f95(f95(f24(a91),x18921),x18922)),x18923),f95(f95(f25(a91),f95(f95(f24(a91),x18924),x18922)),x18925))
% 2.58/2.54 [1893]~P72(f95(f31(a91,x18934),x18931))+~E(f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x18931,x18934)),x18932)),x18933),x18935)+E(f95(f95(f25(a91),f95(f95(f24(a91),x18931),x18932)),x18933),f95(f95(f25(a91),f95(f95(f24(a91),x18934),x18932)),x18935))
% 2.58/2.54 [1948]~P72(f95(f31(a91,x19483),x19482))+P72(f95(f31(a91,x19481),f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19482,x19483)),x19484)),x19485)))+~P72(f95(f31(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19483),x19484)),x19481)),f95(f95(f25(a91),f95(f95(f24(a91),x19482),x19484)),x19485)))
% 2.58/2.54 [1949]~P72(f95(f31(a91,x19493),x19492))+P72(f95(f32(a91,x19491),f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19492,x19493)),x19494)),x19495)))+~P72(f95(f32(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19493),x19494)),x19491)),f95(f95(f25(a91),f95(f95(f24(a91),x19492),x19494)),x19495)))
% 2.58/2.54 [1953]~P72(f95(f31(a91,x19531),x19534))+~P72(f95(f31(a91,x19533),f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19534,x19531)),x19532)),x19535)))+P72(f95(f31(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19531),x19532)),x19533)),f95(f95(f25(a91),f95(f95(f24(a91),x19534),x19532)),x19535)))
% 2.58/2.54 [1954]~P72(f95(f31(a91,x19541),x19544))+~P72(f95(f32(a91,x19543),f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19544,x19541)),x19542)),x19545)))+P72(f95(f32(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19541),x19542)),x19543)),f95(f95(f25(a91),f95(f95(f24(a91),x19544),x19542)),x19545)))
% 2.58/2.54 [1959]~P72(f95(f31(a91,x19592),x19591))+~P72(f95(f31(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19591),x19593)),x19594)),f95(f95(f25(a91),f95(f95(f24(a91),x19592),x19593)),x19595)))+P72(f95(f31(a91,f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19591,x19592)),x19593)),x19594)),x19595))
% 2.58/2.54 [1960]~P72(f95(f31(a91,x19602),x19601))+~P72(f95(f32(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19601),x19603)),x19604)),f95(f95(f25(a91),f95(f95(f24(a91),x19602),x19603)),x19605)))+P72(f95(f32(a91,f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19601,x19602)),x19603)),x19604)),x19605))
% 2.58/2.54 [1964]~P72(f95(f31(a91,x19644),x19641))+P72(f95(f31(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19641),x19642)),x19643)),f95(f95(f25(a91),f95(f95(f24(a91),x19644),x19642)),x19645)))+~P72(f95(f31(a91,f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19641,x19644)),x19642)),x19643)),x19645))
% 2.58/2.54 [1965]~P72(f95(f31(a91,x19654),x19651))+P72(f95(f32(a91,f95(f95(f25(a91),f95(f95(f24(a91),x19651),x19652)),x19653)),f95(f95(f25(a91),f95(f95(f24(a91),x19654),x19652)),x19655)))+~P72(f95(f32(a91,f95(f95(f25(a91),f95(f95(f24(a91),f23(a91,x19651,x19654)),x19652)),x19653)),x19655))
% 2.58/2.54 [1883]~P66(x18832)+~E(f95(f95(f25(x18832),f95(f95(f24(x18832),x18834),x18835)),x18831),f95(f95(f25(x18832),f95(f95(f24(x18832),x18833),x18835)),x18836))+E(x18831,f95(f95(f25(x18832),f95(f95(f24(x18832),f23(x18832,x18833,x18834)),x18835)),x18836))
% 2.58/2.54 [1884]~P66(x18841)+~E(f95(f95(f25(x18841),f95(f95(f24(x18841),x18842),x18844)),x18845),f95(f95(f25(x18841),f95(f95(f24(x18841),x18843),x18844)),x18846))+E(f95(f95(f25(x18841),f95(f95(f24(x18841),f23(x18841,x18842,x18843)),x18844)),x18845),x18846)
% 2.58/2.54 [1894]~P66(x18941)+~E(x18946,f95(f95(f25(x18941),f95(f95(f24(x18941),f23(x18941,x18942,x18945)),x18943)),x18944))+E(f95(f95(f25(x18941),f95(f95(f24(x18941),x18942),x18943)),x18944),f95(f95(f25(x18941),f95(f95(f24(x18941),x18945),x18943)),x18946))
% 2.58/2.54 [1895]~P66(x18951)+~E(f95(f95(f25(x18951),f95(f95(f24(x18951),f23(x18951,x18952,x18955)),x18953)),x18954),x18956)+E(f95(f95(f25(x18951),f95(f95(f24(x18951),x18952),x18953)),x18954),f95(f95(f25(x18951),f95(f95(f24(x18951),x18955),x18953)),x18956))
% 2.58/2.54 [1951]~P60(x19511)+~P72(f95(f31(x19511,f95(f95(f25(x19511),f95(f95(f24(x19511),x19514),x19515)),x19512)),f95(f95(f25(x19511),f95(f95(f24(x19511),x19513),x19515)),x19516)))+P72(f95(f31(x19511,x19512),f95(f95(f25(x19511),f95(f95(f24(x19511),f23(x19511,x19513,x19514)),x19515)),x19516)))
% 2.58/2.54 [1952]~P60(x19521)+~P72(f95(f32(x19521,f95(f95(f25(x19521),f95(f95(f24(x19521),x19524),x19525)),x19522)),f95(f95(f25(x19521),f95(f95(f24(x19521),x19523),x19525)),x19526)))+P72(f95(f32(x19521,x19522),f95(f95(f25(x19521),f95(f95(f24(x19521),f23(x19521,x19523,x19524)),x19525)),x19526)))
% 2.58/2.54 [1956]~P60(x19561)+~P72(f95(f31(x19561,x19564),f95(f95(f25(x19561),f95(f95(f24(x19561),f23(x19561,x19565,x19562)),x19563)),x19566)))+P72(f95(f31(x19561,f95(f95(f25(x19561),f95(f95(f24(x19561),x19562),x19563)),x19564)),f95(f95(f25(x19561),f95(f95(f24(x19561),x19565),x19563)),x19566)))
% 2.58/2.54 [1957]~P60(x19571)+~P72(f95(f32(x19571,x19574),f95(f95(f25(x19571),f95(f95(f24(x19571),f23(x19571,x19575,x19572)),x19573)),x19576)))+P72(f95(f32(x19571,f95(f95(f25(x19571),f95(f95(f24(x19571),x19572),x19573)),x19574)),f95(f95(f25(x19571),f95(f95(f24(x19571),x19575),x19573)),x19576)))
% 2.58/2.54 [1962]~P60(x19621)+~P72(f95(f31(x19621,f95(f95(f25(x19621),f95(f95(f24(x19621),x19622),x19624)),x19625)),f95(f95(f25(x19621),f95(f95(f24(x19621),x19623),x19624)),x19626)))+P72(f95(f31(x19621,f95(f95(f25(x19621),f95(f95(f24(x19621),f23(x19621,x19622,x19623)),x19624)),x19625)),x19626))
% 2.58/2.54 [1963]~P60(x19631)+~P72(f95(f32(x19631,f95(f95(f25(x19631),f95(f95(f24(x19631),x19632),x19634)),x19635)),f95(f95(f25(x19631),f95(f95(f24(x19631),x19633),x19634)),x19636)))+P72(f95(f32(x19631,f95(f95(f25(x19631),f95(f95(f24(x19631),f23(x19631,x19632,x19633)),x19634)),x19635)),x19636))
% 2.58/2.54 [1967]~P60(x19671)+P72(f95(f31(x19671,f95(f95(f25(x19671),f95(f95(f24(x19671),x19672),x19673)),x19674)),f95(f95(f25(x19671),f95(f95(f24(x19671),x19675),x19673)),x19676)))+~P72(f95(f31(x19671,f95(f95(f25(x19671),f95(f95(f24(x19671),f23(x19671,x19672,x19675)),x19673)),x19674)),x19676))
% 2.58/2.54 [1968]~P60(x19681)+P72(f95(f32(x19681,f95(f95(f25(x19681),f95(f95(f24(x19681),x19682),x19683)),x19684)),f95(f95(f25(x19681),f95(f95(f24(x19681),x19685),x19683)),x19686)))+~P72(f95(f32(x19681,f95(f95(f25(x19681),f95(f95(f24(x19681),f23(x19681,x19682,x19685)),x19683)),x19684)),x19686))
% 2.58/2.54 [1111]E(x11111,f4(a92))+~E(f20(a92,x11112,x11111),f4(a92))+P72(f95(f32(a92,x11111),x11112))+P72(f95(f32(a92,x11112),x11111))
% 2.58/2.54 [1117]E(x11171,f4(a92))+~E(f20(a92,x11172,x11171),f4(a92))+P72(f95(f32(a92,x11172),x11171))+P72(f95(f31(a92,x11172),f4(a92)))
% 2.58/2.54 [896]~P38(x8962)+~P69(x8962)+E(x8961,f4(a91))+E(f95(f95(f33(x8962),f4(x8962)),x8961),f4(x8962))
% 2.58/2.54 [1063]~E(x10632,f5(a92))+~E(x10631,f5(a92))+E(f95(f95(f24(a92),x10631),x10632),f5(a92))+~P72(f95(f32(a92,f4(a92)),x10631))
% 2.58/2.54 [1127]E(x11271,f4(a92))+~E(f20(a92,x11272,x11271),f4(a92))+P72(f95(f32(a92,x11271),x11272))+P72(f95(f31(a92,f4(a92)),x11272))
% 2.58/2.54 [1172]E(x11721,x11722)+~E(f35(x11721),f35(x11722))+~P72(f95(f32(a90,f4(a90)),x11721))+~P72(f95(f32(a90,f4(a90)),x11722))
% 2.58/2.54 [1397]~P72(f95(f31(a90,x13971),x13972))+P72(f95(f31(a90,f35(x13971)),f35(x13972)))+~P72(f95(f32(a90,f4(a90)),x13972))+~P72(f95(f32(a90,f4(a90)),x13971))
% 2.58/2.54 [1398]~P72(f95(f32(a90,x13981),x13982))+P72(f95(f32(a90,f35(x13981)),f35(x13982)))+~P72(f95(f32(a90,f4(a90)),x13982))+~P72(f95(f32(a90,f4(a90)),x13981))
% 2.58/2.54 [1420]~P72(f95(f31(a90,f35(x14201)),f35(x14202)))+P72(f95(f31(a90,x14201),x14202))+~P72(f95(f32(a90,f4(a90)),x14202))+~P72(f95(f32(a90,f4(a90)),x14201))
% 2.58/2.54 [1421]~P72(f95(f32(a90,f35(x14211)),f35(x14212)))+P72(f95(f32(a90,x14211),x14212))+~P72(f95(f32(a90,f4(a90)),x14212))+~P72(f95(f32(a90,f4(a90)),x14211))
% 2.58/2.54 [1018]~P47(x10183)+E(x10181,x10182)+P72(f95(f32(x10183,x10181),x10182))+P72(f95(f32(x10183,x10182),x10181))
% 2.58/2.54 [1019]~P8(x10193)+E(x10191,x10192)+P72(f95(f32(x10193,x10191),x10192))+P72(f95(f32(x10193,x10192),x10191))
% 2.58/2.54 [1023]~E(x10232,x10233)+~P8(x10231)+P72(f95(f32(x10231,x10232),x10233))+P72(f95(f31(x10231,x10232),x10233))
% 2.58/2.54 [1082]~P34(x10823)+E(x10821,x10822)+~P72(f95(f31(x10823,x10822),x10821))+P72(f95(f32(x10823,x10822),x10821))
% 2.58/2.54 [1084]~P8(x10843)+E(x10841,x10842)+~P72(f95(f31(x10843,x10841),x10842))+P72(f95(f32(x10843,x10841),x10842))
% 2.58/2.54 [1090]~P34(x10903)+E(x10901,x10902)+~P72(f95(f31(x10903,x10901),x10902))+P72(f95(f32(x10903,x10901),x10902))
% 2.58/2.54 [1144]E(x11441,x11442)+~P34(x11443)+~P72(f95(f31(x11443,x11442),x11441))+~P72(f95(f31(x11443,x11441),x11442))
% 2.58/2.54 [1178]~P6(x11781)+P72(f95(f32(x11781,x11783),x11782))+~P72(f95(f31(x11781,x11783),x11782))+P72(f95(f31(x11781,x11782),x11783))
% 2.58/2.54 [1212]~P72(f95(x12121,x12122))+~P72(f95(x12121,x12123))+~P72(f95(f31(a91,x12123),f104(x12122,x12121)))+P72(f95(x12121,f4(a91)))
% 2.58/2.54 [1290]E(x12901,x12902)+~E(f23(a91,x12901,x12903),f23(a91,x12902,x12903))+~P72(f95(f31(a91,x12903),x12901))+~P72(f95(f31(a91,x12903),x12902))
% 2.58/2.54 [1342]P73(x13422,x13421,x13423)+E(x13421,f4(a92))+P72(f95(f31(a92,f4(a92)),f113(x13423,x13421,x13422)))+P72(f95(f32(a92,x13421),f4(a92)))
% 2.58/2.54 [1381]P73(x13811,x13812,x13813)+P72(f95(f31(a92,f4(a92)),f113(x13813,x13812,x13811)))+~P72(f95(x13811,f4(a92)))+P72(f95(f32(a92,x13812),f4(a92)))
% 2.58/2.54 [1413]P73(x14132,x14131,x14133)+E(x14131,f4(a92))+~P72(f95(x14132,f114(x14133,x14131,x14132)))+P72(f95(f32(a92,x14131),f4(a92)))
% 2.58/2.54 [1459]P73(x14591,x14592,x14593)+~P72(f95(x14591,f114(x14593,x14592,x14591)))+~P72(f95(x14591,f4(a92)))+P72(f95(f32(a92,x14592),f4(a92)))
% 2.58/2.54 [1510]P73(x15102,x15101,x15103)+E(x15101,f4(a92))+P72(f95(f31(a92,f4(a92)),f113(x15103,x15101,x15102)))+P72(f95(f32(a92,x15101),f112(x15103,x15101,x15102)))
% 2.58/2.54 [1547]P73(x15471,x15472,x15473)+P72(f95(f31(a92,f4(a92)),f113(x15473,x15472,x15471)))+P72(f95(f32(a92,x15472),f112(x15473,x15472,x15471)))+~P72(f95(x15471,f4(a92)))
% 2.58/2.54 [1557]P73(x15572,x15571,x15573)+E(x15571,f4(a92))+~P72(f95(x15572,f114(x15573,x15571,x15572)))+P72(f95(f32(a92,x15571),f112(x15573,x15571,x15572)))
% 2.58/2.54 [1570]P73(x15702,x15701,x15703)+E(x15701,f4(a92))+P72(f95(f31(a92,f4(a92)),f113(x15703,x15701,x15702)))+~P72(f95(x15702,f119(x15703,x15701,x15702)))
% 2.58/2.54 [1596]P73(x15961,x15962,x15963)+~P72(f95(x15961,f114(x15963,x15962,x15961)))+P72(f95(f32(a92,x15962),f112(x15963,x15962,x15961)))+~P72(f95(x15961,f4(a92)))
% 2.58/2.54 [1598]P73(x15981,x15982,x15983)+P72(f95(f31(a92,f4(a92)),f113(x15983,x15982,x15981)))+~P72(f95(x15981,f119(x15983,x15982,x15981)))+~P72(f95(x15981,f4(a92)))
% 2.58/2.54 [1607]~P32(x16071)+~P72(f95(f31(x16071,x16073),f4(x16071)))+~P72(f95(f31(x16071,x16072),f4(x16071)))+P72(f95(f31(x16071,f95(f95(f25(x16071),x16072),x16073)),f4(x16071)))
% 2.58/2.54 [1608]~P32(x16081)+~P72(f95(f31(x16081,x16083),f4(x16081)))+~P72(f95(f32(x16081,x16082),f4(x16081)))+P72(f95(f32(x16081,f95(f95(f25(x16081),x16082),x16083)),f4(x16081)))
% 2.58/2.54 [1609]~P32(x16091)+~P72(f95(f31(x16091,x16092),f4(x16091)))+~P72(f95(f32(x16091,x16093),f4(x16091)))+P72(f95(f32(x16091,f95(f95(f25(x16091),x16092),x16093)),f4(x16091)))
% 2.58/2.54 [1610]~P32(x16101)+~P72(f95(f32(x16101,x16103),f4(x16101)))+~P72(f95(f32(x16101,x16102),f4(x16101)))+P72(f95(f32(x16101,f95(f95(f25(x16101),x16102),x16103)),f4(x16101)))
% 2.58/2.54 [1617]P73(x16172,x16171,x16173)+E(x16171,f4(a92))+~P72(f95(x16172,f114(x16173,x16171,x16172)))+~P72(f95(x16172,f119(x16173,x16171,x16172)))
% 2.58/2.54 [1647]P73(x16472,x16471,x16473)+E(x16471,f4(a92))+P72(f95(f31(a92,f4(a92)),f113(x16473,x16471,x16472)))+P72(f95(f31(a92,f112(x16473,x16471,x16472)),f4(a92)))
% 2.58/2.54 [1662]P73(x16621,x16622,x16623)+~P72(f95(x16621,f114(x16623,x16622,x16621)))+~P72(f95(x16621,f119(x16623,x16622,x16621)))+~P72(f95(x16621,f4(a92)))
% 2.58/2.54 [1677]P73(x16773,x16771,x16772)+E(x16771,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x16771),f114(x16772,x16771,x16773))),f113(x16772,x16771,x16773)),x16772)+P72(f95(f32(a92,x16771),f4(a92)))
% 2.58/2.54 [1686]P73(x16861,x16862,x16863)+P72(f95(f31(a92,f4(a92)),f113(x16863,x16862,x16861)))+~P72(f95(x16861,f4(a92)))+P72(f95(f31(a92,f112(x16863,x16862,x16861)),f4(a92)))
% 2.58/2.54 [1695]P73(x16952,x16951,x16953)+E(x16951,f4(a92))+~P72(f95(x16952,f114(x16953,x16951,x16952)))+P72(f95(f31(a92,f112(x16953,x16951,x16952)),f4(a92)))
% 2.58/2.54 [1696]P73(x16963,x16961,x16962)+E(f95(f95(f25(a92),f95(f95(f24(a92),x16961),f114(x16962,x16961,x16963))),f113(x16962,x16961,x16963)),x16962)+~P72(f95(x16963,f4(a92)))+P72(f95(f32(a92,x16961),f4(a92)))
% 2.58/2.54 [1717]~P51(x17171)+~P72(f95(f31(x17171,f95(f95(f24(x17171),x17173),x17172)),f4(x17171)))+P72(f95(f31(x17171,x17172),f4(x17171)))+P72(f95(f31(x17171,x17173),f4(x17171)))
% 2.58/2.54 [1743]P73(x17431,x17432,x17433)+~P72(f95(x17431,f114(x17433,x17432,x17431)))+~P72(f95(x17431,f4(a92)))+P72(f95(f31(a92,f112(x17433,x17432,x17431)),f4(a92)))
% 2.58/2.54 [1765]P73(x17653,x17651,x17652)+E(x17651,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x17651),f114(x17652,x17651,x17653))),f113(x17652,x17651,x17653)),x17652)+P72(f95(f32(a92,x17651),f112(x17652,x17651,x17653)))
% 2.58/2.54 [1766]P73(x17663,x17661,x17662)+E(x17661,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x17661),f119(x17662,x17661,x17663))),f112(x17662,x17661,x17663)),x17662)+P72(f95(f31(a92,f4(a92)),f113(x17662,x17661,x17663)))
% 2.58/2.54 [1775]P73(x17753,x17751,x17752)+E(f95(f95(f25(a92),f95(f95(f24(a92),x17751),f114(x17752,x17751,x17753))),f113(x17752,x17751,x17753)),x17752)+P72(f95(f32(a92,x17751),f112(x17752,x17751,x17753)))+~P72(f95(x17753,f4(a92)))
% 2.58/2.54 [1776]P73(x17763,x17761,x17762)+E(f95(f95(f25(a92),f95(f95(f24(a92),x17761),f119(x17762,x17761,x17763))),f112(x17762,x17761,x17763)),x17762)+P72(f95(f31(a92,f4(a92)),f113(x17762,x17761,x17763)))+~P72(f95(x17763,f4(a92)))
% 2.58/2.54 [1794]P73(x17943,x17941,x17942)+E(x17941,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x17941),f114(x17942,x17941,x17943))),f113(x17942,x17941,x17943)),x17942)+~P72(f95(x17943,f119(x17942,x17941,x17943)))
% 2.58/2.54 [1795]P73(x17953,x17951,x17952)+E(x17951,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x17951),f119(x17952,x17951,x17953))),f112(x17952,x17951,x17953)),x17952)+~P72(f95(x17953,f114(x17952,x17951,x17953)))
% 2.58/2.54 [1797]P73(x17973,x17971,x17972)+E(f95(f95(f25(a92),f95(f95(f24(a92),x17971),f114(x17972,x17971,x17973))),f113(x17972,x17971,x17973)),x17972)+~P72(f95(x17973,f119(x17972,x17971,x17973)))+~P72(f95(x17973,f4(a92)))
% 2.58/2.54 [1798]P73(x17983,x17981,x17982)+E(f95(f95(f25(a92),f95(f95(f24(a92),x17981),f119(x17982,x17981,x17983))),f112(x17982,x17981,x17983)),x17982)+~P72(f95(x17983,f114(x17982,x17981,x17983)))+~P72(f95(x17983,f4(a92)))
% 2.58/2.54 [1818]P73(x18183,x18181,x18182)+E(x18181,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x18181),f114(x18182,x18181,x18183))),f113(x18182,x18181,x18183)),x18182)+P72(f95(f31(a92,f112(x18182,x18181,x18183)),f4(a92)))
% 2.58/2.54 [1836]P73(x18363,x18361,x18362)+E(f95(f95(f25(a92),f95(f95(f24(a92),x18361),f114(x18362,x18361,x18363))),f113(x18362,x18361,x18363)),x18362)+~P72(f95(x18363,f4(a92)))+P72(f95(f31(a92,f112(x18362,x18361,x18363)),f4(a92)))
% 2.58/2.54 [1842]~P72(f95(f31(a91,x18423),x18421))+P72(f95(f31(a91,x18421),x18422))+~P72(f95(f31(a91,x18423),x18422))+~P72(f95(f31(a91,f23(a91,x18421,x18423)),f23(a91,x18422,x18423)))
% 2.58/2.54 [1843]~P72(f95(f31(a91,x18433),x18431))+P72(f95(f32(a91,x18431),x18432))+~P72(f95(f31(a91,x18433),x18432))+~P72(f95(f32(a91,f23(a91,x18431,x18433)),f23(a91,x18432,x18433)))
% 2.58/2.54 [1861]P73(x18613,x18611,x18612)+E(x18611,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x18611),f119(x18612,x18611,x18613))),f112(x18612,x18611,x18613)),x18612)+E(f95(f95(f25(a92),f95(f95(f24(a92),x18611),f114(x18612,x18611,x18613))),f113(x18612,x18611,x18613)),x18612)
% 2.58/2.54 [1866]P73(x18663,x18661,x18662)+E(f95(f95(f25(a92),f95(f95(f24(a92),x18661),f119(x18662,x18661,x18663))),f112(x18662,x18661,x18663)),x18662)+E(f95(f95(f25(a92),f95(f95(f24(a92),x18661),f114(x18662,x18661,x18663))),f113(x18662,x18661,x18663)),x18662)+~P72(f95(x18663,f4(a92)))
% 2.58/2.54 [1906]~P51(x19061)+~E(x19063,f4(x19061))+~E(x19062,f4(x19061))+P72(f95(f31(x19061,f95(f95(f25(x19061),f95(f95(f24(x19061),x19062),x19062)),f95(f95(f24(x19061),x19063),x19063))),f4(x19061)))
% 2.58/2.54 [920]~P53(x9202)+E(x9201,f4(x9202))+E(x9203,f4(x9202))+~E(f95(f95(f24(x9202),x9203),x9201),f4(x9202))
% 2.58/2.54 [921]~P64(x9212)+E(x9211,f4(x9212))+E(x9213,f4(x9212))+~E(f95(f95(f24(x9212),x9213),x9211),f4(x9212))
% 2.58/2.54 [1165]P73(x11651,x11652,x11653)+~P72(f95(x11651,f4(a92)))+P72(f95(f32(a92,x11652),f4(a92)))+P72(f95(f32(a92,f4(a92)),x11652))
% 2.58/2.54 [1237]E(f28(x12371,x12372),x12373)+~E(f95(f95(f33(a90),x12373),x12371),x12372)+~P72(f95(f32(a91,f4(a91)),x12371))+~P72(f95(f31(a90,f4(a90)),x12373))
% 2.58/2.54 [1335]P73(x13352,x13351,x13353)+E(x13351,f4(a92))+P72(f95(f32(a92,x13351),f112(x13353,x13351,x13352)))+P72(f95(f32(a92,f4(a92)),x13351))
% 2.58/2.54 [1374]P73(x13741,x13742,x13743)+P72(f95(f32(a92,x13742),f112(x13743,x13742,x13741)))+~P72(f95(x13741,f4(a92)))+P72(f95(f32(a92,f4(a92)),x13742))
% 2.58/2.54 [1419]P73(x14192,x14191,x14193)+E(x14191,f4(a92))+~P72(f95(x14192,f119(x14193,x14191,x14192)))+P72(f95(f32(a92,f4(a92)),x14191))
% 2.58/2.54 [1469]P73(x14691,x14692,x14693)+~P72(f95(x14691,f119(x14693,x14692,x14691)))+~P72(f95(x14691,f4(a92)))+P72(f95(f32(a92,f4(a92)),x14692))
% 2.58/2.54 [1500]~P72(f95(f32(a91,x15003),x15001))+P72(f95(f31(a90,f28(x15001,x15002)),f28(x15003,x15002)))+~P72(f95(f32(a91,f4(a91)),x15003))+~P72(f95(f31(a90,f5(a90)),x15002))
% 2.58/2.54 [1501]~P72(f95(f32(a91,x15013),x15011))+P72(f95(f32(a90,f28(x15011,x15012)),f28(x15013,x15012)))+~P72(f95(f32(a91,f4(a91)),x15013))+~P72(f95(f32(a90,f5(a90)),x15012))
% 2.58/2.54 [1507]P73(x15072,x15071,x15073)+E(x15071,f4(a92))+P72(f95(f32(a92,x15071),f4(a92)))+P72(f95(f32(a92,f113(x15073,x15071,x15072)),x15071))
% 2.58/2.54 [1521]P73(x15212,x15211,x15213)+E(x15211,f4(a92))+P72(f95(f31(a92,f112(x15213,x15211,x15212)),f4(a92)))+P72(f95(f32(a92,f4(a92)),x15211))
% 2.58/2.54 [1545]P73(x15451,x15452,x15453)+~P72(f95(x15451,f4(a92)))+P72(f95(f32(a92,x15452),f4(a92)))+P72(f95(f32(a92,f113(x15453,x15452,x15451)),x15452))
% 2.58/2.54 [1550]P73(x15501,x15502,x15503)+~P72(f95(x15501,f4(a92)))+P72(f95(f31(a92,f112(x15503,x15502,x15501)),f4(a92)))+P72(f95(f32(a92,f4(a92)),x15502))
% 2.58/2.54 [1619]~P51(x16191)+~P72(f95(f31(x16191,x16193),f4(x16191)))+P72(f95(f31(x16191,f95(f95(f24(x16191),x16192),x16193)),f4(x16191)))+~P72(f95(f31(x16191,f4(x16191)),x16192))
% 2.58/2.54 [1620]~P51(x16201)+~P72(f95(f31(x16201,x16202),f4(x16201)))+P72(f95(f31(x16201,f95(f95(f24(x16201),x16202),x16203)),f4(x16201)))+~P72(f95(f31(x16201,f4(x16201)),x16203))
% 2.58/2.54 [1622]~P52(x16221)+~P72(f95(f31(x16221,x16223),f4(x16221)))+P72(f95(f31(x16221,f95(f95(f24(x16221),x16222),x16223)),f4(x16221)))+~P72(f95(f31(x16221,f4(x16221)),x16222))
% 2.58/2.54 [1624]~P52(x16241)+~P72(f95(f31(x16241,x16242),f4(x16241)))+P72(f95(f31(x16241,f95(f95(f24(x16241),x16242),x16243)),f4(x16241)))+~P72(f95(f31(x16241,f4(x16241)),x16243))
% 2.58/2.54 [1626]~P55(x16261)+~P72(f95(f32(x16261,x16263),f4(x16261)))+P72(f95(f32(x16261,f95(f95(f24(x16261),x16262),x16263)),f4(x16261)))+~P72(f95(f32(x16261,f4(x16261)),x16262))
% 2.58/2.54 [1627]~P55(x16271)+~P72(f95(f32(x16271,x16272),f4(x16271)))+P72(f95(f32(x16271,f95(f95(f24(x16271),x16272),x16273)),f4(x16271)))+~P72(f95(f32(x16271,f4(x16271)),x16273))
% 2.58/2.54 [1638]P73(x16382,x16381,x16383)+E(x16381,f4(a92))+P72(f95(f32(a92,x16381),f112(x16383,x16381,x16382)))+P72(f95(f32(a92,f113(x16383,x16381,x16382)),x16381))
% 2.58/2.54 [1678]P73(x16781,x16782,x16783)+P72(f95(f32(a92,x16782),f112(x16783,x16782,x16781)))+~P72(f95(x16781,f4(a92)))+P72(f95(f32(a92,f113(x16783,x16782,x16781)),x16782))
% 2.58/2.54 [1679]P73(x16793,x16791,x16792)+E(x16791,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x16791),f119(x16792,x16791,x16793))),f112(x16792,x16791,x16793)),x16792)+P72(f95(f32(a92,f4(a92)),x16791))
% 2.58/2.54 [1693]P73(x16932,x16931,x16933)+E(x16931,f4(a92))+~P72(f95(x16932,f119(x16933,x16931,x16932)))+P72(f95(f32(a92,f113(x16933,x16931,x16932)),x16931))
% 2.58/2.54 [1703]P73(x17033,x17031,x17032)+E(f95(f95(f25(a92),f95(f95(f24(a92),x17031),f119(x17032,x17031,x17033))),f112(x17032,x17031,x17033)),x17032)+~P72(f95(x17033,f4(a92)))+P72(f95(f32(a92,f4(a92)),x17031))
% 2.58/2.54 [1726]P73(x17261,x17262,x17263)+~P72(f95(x17261,f119(x17263,x17262,x17261)))+~P72(f95(x17261,f4(a92)))+P72(f95(f32(a92,f113(x17263,x17262,x17261)),x17262))
% 2.58/2.54 [1727]~P51(x17271)+~P72(f95(f31(x17271,f95(f95(f24(x17271),x17273),x17272)),f4(x17271)))+P72(f95(f31(x17271,x17272),f4(x17271)))+P72(f95(f31(x17271,f4(x17271)),x17272))
% 2.58/2.54 [1728]~P51(x17281)+~P72(f95(f31(x17281,f95(f95(f24(x17281),x17282),x17283)),f4(x17281)))+P72(f95(f31(x17281,x17282),f4(x17281)))+P72(f95(f31(x17281,f4(x17281)),x17282))
% 2.58/2.54 [1744]~P51(x17441)+~P72(f95(f31(x17441,f95(f95(f24(x17441),x17442),x17443)),f4(x17441)))+P72(f95(f31(x17441,f4(x17441)),x17442))+P72(f95(f31(x17441,f4(x17441)),x17443))
% 2.58/2.54 [1757]P73(x17572,x17571,x17573)+E(x17571,f4(a92))+P72(f95(f31(a92,f112(x17573,x17571,x17572)),f4(a92)))+P72(f95(f32(a92,f113(x17573,x17571,x17572)),x17571))
% 2.58/2.54 [1759]~P72(f95(f31(a92,x17592),x17593))+P72(f95(f31(a92,f20(a92,x17591,x17592)),f20(a92,x17591,x17593)))+~P72(f95(f32(a92,x17591),f4(a92)))+~P72(f95(f32(a92,f4(a92)),x17592))
% 2.58/2.54 [1761]~P72(f95(f31(a92,x17613),x17612))+P72(f95(f31(a92,f20(a92,x17611,x17612)),f20(a92,x17611,x17613)))+~P72(f95(f31(a92,f4(a92)),x17611))+~P72(f95(f32(a92,f4(a92)),x17613))
% 2.58/2.54 [1767]P73(x17671,x17672,x17673)+~P72(f95(x17671,f4(a92)))+P72(f95(f31(a92,f112(x17673,x17672,x17671)),f4(a92)))+P72(f95(f32(a92,f113(x17673,x17672,x17671)),x17672))
% 2.58/2.54 [1817]P73(x18173,x18171,x18172)+E(x18171,f4(a92))+E(f95(f95(f25(a92),f95(f95(f24(a92),x18171),f119(x18172,x18171,x18173))),f112(x18172,x18171,x18173)),x18172)+P72(f95(f32(a92,f113(x18172,x18171,x18173)),x18171))
% 2.58/2.54 [1835]P73(x18353,x18351,x18352)+E(f95(f95(f25(a92),f95(f95(f24(a92),x18351),f119(x18352,x18351,x18353))),f112(x18352,x18351,x18353)),x18352)+~P72(f95(x18353,f4(a92)))+P72(f95(f32(a92,f113(x18352,x18351,x18353)),x18351))
% 2.58/2.54 [1865]~P57(x18651)+~P72(f95(f32(x18651,x18652),f5(x18651)))+P72(f95(f32(x18651,f95(f95(f33(x18651),x18652),f95(f95(f25(a91),x18653),f5(a91)))),f5(x18651)))+~P72(f95(f32(x18651,f4(x18651)),x18652))
% 2.58/2.54 [1916]P72(f95(f31(a92,x19161),f4(a92)))+~P72(f95(f32(a92,f95(f95(f25(a92),f95(f95(f24(a92),x19163),x19161)),x19162)),f4(a92)))+~P72(f95(f31(a92,f4(a92)),x19162))+~P72(f95(f32(a92,f4(a92)),x19163))
% 2.58/2.54 [1261]~P51(x12611)+~E(x12613,f4(x12611))+~E(x12612,f4(x12611))+E(f95(f95(f25(x12611),f95(f95(f24(x12611),x12612),x12612)),f95(f95(f24(x12611),x12613),x12613)),f4(x12611))
% 2.58/2.54 [1443]~P63(x14431)+~P72(f95(f31(x14431,x14432),f4(x14431)))+~P72(f95(f31(x14431,x14433),f4(x14431)))+E(f95(f95(f24(x14431),f19(x14431,x14432)),f19(x14431,x14433)),f19(x14431,f95(f95(f24(x14431),x14432),x14433)))
% 2.58/2.54 [1449]~E(f95(f95(f25(a92),x14492),f95(f95(f24(a92),x14493),x14491)),x14493)+~P72(f95(f32(a92,x14492),x14493))+~P72(f95(f32(a92,f4(a92)),x14493))+P72(f95(f31(a92,f5(a92)),x14491))
% 2.58/2.54 [1452]~P63(x14521)+~P72(f95(f31(x14521,x14522),f4(x14521)))+E(f95(f95(f24(x14521),f19(x14521,x14522)),f19(x14521,x14523)),f19(x14521,f95(f95(f24(x14521),x14522),x14523)))+~P72(f95(f31(x14521,f4(x14521)),x14523))
% 2.58/2.54 [1453]~P63(x14531)+~P72(f95(f31(x14531,x14533),f4(x14531)))+E(f95(f95(f24(x14531),f19(x14531,x14532)),f19(x14531,x14533)),f19(x14531,f95(f95(f24(x14531),x14532),x14533)))+~P72(f95(f31(x14531,f4(x14531)),x14532))
% 2.58/2.54 [1458]~E(f95(f95(f25(a92),x14582),f95(f95(f24(a92),x14583),x14581)),x14583)+P72(f95(f31(a92,x14581),f5(a92)))+~P72(f95(f31(a92,f4(a92)),x14582))+~P72(f95(f32(a92,f4(a92)),x14583))
% 2.58/2.54 [1470]~P63(x14701)+E(f95(f95(f24(x14701),f19(x14701,x14702)),f19(x14701,x14703)),f19(x14701,f95(f95(f24(x14701),x14702),x14703)))+~P72(f95(f31(x14701,f4(x14701)),x14702))+~P72(f95(f31(x14701,f4(x14701)),x14703))
% 2.58/2.54 [1482]~P51(x14821)+~P72(f95(f31(x14821,x14823),f4(x14821)))+~P72(f95(f31(x14821,x14822),f4(x14821)))+P72(f95(f31(x14821,f4(x14821)),f95(f95(f24(x14821),x14822),x14823)))
% 2.58/2.54 [1484]~P60(x14841)+~P72(f95(f31(x14841,x14843),f4(x14841)))+~P72(f95(f31(x14841,x14842),f4(x14841)))+P72(f95(f31(x14841,f4(x14841)),f95(f95(f24(x14841),x14842),x14843)))
% 2.58/2.54 [1485]~P51(x14851)+~P72(f95(f32(x14851,x14853),f4(x14851)))+~P72(f95(f32(x14851,x14852),f4(x14851)))+P72(f95(f32(x14851,f4(x14851)),f95(f95(f24(x14851),x14852),x14853)))
% 2.58/2.54 [1497]~P57(x14971)+~P72(f95(f32(a91,f4(a91)),x14973))+~P72(f95(f32(x14971,f5(x14971)),x14972))+P72(f95(f32(x14971,f5(x14971)),f95(f95(f33(x14971),x14972),x14973)))
% 2.58/2.54 [1511]~P51(x15111)+~P72(f95(f31(x15111,f4(x15111)),x15113))+~P72(f95(f31(x15111,f4(x15111)),x15112))+P72(f95(f31(x15111,f4(x15111)),f95(f95(f24(x15111),x15112),x15113)))
% 2.58/2.54 [1512]~P52(x15121)+~P72(f95(f31(x15121,f4(x15121)),x15123))+~P72(f95(f31(x15121,f4(x15121)),x15122))+P72(f95(f31(x15121,f4(x15121)),f95(f95(f24(x15121),x15122),x15123)))
% 2.58/2.54 [1513]~P60(x15131)+~P72(f95(f31(x15131,f4(x15131)),x15133))+~P72(f95(f31(x15131,f4(x15131)),x15132))+P72(f95(f31(x15131,f4(x15131)),f95(f95(f24(x15131),x15132),x15133)))
% 2.58/2.54 [1515]~P55(x15151)+~P72(f95(f32(x15151,f4(x15151)),x15153))+~P72(f95(f32(x15151,f4(x15151)),x15152))+P72(f95(f32(x15151,f4(x15151)),f95(f95(f24(x15151),x15152),x15153)))
% 2.58/2.54 [1518]~P32(x15181)+~P72(f95(f32(x15181,f4(x15181)),x15183))+~P72(f95(f32(x15181,f4(x15181)),x15182))+P72(f95(f32(x15181,f4(x15181)),f95(f95(f25(x15181),x15182),x15183)))
% 2.58/2.54 [1519]~P57(x15191)+~P72(f95(f32(x15191,f5(x15191)),x15193))+~P72(f95(f32(x15191,f5(x15191)),x15192))+P72(f95(f32(x15191,f5(x15191)),f95(f95(f24(x15191),x15192),x15193)))
% 2.58/2.54 [1539]~P51(x15391)+P72(f95(f31(x15391,x15392),f4(x15391)))+P72(f95(f31(x15391,f4(x15391)),x15393))+~P72(f95(f31(x15391,f4(x15391)),f95(f95(f24(x15391),x15393),x15392)))
% 2.58/2.54 [1540]~P51(x15401)+P72(f95(f31(x15401,x15402),f4(x15401)))+P72(f95(f31(x15401,f4(x15401)),x15403))+~P72(f95(f31(x15401,f4(x15401)),f95(f95(f24(x15401),x15402),x15403)))
% 2.58/2.54 [1541]~P51(x15411)+P72(f95(f31(x15411,x15412),f4(x15411)))+P72(f95(f31(x15411,f4(x15411)),x15412))+~P72(f95(f31(x15411,f4(x15411)),f95(f95(f24(x15411),x15413),x15412)))
% 2.58/2.54 [1542]~P51(x15421)+P72(f95(f31(x15421,x15422),f4(x15421)))+P72(f95(f31(x15421,f4(x15421)),x15422))+~P72(f95(f31(x15421,f4(x15421)),f95(f95(f24(x15421),x15422),x15423)))
% 2.58/2.54 [1591]~P55(x15911)+P72(f95(f32(x15911,f4(x15911)),x15912))+~P72(f95(f32(x15911,f4(x15911)),x15913))+~P72(f95(f32(x15911,f4(x15911)),f95(f95(f24(x15911),x15913),x15912)))
% 2.58/2.54 [1592]~P55(x15921)+P72(f95(f32(x15921,f4(x15921)),x15922))+~P72(f95(f32(x15921,f4(x15921)),x15923))+~P72(f95(f32(x15921,f4(x15921)),f95(f95(f24(x15921),x15922),x15923)))
% 2.58/2.54 [1872]~P57(x18721)+~P72(f95(f32(x18721,x18722),f5(x18721)))+~P72(f95(f32(x18721,f4(x18721)),x18722))+P72(f95(f32(x18721,f95(f95(f24(x18721),x18722),f95(f95(f33(x18721),x18722),x18723))),f95(f95(f33(x18721),x18722),x18723)))
% 2.58/2.54 [1862]~P57(x18621)+~P72(f95(f31(x18621,x18622),f5(x18621)))+~P72(f95(f31(x18621,f4(x18621)),x18622))+P72(f95(f31(x18621,f95(f95(f33(x18621),x18622),f95(f95(f25(a91),x18623),f5(a91)))),x18622))
% 2.58/2.54 [1877]E(x18771,f20(a91,x18772,x18773))+~P72(f95(f32(a91,f4(a91)),x18773))+~P72(f95(f32(a91,x18772),f95(f95(f24(a91),x18773),f95(f95(f25(a91),x18771),f5(a91)))))+~P72(f95(f31(a91,f95(f95(f24(a91),x18773),x18771)),x18772))
% 2.58/2.54 [1901]~P51(x19012)+~E(x19011,f4(x19012))+~E(x19013,f4(x19012))+~P72(f95(f32(x19012,f4(x19012)),f95(f95(f25(x19012),f95(f95(f24(x19012),x19013),x19013)),f95(f95(f24(x19012),x19011),x19011))))
% 2.58/2.54 [1918]~P35(x19181)+P4(x19181,x19182)+~P72(f95(f32(a90,f4(a90)),x19183))+~P72(f95(f31(a90,f37(x19181,f95(x19182,f60(x19182,x19181,x19183)))),x19183))
% 2.58/2.54 [1919]~P35(x19191)+P4(x19191,x19192)+~P72(f95(f32(a90,f4(a90)),x19193))+~P72(f95(f31(a90,f37(x19191,f95(x19192,f69(x19192,x19193,x19191)))),x19193))
% 2.58/2.54 [1880]~P72(f95(f32(a92,x18802),x18803))+~P72(f95(f32(a92,f4(a92)),x18803))+P72(f95(f31(a92,f4(a92)),x18801))+~P72(f95(f31(a92,f4(a92)),f95(f95(f25(a92),f95(f95(f24(a92),x18803),x18801)),x18802)))
% 2.58/2.54 [1223]~P34(x12231)+~P72(f95(f31(x12231,x12234),x12233))+P72(f95(f31(x12231,x12232),x12233))+~P72(f95(f31(x12231,x12232),x12234))
% 2.58/2.54 [1224]~P6(x12241)+~P72(f95(f31(x12241,x12242),x12244))+P72(f95(f31(x12241,x12242),x12243))+~P72(f95(f31(x12241,x12244),x12243))
% 2.58/2.54 [1225]~P34(x12251)+~P72(f95(f32(x12251,x12254),x12253))+P72(f95(f32(x12251,x12252),x12253))+~P72(f95(f31(x12251,x12252),x12254))
% 2.58/2.54 [1226]~P34(x12261)+~P72(f95(f32(x12261,x12262),x12264))+P72(f95(f32(x12261,x12262),x12263))+~P72(f95(f31(x12261,x12264),x12263))
% 2.58/2.54 [1227]~P34(x12271)+~P72(f95(f32(x12271,x12274),x12273))+P72(f95(f32(x12271,x12272),x12273))+~P72(f95(f32(x12271,x12272),x12274))
% 2.58/2.54 [1228]~P6(x12281)+~P72(f95(f32(x12281,x12282),x12284))+P72(f95(f32(x12281,x12282),x12283))+~P72(f95(f31(x12281,x12284),x12283))
% 2.58/2.54 [1229]~P6(x12291)+~P72(f95(f32(x12291,x12294),x12293))+P72(f95(f32(x12291,x12292),x12293))+~P72(f95(f31(x12291,x12292),x12294))
% 2.58/2.54 [1230]~P6(x12301)+~P72(f95(f32(x12301,x12302),x12304))+P72(f95(f32(x12301,x12302),x12303))+~P72(f95(f32(x12301,x12304),x12303))
% 2.58/2.54 [1262]~P34(x12621)+~P3(x12621,x12622)+P72(f95(f31(x12621,f95(x12622,x12623)),f95(x12622,x12624)))+~P72(f95(f31(a91,x12624),x12623))
% 2.58/2.54 [1263]~P34(x12631)+~P5(x12631,x12632)+P72(f95(f31(x12631,f95(x12632,x12633)),f95(x12632,x12634)))+~P72(f95(f31(a91,x12633),x12634))
% 2.58/2.54 [1219]~P57(x12193)+E(x12191,x12192)+~E(f95(f95(f33(x12193),x12194),x12191),f95(f95(f33(x12193),x12194),x12192))+~P72(f95(f32(x12193,f5(x12193)),x12194))
% 2.58/2.54 [1529]~P7(x15292)+P72(f95(f32(f123(x15291,x15292),x15294),x15293))+~P72(f95(f31(f123(x15291,x15292),x15294),x15293))+P72(f95(f31(f123(x15291,x15292),x15293),x15294))
% 2.58/2.54 [1649]~P35(x16492)+E(x16491,f4(x16492))+~P72(f95(f31(a90,x16493),f4(a90)))+~P72(f95(f31(a90,f37(x16492,x16491)),f95(f95(f24(a90),x16493),f37(x16492,x16494))))
% 2.58/2.54 [1471]~P32(x14711)+~P72(f95(f31(x14711,x14712),x14713))+~P72(f95(f31(x14711,f4(x14711)),x14714))+P72(f95(f31(x14711,x14712),f95(f95(f25(x14711),x14713),x14714)))
% 2.58/2.54 [1472]~P32(x14721)+~P72(f95(f31(x14721,x14722),x14724))+~P72(f95(f31(x14721,f4(x14721)),x14723))+P72(f95(f31(x14721,x14722),f95(f95(f25(x14721),x14723),x14724)))
% 2.58/2.54 [1473]~P57(x14731)+~P72(f95(f32(x14731,x14732),x14734))+~P72(f95(f32(x14731,f4(x14731)),x14733))+P72(f95(f32(x14731,x14732),f95(f95(f25(x14731),x14733),x14734)))
% 2.58/2.54 [1474]~P32(x14741)+~P72(f95(f31(x14741,x14742),x14744))+~P72(f95(f32(x14741,f4(x14741)),x14743))+P72(f95(f32(x14741,x14742),f95(f95(f25(x14741),x14743),x14744)))
% 2.58/2.54 [1475]~P32(x14751)+~P72(f95(f32(x14751,x14752),x14754))+~P72(f95(f31(x14751,f4(x14751)),x14753))+P72(f95(f32(x14751,x14752),f95(f95(f25(x14751),x14753),x14754)))
% 2.58/2.54 [1706]~P51(x17061)+~P72(f95(f31(x17061,x17064),x17063))+~P72(f95(f32(x17061,x17062),f4(x17061)))+P72(f95(f31(x17061,f95(f95(f24(x17061),x17062),x17063)),f95(f95(f24(x17061),x17062),x17064)))
% 2.58/2.54 [1707]~P60(x17071)+~P72(f95(f31(x17071,x17074),x17073))+~P72(f95(f31(x17071,x17072),f4(x17071)))+P72(f95(f31(x17071,f95(f95(f24(x17071),x17072),x17073)),f95(f95(f24(x17071),x17072),x17074)))
% 2.58/2.54 [1708]~P60(x17081)+~P72(f95(f31(x17081,x17084),x17082))+~P72(f95(f31(x17081,x17083),f4(x17081)))+P72(f95(f31(x17081,f95(f95(f24(x17081),x17082),x17083)),f95(f95(f24(x17081),x17084),x17083)))
% 2.58/2.54 [1712]~P51(x17121)+~P72(f95(f32(x17121,x17124),x17122))+~P72(f95(f32(x17121,x17123),f4(x17121)))+P72(f95(f32(x17121,f95(f95(f24(x17121),x17122),x17123)),f95(f95(f24(x17121),x17124),x17123)))
% 2.58/2.54 [1713]~P51(x17131)+~P72(f95(f32(x17131,x17134),x17133))+~P72(f95(f32(x17131,x17132),f4(x17131)))+P72(f95(f32(x17131,f95(f95(f24(x17131),x17132),x17133)),f95(f95(f24(x17131),x17132),x17134)))
% 2.58/2.54 [1718]~P57(x17181)+~P72(f95(f31(a91,x17183),x17184))+~P72(f95(f32(x17181,f5(x17181)),x17182))+P72(f95(f31(x17181,f95(f95(f33(x17181),x17182),x17183)),f95(f95(f33(x17181),x17182),x17184)))
% 2.58/2.54 [1719]~P57(x17191)+~P72(f95(f31(a91,x17193),x17194))+~P72(f95(f31(x17191,f5(x17191)),x17192))+P72(f95(f31(x17191,f95(f95(f33(x17191),x17192),x17193)),f95(f95(f33(x17191),x17192),x17194)))
% 2.58/2.54 [1721]~P57(x17211)+~P72(f95(f32(a91,x17213),x17214))+~P72(f95(f32(x17211,f5(x17211)),x17212))+P72(f95(f32(x17211,f95(f95(f33(x17211),x17212),x17213)),f95(f95(f33(x17211),x17212),x17214)))
% 2.58/2.54 [1729]~P51(x17291)+~P72(f95(f31(x17291,x17293),x17294))+~P72(f95(f32(x17291,f4(x17291)),x17292))+P72(f95(f31(x17291,f95(f95(f24(x17291),x17292),x17293)),f95(f95(f24(x17291),x17292),x17294)))
% 2.58/2.54 [1730]~P62(x17301)+~P72(f95(f31(x17301,x17303),x17304))+~P72(f95(f31(x17301,f4(x17301)),x17302))+P72(f95(f31(x17301,f95(f95(f24(x17301),x17302),x17303)),f95(f95(f24(x17301),x17302),x17304)))
% 2.58/2.54 [1731]~P61(x17311)+~P72(f95(f31(x17311,x17313),x17314))+~P72(f95(f31(x17311,f4(x17311)),x17312))+P72(f95(f31(x17311,f95(f95(f24(x17311),x17312),x17313)),f95(f95(f24(x17311),x17312),x17314)))
% 2.58/2.54 [1732]~P62(x17321)+~P72(f95(f31(x17321,x17322),x17324))+~P72(f95(f31(x17321,f4(x17321)),x17323))+P72(f95(f31(x17321,f95(f95(f24(x17321),x17322),x17323)),f95(f95(f24(x17321),x17324),x17323)))
% 2.58/2.54 [1733]~P57(x17331)+~P72(f95(f31(x17331,x17332),x17334))+~P72(f95(f31(x17331,f4(x17331)),x17332))+P72(f95(f31(x17331,f95(f95(f33(x17331),x17332),x17333)),f95(f95(f33(x17331),x17334),x17333)))
% 2.58/2.54 [1735]~P55(x17351)+~P72(f95(f32(x17351,x17353),x17354))+~P72(f95(f32(x17351,f4(x17351)),x17352))+P72(f95(f32(x17351,f95(f95(f24(x17351),x17352),x17353)),f95(f95(f24(x17351),x17352),x17354)))
% 2.58/2.54 [1736]~P48(x17361)+~P72(f95(f32(x17361,x17363),x17364))+~P72(f95(f32(x17361,f4(x17361)),x17362))+P72(f95(f32(x17361,f95(f95(f24(x17361),x17362),x17363)),f95(f95(f24(x17361),x17362),x17364)))
% 2.58/2.54 [1737]~P51(x17371)+~P72(f95(f32(x17371,x17372),x17374))+~P72(f95(f32(x17371,f4(x17371)),x17373))+P72(f95(f32(x17371,f95(f95(f24(x17371),x17372),x17373)),f95(f95(f24(x17371),x17374),x17373)))
% 2.58/2.54 [1738]~P55(x17381)+~P72(f95(f32(x17381,x17382),x17384))+~P72(f95(f32(x17381,f4(x17381)),x17383))+P72(f95(f32(x17381,f95(f95(f24(x17381),x17382),x17383)),f95(f95(f24(x17381),x17384),x17383)))
% 2.58/2.54 [1739]~P51(x17391)+~P72(f95(f32(x17391,x17393),x17394))+~P72(f95(f32(x17391,f4(x17391)),x17392))+P72(f95(f32(x17391,f95(f95(f24(x17391),x17392),x17393)),f95(f95(f24(x17391),x17392),x17394)))
% 2.58/2.54 [1801]~P51(x18011)+P72(f95(f32(x18011,x18013),x18012))+P72(f95(f32(x18011,x18012),x18013))+~P72(f95(f32(x18011,f95(f95(f24(x18011),x18014),x18012)),f95(f95(f24(x18011),x18014),x18013)))
% 2.58/2.54 [1802]~P51(x18021)+P72(f95(f32(x18021,x18023),x18022))+P72(f95(f32(x18021,x18022),x18023))+~P72(f95(f32(x18021,f95(f95(f24(x18021),x18022),x18024)),f95(f95(f24(x18021),x18023),x18024)))
% 2.58/2.54 [1803]~P51(x18031)+P72(f95(f32(x18031,x18032),x18033))+P72(f95(f32(x18031,x18034),f4(x18031)))+~P72(f95(f32(x18031,f95(f95(f24(x18031),x18032),x18034)),f95(f95(f24(x18031),x18033),x18034)))
% 2.58/2.54 [1804]~P51(x18041)+P72(f95(f32(x18041,x18042),x18043))+P72(f95(f32(x18041,x18044),f4(x18041)))+~P72(f95(f32(x18041,f95(f95(f24(x18041),x18044),x18042)),f95(f95(f24(x18041),x18044),x18043)))
% 2.58/2.54 [1807]~P51(x18071)+P72(f95(f32(x18071,x18072),x18073))+P72(f95(f32(x18071,f4(x18071)),x18074))+~P72(f95(f32(x18071,f95(f95(f24(x18071),x18074),x18073)),f95(f95(f24(x18071),x18074),x18072)))
% 2.58/2.54 [1808]~P51(x18081)+P72(f95(f32(x18081,x18082),x18083))+P72(f95(f32(x18081,f4(x18081)),x18084))+~P72(f95(f32(x18081,f95(f95(f24(x18081),x18083),x18084)),f95(f95(f24(x18081),x18082),x18084)))
% 2.58/2.54 [1815]~P51(x18151)+P72(f95(f32(x18151,x18152),f4(x18151)))+P72(f95(f32(x18151,f4(x18151)),x18152))+~P72(f95(f32(x18151,f95(f95(f24(x18151),x18153),x18152)),f95(f95(f24(x18151),x18154),x18152)))
% 2.58/2.54 [1816]~P51(x18161)+P72(f95(f32(x18161,x18162),f4(x18161)))+P72(f95(f32(x18161,f4(x18161)),x18162))+~P72(f95(f32(x18161,f95(f95(f24(x18161),x18162),x18163)),f95(f95(f24(x18161),x18162),x18164)))
% 2.58/2.54 [1819]~P51(x18191)+P72(f95(f31(x18191,x18192),x18193))+~P72(f95(f32(x18191,x18194),f4(x18191)))+~P72(f95(f31(x18191,f95(f95(f24(x18191),x18194),x18193)),f95(f95(f24(x18191),x18194),x18192)))
% 2.58/2.54 [1820]~P51(x18201)+P72(f95(f32(x18201,x18202),x18203))+~P72(f95(f32(x18201,x18204),f4(x18201)))+~P72(f95(f32(x18201,f95(f95(f24(x18201),x18204),x18203)),f95(f95(f24(x18201),x18204),x18202)))
% 2.58/2.54 [1822]~P57(x18223)+P72(f95(f31(a91,x18221),x18222))+~P72(f95(f32(x18223,f5(x18223)),x18224))+~P72(f95(f31(x18223,f95(f95(f33(x18223),x18224),x18221)),f95(f95(f33(x18223),x18224),x18222)))
% 2.58/2.54 [1824]~P57(x18243)+P72(f95(f32(a91,x18241),x18242))+~P72(f95(f32(x18243,f5(x18243)),x18244))+~P72(f95(f32(x18243,f95(f95(f33(x18243),x18244),x18241)),f95(f95(f33(x18243),x18244),x18242)))
% 2.58/2.54 [1825]~P51(x18251)+P72(f95(f31(x18251,x18252),x18253))+~P72(f95(f32(x18251,f4(x18251)),x18254))+~P72(f95(f31(x18251,f95(f95(f24(x18251),x18254),x18252)),f95(f95(f24(x18251),x18254),x18253)))
% 2.58/2.54 [1826]~P55(x18261)+P72(f95(f31(x18261,x18262),x18263))+~P72(f95(f32(x18261,f4(x18261)),x18264))+~P72(f95(f31(x18261,f95(f95(f24(x18261),x18264),x18262)),f95(f95(f24(x18261),x18264),x18263)))
% 2.58/2.54 [1827]~P55(x18271)+P72(f95(f31(x18271,x18272),x18273))+~P72(f95(f32(x18271,f4(x18271)),x18274))+~P72(f95(f31(x18271,f95(f95(f24(x18271),x18272),x18274)),f95(f95(f24(x18271),x18273),x18274)))
% 2.58/2.54 [1828]~P51(x18281)+P72(f95(f32(x18281,x18282),x18283))+~P72(f95(f32(x18281,f4(x18281)),x18284))+~P72(f95(f32(x18281,f95(f95(f24(x18281),x18284),x18282)),f95(f95(f24(x18281),x18284),x18283)))
% 2.58/2.54 [1829]~P55(x18291)+P72(f95(f32(x18291,x18292),x18293))+~P72(f95(f31(x18291,f4(x18291)),x18294))+~P72(f95(f32(x18291,f95(f95(f24(x18291),x18294),x18292)),f95(f95(f24(x18291),x18294),x18293)))
% 2.58/2.54 [1830]~P56(x18301)+P72(f95(f32(x18301,x18302),x18303))+~P72(f95(f31(x18301,f4(x18301)),x18304))+~P72(f95(f32(x18301,f95(f95(f24(x18301),x18304),x18302)),f95(f95(f24(x18301),x18304),x18303)))
% 2.58/2.54 [1831]~P55(x18311)+P72(f95(f32(x18311,x18312),x18313))+~P72(f95(f31(x18311,f4(x18311)),x18314))+~P72(f95(f32(x18311,f95(f95(f24(x18311),x18312),x18314)),f95(f95(f24(x18311),x18313),x18314)))
% 2.58/2.54 [1832]~P56(x18321)+P72(f95(f32(x18321,x18322),x18323))+~P72(f95(f31(x18321,f4(x18321)),x18324))+~P72(f95(f32(x18321,f95(f95(f24(x18321),x18322),x18324)),f95(f95(f24(x18321),x18323),x18324)))
% 2.58/2.54 [1833]~P57(x18331)+P72(f95(f32(x18331,x18332),x18333))+~P72(f95(f31(x18331,f4(x18331)),x18333))+~P72(f95(f32(x18331,f95(f95(f33(x18331),x18332),x18334)),f95(f95(f33(x18331),x18333),x18334)))
% 2.58/2.54 [1867]~P34(x18671)+~P2(x18671,x18672)+P72(f95(f31(x18671,f95(x18672,f95(f95(f25(a91),x18674),f5(a91)))),f95(x18672,x18674)))+P72(f95(f31(x18671,f95(x18672,x18673)),f95(x18672,f95(f95(f25(a91),x18673),f5(a91)))))
% 2.58/2.54 [1898]~P47(x18981)+~P72(f95(f32(x18981,f23(x18981,x18983,x18984)),x18982))+~P72(f95(f32(x18981,x18982),f95(f95(f25(x18981),x18983),x18984)))+P72(f95(f32(x18981,f19(x18981,f23(x18981,x18982,x18983))),x18984))
% 2.58/2.54 [1910]~P57(x19101)+P72(f95(f31(x19101,x19102),x19103))+~P72(f95(f31(x19101,f4(x19101)),x19103))+~P72(f95(f31(x19101,f95(f95(f33(x19101),x19102),f95(f95(f25(a91),x19104),f5(a91)))),f95(f95(f33(x19101),x19103),f95(f95(f25(a91),x19104),f5(a91)))))
% 2.58/2.54 [1888]~P72(f95(x18881,x18884))+P72(f95(x18881,f20(a91,x18882,x18883)))+~P72(f95(f32(a91,x18882),f95(f95(f24(a91),x18883),f95(f95(f25(a91),x18884),f5(a91)))))+~P72(f95(f31(a91,f95(f95(f24(a91),x18883),x18884)),x18882))
% 2.58/2.54 [1939]~P35(x19391)+~P72(f95(f32(a90,f4(a90)),x19394))+P72(f95(f31(a90,f37(x19391,f95(x19392,x19393))),f36(a91,f95(f95(f25(a91),f70(x19392,x19391)),f5(a91)))))+~P72(f95(f31(a90,f37(x19391,f95(x19392,f71(x19392,x19391,x19394)))),x19394))
% 2.58/2.54 [1940]~P35(x19401)+~P72(f95(f32(a90,f4(a90)),x19404))+P72(f95(f32(a90,f37(x19401,f95(x19402,x19403))),f36(a91,f95(f95(f25(a91),f77(x19402,x19401)),f5(a91)))))+~P72(f95(f31(a90,f37(x19401,f95(x19402,f78(x19402,x19401,x19404)))),x19404))
% 2.58/2.54 [1032]~P12(x10325)+E(x10321,x10322)+~E(x10323,x10324)+~E(f23(x10325,x10323,x10324),f23(x10325,x10321,x10322))
% 2.58/2.54 [1275]~P29(x12751)+~E(f23(x12751,x12754,x12755),f23(x12751,x12752,x12753))+~P72(f95(f31(x12751,x12754),x12755))+P72(f95(f31(x12751,x12752),x12753))
% 2.58/2.54 [1277]~P29(x12771)+~E(f23(x12771,x12774,x12775),f23(x12771,x12772,x12773))+~P72(f95(f32(x12771,x12774),x12775))+P72(f95(f32(x12771,x12772),x12773))
% 2.58/2.54 [1699]~P28(x16991)+~P72(f95(f31(x16991,x16993),x16995))+~P72(f95(f31(x16991,x16992),x16994))+P72(f95(f31(x16991,f95(f95(f25(x16991),x16992),x16993)),f95(f95(f25(x16991),x16994),x16995)))
% 2.58/2.54 [1700]~P31(x17001)+~P72(f95(f31(x17001,x17003),x17005))+~P72(f95(f32(x17001,x17002),x17004))+P72(f95(f32(x17001,f95(f95(f25(x17001),x17002),x17003)),f95(f95(f25(x17001),x17004),x17005)))
% 2.58/2.54 [1701]~P31(x17011)+~P72(f95(f31(x17011,x17012),x17014))+~P72(f95(f32(x17011,x17013),x17015))+P72(f95(f32(x17011,f95(f95(f25(x17011),x17012),x17013)),f95(f95(f25(x17011),x17014),x17015)))
% 2.58/2.54 [1702]~P31(x17021)+~P72(f95(f32(x17021,x17023),x17025))+~P72(f95(f32(x17021,x17022),x17024))+P72(f95(f32(x17021,f95(f95(f25(x17021),x17022),x17023)),f95(f95(f25(x17021),x17024),x17025)))
% 2.58/2.54 [1772]~P71(x17725)+E(x17721,x17722)+E(x17723,x17724)+~E(f95(f95(f25(x17725),f95(f95(f24(x17725),x17723),x17721)),f95(f95(f24(x17725),x17724),x17722)),f95(f95(f25(x17725),f95(f95(f24(x17725),x17723),x17722)),f95(f95(f24(x17725),x17724),x17721)))
% 2.58/2.54 [1870]~P37(x18701)+~P72(f95(f32(a90,f37(x18701,x18703)),x18705))+~P72(f95(f32(a90,f37(x18701,x18702)),x18704))+P72(f95(f32(a90,f37(x18701,f95(f95(f24(x18701),x18702),x18703))),f95(f95(f24(a90),x18704),x18705)))
% 2.58/2.54 [1871]~P35(x18711)+~P72(f95(f32(a90,f37(x18711,x18713)),x18715))+~P72(f95(f32(a90,f37(x18711,x18712)),x18714))+P72(f95(f32(a90,f37(x18711,f95(f95(f25(x18711),x18712),x18713))),f95(f95(f25(a90),x18714),x18715)))
% 2.58/2.54 [1881]~P47(x18811)+~P72(f95(f32(x18811,f19(x18811,x18812)),x18814))+~P72(f95(f32(x18811,f19(x18811,x18813)),x18815))+P72(f95(f32(x18811,f95(f95(f24(x18811),f19(x18811,x18812)),f19(x18811,x18813))),f95(f95(f24(x18811),x18814),x18815)))
% 2.58/2.54 [1924]~E(f37(a94,x19241),f5(a90))+P72(f95(f32(a90,f37(a94,f95(f95(f25(a94),x19241),f5(a94)))),f5(a90)))+P72(f95(f32(a90,f37(a94,f23(a94,x19241,f5(a94)))),f5(a90)))+P72(f95(f32(a90,f37(a94,f95(f95(f25(a94),x19241),a17))),f5(a90)))+P72(f95(f32(a90,f37(a94,f23(a94,x19241,a17))),f5(a90)))
% 2.58/2.54 [1333]~P32(x13332)+E(x13331,f4(x13332))+~E(f95(f95(f25(x13332),x13333),x13331),f4(x13332))+~P72(f95(f31(x13332,f4(x13332)),x13333))+~P72(f95(f31(x13332,f4(x13332)),x13331))
% 2.58/2.54 [1334]~P32(x13342)+E(x13341,f4(x13342))+~E(f95(f95(f25(x13342),x13341),x13343),f4(x13342))+~P72(f95(f31(x13342,f4(x13342)),x13343))+~P72(f95(f31(x13342,f4(x13342)),x13341))
% 2.58/2.54 [1392]E(x13921,f101(x13922,x13923))+~E(f95(f95(f33(a90),x13921),x13923),x13922)+~P72(f95(f32(a90,f4(a90)),x13922))+~P72(f95(f32(a90,f4(a90)),x13921))+~P72(f95(f32(a91,f4(a91)),x13923))
% 2.58/2.54 [1575]~P72(f95(f32(a91,x15751),x15753))+P72(f95(f31(a90,f28(x15751,x15752)),f28(x15753,x15752)))+~P72(f95(f31(a90,x15752),f5(a90)))+~P72(f95(f31(a90,f4(a90)),x15752))+~P72(f95(f32(a91,f4(a91)),x15751))
% 2.58/2.54 [1576]~P72(f95(f32(a91,x15761),x15763))+P72(f95(f32(a90,f28(x15761,x15762)),f28(x15763,x15762)))+~P72(f95(f32(a90,x15762),f5(a90)))+~P72(f95(f32(a90,f4(a90)),x15762))+~P72(f95(f32(a91,f4(a91)),x15761))
% 2.58/2.54 [1714]~P47(x17141)+~P72(f95(f31(x17141,x17142),f5(x17141)))+~P72(f95(f31(x17141,f4(x17141)),x17142))+~P72(f95(f31(x17141,f4(x17141)),x17143))+P72(f95(f31(x17141,f95(f95(f24(x17141),x17142),x17143)),x17143))
% 2.58/2.54 [1715]~P47(x17151)+~P72(f95(f31(x17151,x17153),f5(x17151)))+~P72(f95(f31(x17151,f4(x17151)),x17153))+~P72(f95(f31(x17151,f4(x17151)),x17152))+P72(f95(f31(x17151,f95(f95(f24(x17151),x17152),x17153)),x17152))
% 2.58/2.54 [1611]~P57(x16113)+E(x16111,x16112)+~E(f95(f95(f33(x16113),x16111),f95(f95(f25(a91),x16114),f5(a91))),f95(f95(f33(x16113),x16112),f95(f95(f25(a91),x16114),f5(a91))))+~P72(f95(f31(x16113,f4(x16113)),x16112))+~P72(f95(f31(x16113,f4(x16113)),x16111))
% 2.58/2.54 [1768]~P57(x17681)+~P72(f95(f31(x17681,x17682),f5(x17681)))+~P72(f95(f31(a91,x17684),x17683))+~P72(f95(f31(x17681,f4(x17681)),x17682))+P72(f95(f31(x17681,f95(f95(f33(x17681),x17682),x17683)),f95(f95(f33(x17681),x17682),x17684)))
% 2.58/2.54 [1769]~P57(x17691)+~P72(f95(f32(x17691,x17692),f5(x17691)))+~P72(f95(f32(a91,x17694),x17693))+~P72(f95(f32(x17691,f4(x17691)),x17692))+P72(f95(f32(x17691,f95(f95(f33(x17691),x17692),x17693)),f95(f95(f33(x17691),x17692),x17694)))
% 2.58/2.54 [1770]~P57(x17701)+~P72(f95(f32(x17701,x17702),x17704))+~P72(f95(f31(x17701,f4(x17701)),x17702))+~P72(f95(f32(a91,f4(a91)),x17703))+P72(f95(f32(x17701,f95(f95(f33(x17701),x17702),x17703)),f95(f95(f33(x17701),x17704),x17703)))
% 2.58/2.54 [1889]~P7(x18891)+~P35(x18894)+P72(f95(f31(x18891,x18892),f117(x18893,x18892,x18891,x18894)))+~P72(f95(f31(x18891,x18892),x18895))+P72(f95(f32(a90,f37(x18894,f95(x18893,x18895))),f95(f95(f25(a90),f5(a90)),f37(x18894,f95(x18893,x18892)))))
% 2.58/2.54 [1969]~P35(x19691)+~P7(x19695)+~P72(f95(f31(x19695,x19694),x19693))+~P72(f95(f32(a90,f37(x19691,f23(x19691,f95(x19692,x19694),f95(x19692,f117(x19692,x19694,x19695,x19691))))),f5(a90)))+P72(f95(f32(a90,f37(x19691,f95(x19692,x19693))),f95(f95(f25(a90),f5(a90)),f37(x19691,f95(x19692,x19694)))))
% 2.58/2.54 [1670]E(x16701,f4(a91))+P72(f95(x16702,x16703))+~P72(f95(x16702,f20(a91,x16704,x16701)))+~P72(f95(f32(a91,x16705),x16701))+~E(x16704,f95(f95(f25(a91),f95(f95(f24(a91),x16701),x16703)),x16705))
% 2.58/2.54 [1941]~P72(f95(f32(a92,x19413),x19415))+P72(f95(f31(a92,x19411),x19412))+~P72(f95(f32(a92,x19413),x19414))+~P72(f95(f31(a92,x19414),f4(a92)))+~P72(f95(f31(a92,f95(f95(f25(a92),f95(f95(f24(a92),x19413),x19412)),x19415)),f95(f95(f25(a92),f95(f95(f24(a92),x19413),x19411)),x19414)))
% 2.58/2.54 [1942]P72(f95(f31(a92,x19421),x19422))+~P72(f95(f32(a92,x19423),x19424))+~P72(f95(f32(a92,x19425),x19424))+~P72(f95(f31(a92,f4(a92)),x19425))+~P72(f95(f31(a92,f95(f95(f25(a92),f95(f95(f24(a92),x19424),x19421)),x19425)),f95(f95(f25(a92),f95(f95(f24(a92),x19424),x19422)),x19423)))
% 2.58/2.54 [1389]~P71(x13894)+E(x13891,x13892)+~E(x13895,x13896)+E(x13893,f4(x13894))+~E(f95(f95(f25(x13894),x13895),f95(f95(f24(x13894),x13893),x13891)),f95(f95(f25(x13894),x13896),f95(f95(f24(x13894),x13893),x13892)))
% 2.58/2.54 [931]~P53(x9312)+~P54(x9312)+~P68(x9312)+~P38(x9312)+E(x9311,f4(x9312))+~E(f95(f95(f33(x9312),x9311),x9313),f4(x9312))
% 2.58/2.54 [939]~P53(x9392)+~P54(x9392)+~P68(x9392)+~P38(x9392)+~E(x9391,f4(a91))+~E(f95(f95(f33(x9392),x9393),x9391),f4(x9392))
% 2.58/2.54 [1302]~P32(x13021)+~E(x13023,f4(x13021))+~E(x13022,f4(x13021))+E(f95(f95(f25(x13021),x13022),x13023),f4(x13021))+~P72(f95(f31(x13021,f4(x13021)),x13023))+~P72(f95(f31(x13021,f4(x13021)),x13022))
% 2.58/2.54 [1509]~P57(x15093)+E(x15091,x15092)+~E(f95(f95(f33(x15093),x15091),x15094),f95(f95(f33(x15093),x15092),x15094))+~P72(f95(f31(x15093,f4(x15093)),x15092))+~P72(f95(f31(x15093,f4(x15093)),x15091))+~P72(f95(f32(a91,f4(a91)),x15094))
% 2.58/2.54 [1574]E(f20(a92,x15742,x15741),x15743)+E(x15741,f4(a92))+~P72(f95(f32(a92,x15741),x15744))+~P72(f95(f31(a92,x15744),f4(a92)))+~E(x15742,f95(f95(f25(a92),f95(f95(f24(a92),x15741),x15743)),x15744))+P72(f95(f32(a92,f4(a92)),x15741))
% 2.58/2.54 [1612]E(f20(a92,x16122,x16121),x16123)+E(x16121,f4(a92))+~P72(f95(f32(a92,x16124),x16121))+~E(x16122,f95(f95(f25(a92),f95(f95(f24(a92),x16121),x16123)),x16124))+~P72(f95(f31(a92,f4(a92)),x16124))+~P72(f95(f32(a92,f4(a92)),x16121))
% 2.58/2.54 [1809]~P62(x18091)+~P72(f95(f31(x18091,x18093),x18095))+~P72(f95(f31(x18091,x18092),x18094))+~P72(f95(f31(x18091,f4(x18091)),x18093))+~P72(f95(f31(x18091,f4(x18091)),x18094))+P72(f95(f31(x18091,f95(f95(f24(x18091),x18092),x18093)),f95(f95(f24(x18091),x18094),x18095)))
% 2.58/2.54 [1810]~P62(x18101)+~P72(f95(f31(x18101,x18103),x18105))+~P72(f95(f31(x18101,x18102),x18104))+~P72(f95(f31(x18101,f4(x18101)),x18103))+~P72(f95(f31(x18101,f4(x18101)),x18102))+P72(f95(f31(x18101,f95(f95(f24(x18101),x18102),x18103)),f95(f95(f24(x18101),x18104),x18105)))
% 2.58/2.54 [1811]~P55(x18111)+~P72(f95(f31(x18111,x18113),x18115))+~P72(f95(f32(x18111,x18112),x18114))+~P72(f95(f31(x18111,f4(x18111)),x18112))+~P72(f95(f32(x18111,f4(x18111)),x18113))+P72(f95(f32(x18111,f95(f95(f24(x18111),x18112),x18113)),f95(f95(f24(x18111),x18114),x18115)))
% 2.58/2.54 [1812]~P55(x18121)+~P72(f95(f31(x18121,x18122),x18124))+~P72(f95(f32(x18121,x18123),x18125))+~P72(f95(f31(x18121,f4(x18121)),x18123))+~P72(f95(f32(x18121,f4(x18121)),x18122))+P72(f95(f32(x18121,f95(f95(f24(x18121),x18122),x18123)),f95(f95(f24(x18121),x18124),x18125)))
% 2.58/2.54 [1813]~P55(x18131)+~P72(f95(f32(x18131,x18133),x18135))+~P72(f95(f32(x18131,x18132),x18134))+~P72(f95(f31(x18131,f4(x18131)),x18133))+~P72(f95(f31(x18131,f4(x18131)),x18132))+P72(f95(f32(x18131,f95(f95(f24(x18131),x18132),x18133)),f95(f95(f24(x18131),x18134),x18135)))
% 2.58/2.54 [1814]~P55(x18141)+~P72(f95(f32(x18141,x18143),x18145))+~P72(f95(f32(x18141,x18142),x18144))+~P72(f95(f31(x18141,f4(x18141)),x18143))+~P72(f95(f32(x18141,f4(x18141)),x18144))+P72(f95(f32(x18141,f95(f95(f24(x18141),x18142),x18143)),f95(f95(f24(x18141),x18144),x18145)))
% 2.58/2.54 [1639]~P73(x16391,x16394,x16393)+P72(f95(x16391,x16392))+~P72(f95(f32(a92,x16394),x16395))+~P72(f95(f32(a92,x16394),f4(a92)))+~P72(f95(f31(a92,x16395),f4(a92)))+~E(x16393,f95(f95(f25(a92),f95(f95(f24(a92),x16394),x16392)),x16395))
% 2.58/2.54 [1650]~P73(x16501,x16504,x16503)+P72(f95(x16501,x16502))+~P72(f95(f32(a92,x16505),x16504))+~E(x16503,f95(f95(f25(a92),f95(f95(f24(a92),x16504),x16502)),x16505))+~P72(f95(f31(a92,f4(a92)),x16505))+~P72(f95(f32(a92,f4(a92)),x16504))
% 2.58/2.54 [1572]~P34(x15721)+~P2(x15721,x15722)+P72(f95(f31(x15721,f95(x15722,x15723)),f95(x15722,x15724)))+P72(f95(f31(x15721,f95(x15722,x15725)),f95(x15722,x15726)))+~P72(f95(f31(a91,x15724),x15723))+~P72(f95(f31(a91,x15725),x15726))
% 2.58/2.54 [909]~P53(x9092)+~P54(x9092)+~P68(x9092)+~P38(x9092)+~E(x9093,f4(x9092))+E(x9091,f4(a91))+E(f95(f95(f33(x9092),x9093),x9091),f4(x9092))
% 2.58/2.54 [1685]E(f20(a92,x16852,x16851),x16853)+E(x16851,f4(a92))+~P72(f95(f32(a92,x16854),x16851))+~P72(f95(f32(a92,x16851),x16854))+~P72(f95(f31(a92,x16854),f4(a92)))+~E(x16852,f95(f95(f25(a92),f95(f95(f24(a92),x16851),x16853)),x16854))+~P72(f95(f31(a92,f4(a92)),x16854))
% 2.58/2.54 [1930]~P72(f95(f31(a92,x19305),x19303))+~P72(f95(f32(a92,x19304),x19303))+P72(f95(f31(a92,x19301),x19302))+~P72(f95(f32(a92,f95(f95(f25(a92),f95(f95(f24(a92),x19305),x19301)),x19306)),f4(a92)))+~E(f95(f95(f25(a92),f95(f95(f24(a92),x19303),x19302)),x19304),f95(f95(f25(a92),f95(f95(f24(a92),x19305),x19301)),x19306))+~P72(f95(f31(a92,f4(a92)),x19306))+~P72(f95(f32(a92,f4(a92)),x19305))
% 2.58/2.54 [1905]~P72(f95(f31(a92,x19055),x19053))+~P72(f95(f32(a92,x19056),x19055))+P72(f95(f31(a92,x19051),x19052))+~E(f95(f95(f25(a92),f95(f95(f24(a92),x19053),x19051)),x19054),f95(f95(f25(a92),f95(f95(f24(a92),x19055),x19052)),x19056))+~P72(f95(f31(a92,f4(a92)),x19054))+~P72(f95(f32(a92,f4(a92)),x19055))+~P72(f95(f31(a92,f4(a92)),f95(f95(f25(a92),f95(f95(f24(a92),x19055),x19052)),x19056)))
% 2.58/2.54 [1920]~P58(x19201)+~E(f95(f95(f25(x19201),x19202),x19204),f5(x19201))+~P72(f95(f31(x19201,x19205),x19206))+~P72(f95(f31(x19201,x19203),x19206))+~P72(f95(f31(x19201,f4(x19201)),x19204))+~P72(f95(f31(x19201,f4(x19201)),x19202))+P72(f95(f31(x19201,f95(f95(f25(x19201),f95(f95(f24(x19201),x19202),x19203)),f95(f95(f24(x19201),x19204),x19205))),x19206))
% 2.58/2.54 [1921]~P59(x19211)+~E(f95(f95(f25(x19211),x19212),x19214),f5(x19211))+~P72(f95(f32(x19211,x19215),x19216))+~P72(f95(f32(x19211,x19213),x19216))+~P72(f95(f31(x19211,f4(x19211)),x19214))+~P72(f95(f31(x19211,f4(x19211)),x19212))+P72(f95(f32(x19211,f95(f95(f25(x19211),f95(f95(f24(x19211),x19212),x19213)),f95(f95(f24(x19211),x19214),x19215))),x19216))
% 2.58/2.54 %EqnAxiom
% 2.58/2.54 [1]E(x11,x11)
% 2.58/2.54 [2]E(x22,x21)+~E(x21,x22)
% 2.58/2.54 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 2.58/2.54 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 2.58/2.54 [5]~E(x51,x52)+E(f26(x51),f26(x52))
% 2.58/2.54 [6]~E(x61,x62)+E(f95(x61,x63),f95(x62,x63))
% 2.58/2.54 [7]~E(x71,x72)+E(f95(x73,x71),f95(x73,x72))
% 2.58/2.54 [8]~E(x81,x82)+E(f5(x81),f5(x82))
% 2.58/2.54 [9]~E(x91,x92)+E(f33(x91),f33(x92))
% 2.58/2.54 [10]~E(x101,x102)+E(f32(x101,x103),f32(x102,x103))
% 2.58/2.54 [11]~E(x111,x112)+E(f32(x113,x111),f32(x113,x112))
% 2.58/2.54 [12]~E(x121,x122)+E(f119(x121,x123,x124),f119(x122,x123,x124))
% 2.58/2.54 [13]~E(x131,x132)+E(f119(x133,x131,x134),f119(x133,x132,x134))
% 2.58/2.54 [14]~E(x141,x142)+E(f119(x143,x144,x141),f119(x143,x144,x142))
% 2.58/2.54 [15]~E(x151,x152)+E(f27(x151),f27(x152))
% 2.58/2.54 [16]~E(x161,x162)+E(f24(x161),f24(x162))
% 2.58/2.54 [17]~E(x171,x172)+E(f28(x171,x173),f28(x172,x173))
% 2.58/2.54 [18]~E(x181,x182)+E(f28(x183,x181),f28(x183,x182))
% 2.58/2.54 [19]~E(x191,x192)+E(f113(x191,x193,x194),f113(x192,x193,x194))
% 2.58/2.54 [20]~E(x201,x202)+E(f113(x203,x201,x204),f113(x203,x202,x204))
% 2.58/2.54 [21]~E(x211,x212)+E(f113(x213,x214,x211),f113(x213,x214,x212))
% 2.58/2.54 [22]~E(x221,x222)+E(f31(x221,x223),f31(x222,x223))
% 2.58/2.54 [23]~E(x231,x232)+E(f31(x233,x231),f31(x233,x232))
% 2.58/2.54 [24]~E(x241,x242)+E(f19(x241,x243),f19(x242,x243))
% 2.58/2.54 [25]~E(x251,x252)+E(f19(x253,x251),f19(x253,x252))
% 2.58/2.54 [26]~E(x261,x262)+E(f35(x261),f35(x262))
% 2.58/2.54 [27]~E(x271,x272)+E(f25(x271),f25(x272))
% 2.58/2.54 [28]~E(x281,x282)+E(f23(x281,x283,x284),f23(x282,x283,x284))
% 2.58/2.54 [29]~E(x291,x292)+E(f23(x293,x291,x294),f23(x293,x292,x294))
% 2.58/2.54 [30]~E(x301,x302)+E(f23(x303,x304,x301),f23(x303,x304,x302))
% 2.58/2.54 [31]~E(x311,x312)+E(f6(x311),f6(x312))
% 2.58/2.54 [32]~E(x321,x322)+E(f85(x321,x323),f85(x322,x323))
% 2.58/2.54 [33]~E(x331,x332)+E(f85(x333,x331),f85(x333,x332))
% 2.58/2.54 [34]~E(x341,x342)+E(f36(x341,x343),f36(x342,x343))
% 2.58/2.54 [35]~E(x351,x352)+E(f36(x353,x351),f36(x353,x352))
% 2.58/2.54 [36]~E(x361,x362)+E(f114(x361,x363,x364),f114(x362,x363,x364))
% 2.58/2.54 [37]~E(x371,x372)+E(f114(x373,x371,x374),f114(x373,x372,x374))
% 2.58/2.54 [38]~E(x381,x382)+E(f114(x383,x384,x381),f114(x383,x384,x382))
% 2.58/2.54 [39]~E(x391,x392)+E(f20(x391,x393,x394),f20(x392,x393,x394))
% 2.58/2.54 [40]~E(x401,x402)+E(f20(x403,x401,x404),f20(x403,x402,x404))
% 2.58/2.54 [41]~E(x411,x412)+E(f20(x413,x414,x411),f20(x413,x414,x412))
% 2.58/2.54 [42]~E(x421,x422)+E(f112(x421,x423,x424),f112(x422,x423,x424))
% 2.58/2.54 [43]~E(x431,x432)+E(f112(x433,x431,x434),f112(x433,x432,x434))
% 2.58/2.54 [44]~E(x441,x442)+E(f112(x443,x444,x441),f112(x443,x444,x442))
% 2.58/2.54 [45]~E(x451,x452)+E(f57(x451,x453),f57(x452,x453))
% 2.58/2.54 [46]~E(x461,x462)+E(f57(x463,x461),f57(x463,x462))
% 2.58/2.54 [47]~E(x471,x472)+E(f18(x471,x473),f18(x472,x473))
% 2.58/2.54 [48]~E(x481,x482)+E(f18(x483,x481),f18(x483,x482))
% 2.58/2.54 [49]~E(x491,x492)+E(f37(x491,x493),f37(x492,x493))
% 2.58/2.54 [50]~E(x501,x502)+E(f37(x503,x501),f37(x503,x502))
% 2.58/2.54 [51]~E(x511,x512)+E(f122(x511),f122(x512))
% 2.58/2.54 [52]~E(x521,x522)+E(f76(x521,x523,x524),f76(x522,x523,x524))
% 2.58/2.54 [53]~E(x531,x532)+E(f76(x533,x531,x534),f76(x533,x532,x534))
% 2.58/2.54 [54]~E(x541,x542)+E(f76(x543,x544,x541),f76(x543,x544,x542))
% 2.58/2.54 [55]~E(x551,x552)+E(f67(x551,x553),f67(x552,x553))
% 2.58/2.54 [56]~E(x561,x562)+E(f67(x563,x561),f67(x563,x562))
% 2.58/2.54 [57]~E(x571,x572)+E(f115(x571,x573,x574),f115(x572,x573,x574))
% 2.58/2.54 [58]~E(x581,x582)+E(f115(x583,x581,x584),f115(x583,x582,x584))
% 2.58/2.54 [59]~E(x591,x592)+E(f115(x593,x594,x591),f115(x593,x594,x592))
% 2.58/2.54 [60]~E(x601,x602)+E(f9(x601,x603,x604,x605,x606),f9(x602,x603,x604,x605,x606))
% 2.58/2.54 [61]~E(x611,x612)+E(f9(x613,x611,x614,x615,x616),f9(x613,x612,x614,x615,x616))
% 2.58/2.54 [62]~E(x621,x622)+E(f9(x623,x624,x621,x625,x626),f9(x623,x624,x622,x625,x626))
% 2.58/2.54 [63]~E(x631,x632)+E(f9(x633,x634,x635,x631,x636),f9(x633,x634,x635,x632,x636))
% 2.58/2.54 [64]~E(x641,x642)+E(f9(x643,x644,x645,x646,x641),f9(x643,x644,x645,x646,x642))
% 2.58/2.54 [65]~E(x651,x652)+E(f39(x651),f39(x652))
% 2.58/2.54 [66]~E(x661,x662)+E(f123(x661,x663),f123(x662,x663))
% 2.58/2.54 [67]~E(x671,x672)+E(f123(x673,x671),f123(x673,x672))
% 2.58/2.54 [68]~E(x681,x682)+E(f118(x681,x683,x684),f118(x682,x683,x684))
% 2.58/2.54 [69]~E(x691,x692)+E(f118(x693,x691,x694),f118(x693,x692,x694))
% 2.58/2.54 [70]~E(x701,x702)+E(f118(x703,x704,x701),f118(x703,x704,x702))
% 2.58/2.54 [71]~E(x711,x712)+E(f30(x711,x713),f30(x712,x713))
% 2.58/2.54 [72]~E(x721,x722)+E(f30(x723,x721),f30(x723,x722))
% 2.58/2.54 [73]~E(x731,x732)+E(f59(x731,x733),f59(x732,x733))
% 2.58/2.54 [74]~E(x741,x742)+E(f59(x743,x741),f59(x743,x742))
% 2.58/2.54 [75]~E(x751,x752)+E(f10(x751,x753,x754,x755,x756),f10(x752,x753,x754,x755,x756))
% 2.58/2.54 [76]~E(x761,x762)+E(f10(x763,x761,x764,x765,x766),f10(x763,x762,x764,x765,x766))
% 2.58/2.54 [77]~E(x771,x772)+E(f10(x773,x774,x771,x775,x776),f10(x773,x774,x772,x775,x776))
% 2.58/2.54 [78]~E(x781,x782)+E(f10(x783,x784,x785,x781,x786),f10(x783,x784,x785,x782,x786))
% 2.58/2.54 [79]~E(x791,x792)+E(f10(x793,x794,x795,x796,x791),f10(x793,x794,x795,x796,x792))
% 2.58/2.54 [80]~E(x801,x802)+E(f116(x801,x803,x804),f116(x802,x803,x804))
% 2.58/2.54 [81]~E(x811,x812)+E(f116(x813,x811,x814),f116(x813,x812,x814))
% 2.58/2.54 [82]~E(x821,x822)+E(f116(x823,x824,x821),f116(x823,x824,x822))
% 2.58/2.54 [83]~E(x831,x832)+E(f96(x831),f96(x832))
% 2.58/2.54 [84]~E(x841,x842)+E(f12(x841,x843),f12(x842,x843))
% 2.58/2.54 [85]~E(x851,x852)+E(f12(x853,x851),f12(x853,x852))
% 2.58/2.54 [86]~E(x861,x862)+E(f38(x861,x863,x864),f38(x862,x863,x864))
% 2.58/2.54 [87]~E(x871,x872)+E(f38(x873,x871,x874),f38(x873,x872,x874))
% 2.58/2.54 [88]~E(x881,x882)+E(f38(x883,x884,x881),f38(x883,x884,x882))
% 2.58/2.54 [89]~E(x891,x892)+E(f74(x891,x893,x894),f74(x892,x893,x894))
% 2.58/2.54 [90]~E(x901,x902)+E(f74(x903,x901,x904),f74(x903,x902,x904))
% 2.58/2.54 [91]~E(x911,x912)+E(f74(x913,x914,x911),f74(x913,x914,x912))
% 2.58/2.54 [92]~E(x921,x922)+E(f44(x921,x923),f44(x922,x923))
% 2.58/2.54 [93]~E(x931,x932)+E(f44(x933,x931),f44(x933,x932))
% 2.58/2.54 [94]~E(x941,x942)+E(f68(x941,x943,x944,x945),f68(x942,x943,x944,x945))
% 2.58/2.54 [95]~E(x951,x952)+E(f68(x953,x951,x954,x955),f68(x953,x952,x954,x955))
% 2.58/2.54 [96]~E(x961,x962)+E(f68(x963,x964,x961,x965),f68(x963,x964,x962,x965))
% 2.58/2.54 [97]~E(x971,x972)+E(f68(x973,x974,x975,x971),f68(x973,x974,x975,x972))
% 2.58/2.54 [98]~E(x981,x982)+E(f105(x981,x983),f105(x982,x983))
% 2.58/2.54 [99]~E(x991,x992)+E(f105(x993,x991),f105(x993,x992))
% 2.58/2.54 [100]~E(x1001,x1002)+E(f72(x1001,x1003),f72(x1002,x1003))
% 2.58/2.54 [101]~E(x1011,x1012)+E(f72(x1013,x1011),f72(x1013,x1012))
% 2.58/2.54 [102]~E(x1021,x1022)+E(f56(x1021),f56(x1022))
% 2.58/2.54 [103]~E(x1031,x1032)+E(f97(x1031),f97(x1032))
% 2.58/2.54 [104]~E(x1041,x1042)+E(f104(x1041,x1043),f104(x1042,x1043))
% 2.58/2.54 [105]~E(x1051,x1052)+E(f104(x1053,x1051),f104(x1053,x1052))
% 2.58/2.54 [106]~E(x1061,x1062)+E(f102(x1061,x1063),f102(x1062,x1063))
% 2.58/2.54 [107]~E(x1071,x1072)+E(f102(x1073,x1071),f102(x1073,x1072))
% 2.58/2.54 [108]~E(x1081,x1082)+E(f109(x1081,x1083,x1084),f109(x1082,x1083,x1084))
% 2.58/2.54 [109]~E(x1091,x1092)+E(f109(x1093,x1091,x1094),f109(x1093,x1092,x1094))
% 2.58/2.54 [110]~E(x1101,x1102)+E(f109(x1103,x1104,x1101),f109(x1103,x1104,x1102))
% 2.58/2.54 [111]~E(x1111,x1112)+E(f62(x1111,x1113,x1114,x1115),f62(x1112,x1113,x1114,x1115))
% 2.58/2.54 [112]~E(x1121,x1122)+E(f62(x1123,x1121,x1124,x1125),f62(x1123,x1122,x1124,x1125))
% 2.58/2.54 [113]~E(x1131,x1132)+E(f62(x1133,x1134,x1131,x1135),f62(x1133,x1134,x1132,x1135))
% 2.58/2.54 [114]~E(x1141,x1142)+E(f62(x1143,x1144,x1145,x1141),f62(x1143,x1144,x1145,x1142))
% 2.58/2.54 [115]~E(x1151,x1152)+E(f121(x1151,x1153),f121(x1152,x1153))
% 2.58/2.54 [116]~E(x1161,x1162)+E(f121(x1163,x1161),f121(x1163,x1162))
% 2.58/2.54 [117]~E(x1171,x1172)+E(f117(x1171,x1173,x1174,x1175),f117(x1172,x1173,x1174,x1175))
% 2.58/2.54 [118]~E(x1181,x1182)+E(f117(x1183,x1181,x1184,x1185),f117(x1183,x1182,x1184,x1185))
% 2.58/2.54 [119]~E(x1191,x1192)+E(f117(x1193,x1194,x1191,x1195),f117(x1193,x1194,x1192,x1195))
% 2.58/2.54 [120]~E(x1201,x1202)+E(f117(x1203,x1204,x1205,x1201),f117(x1203,x1204,x1205,x1202))
% 2.58/2.54 [121]~E(x1211,x1212)+E(f45(x1211,x1213),f45(x1212,x1213))
% 2.58/2.54 [122]~E(x1221,x1222)+E(f45(x1223,x1221),f45(x1223,x1222))
% 2.58/2.54 [123]~E(x1231,x1232)+E(f84(x1231,x1233),f84(x1232,x1233))
% 2.58/2.54 [124]~E(x1241,x1242)+E(f84(x1243,x1241),f84(x1243,x1242))
% 2.58/2.54 [125]~E(x1251,x1252)+E(f107(x1251,x1253),f107(x1252,x1253))
% 2.58/2.54 [126]~E(x1261,x1262)+E(f107(x1263,x1261),f107(x1263,x1262))
% 2.58/2.54 [127]~E(x1271,x1272)+E(f103(x1271,x1273),f103(x1272,x1273))
% 2.58/2.54 [128]~E(x1281,x1282)+E(f103(x1283,x1281),f103(x1283,x1282))
% 2.58/2.54 [129]~E(x1291,x1292)+E(f46(x1291,x1293),f46(x1292,x1293))
% 2.58/2.54 [130]~E(x1301,x1302)+E(f46(x1303,x1301),f46(x1303,x1302))
% 2.58/2.54 [131]~E(x1311,x1312)+E(f110(x1311,x1313),f110(x1312,x1313))
% 2.58/2.54 [132]~E(x1321,x1322)+E(f110(x1323,x1321),f110(x1323,x1322))
% 2.58/2.54 [133]~E(x1331,x1332)+E(f16(x1331,x1333,x1334),f16(x1332,x1333,x1334))
% 2.58/2.54 [134]~E(x1341,x1342)+E(f16(x1343,x1341,x1344),f16(x1343,x1342,x1344))
% 2.58/2.54 [135]~E(x1351,x1352)+E(f16(x1353,x1354,x1351),f16(x1353,x1354,x1352))
% 2.58/2.54 [136]~E(x1361,x1362)+E(f22(x1361,x1363),f22(x1362,x1363))
% 2.58/2.54 [137]~E(x1371,x1372)+E(f22(x1373,x1371),f22(x1373,x1372))
% 2.58/2.54 [138]~E(x1381,x1382)+E(f69(x1381,x1383,x1384),f69(x1382,x1383,x1384))
% 2.58/2.54 [139]~E(x1391,x1392)+E(f69(x1393,x1391,x1394),f69(x1393,x1392,x1394))
% 2.58/2.54 [140]~E(x1401,x1402)+E(f69(x1403,x1404,x1401),f69(x1403,x1404,x1402))
% 2.58/2.54 [141]~E(x1411,x1412)+E(f99(x1411,x1413),f99(x1412,x1413))
% 2.58/2.54 [142]~E(x1421,x1422)+E(f99(x1423,x1421),f99(x1423,x1422))
% 2.58/2.54 [143]~E(x1431,x1432)+E(f21(x1431,x1433,x1434,x1435,x1436),f21(x1432,x1433,x1434,x1435,x1436))
% 2.58/2.54 [144]~E(x1441,x1442)+E(f21(x1443,x1441,x1444,x1445,x1446),f21(x1443,x1442,x1444,x1445,x1446))
% 2.58/2.54 [145]~E(x1451,x1452)+E(f21(x1453,x1454,x1451,x1455,x1456),f21(x1453,x1454,x1452,x1455,x1456))
% 2.58/2.54 [146]~E(x1461,x1462)+E(f21(x1463,x1464,x1465,x1461,x1466),f21(x1463,x1464,x1465,x1462,x1466))
% 2.58/2.54 [147]~E(x1471,x1472)+E(f21(x1473,x1474,x1475,x1476,x1471),f21(x1473,x1474,x1475,x1476,x1472))
% 2.58/2.54 [148]~E(x1481,x1482)+E(f83(x1481),f83(x1482))
% 2.58/2.54 [149]~E(x1491,x1492)+E(f87(x1491,x1493),f87(x1492,x1493))
% 2.58/2.54 [150]~E(x1501,x1502)+E(f87(x1503,x1501),f87(x1503,x1502))
% 2.58/2.54 [151]~E(x1511,x1512)+E(f120(x1511,x1513),f120(x1512,x1513))
% 2.58/2.54 [152]~E(x1521,x1522)+E(f120(x1523,x1521),f120(x1523,x1522))
% 2.58/2.54 [153]~E(x1531,x1532)+E(f71(x1531,x1533,x1534),f71(x1532,x1533,x1534))
% 2.58/2.54 [154]~E(x1541,x1542)+E(f71(x1543,x1541,x1544),f71(x1543,x1542,x1544))
% 2.58/2.54 [155]~E(x1551,x1552)+E(f71(x1553,x1554,x1551),f71(x1553,x1554,x1552))
% 2.58/2.54 [156]~E(x1561,x1562)+E(f14(x1561),f14(x1562))
% 2.58/2.54 [157]~E(x1571,x1572)+E(f8(x1571,x1573,x1574),f8(x1572,x1573,x1574))
% 2.58/2.54 [158]~E(x1581,x1582)+E(f8(x1583,x1581,x1584),f8(x1583,x1582,x1584))
% 2.58/2.54 [159]~E(x1591,x1592)+E(f8(x1593,x1594,x1591),f8(x1593,x1594,x1592))
% 2.58/2.54 [160]~E(x1601,x1602)+E(f40(x1601,x1603),f40(x1602,x1603))
% 2.58/2.54 [161]~E(x1611,x1612)+E(f40(x1613,x1611),f40(x1613,x1612))
% 2.58/2.54 [162]~E(x1621,x1622)+E(f48(x1621,x1623),f48(x1622,x1623))
% 2.58/2.54 [163]~E(x1631,x1632)+E(f48(x1633,x1631),f48(x1633,x1632))
% 2.58/2.54 [164]~E(x1641,x1642)+E(f13(x1641),f13(x1642))
% 2.58/2.54 [165]~E(x1651,x1652)+E(f101(x1651,x1653),f101(x1652,x1653))
% 2.58/2.54 [166]~E(x1661,x1662)+E(f101(x1663,x1661),f101(x1663,x1662))
% 2.58/2.54 [167]~E(x1671,x1672)+E(f41(x1671,x1673),f41(x1672,x1673))
% 2.58/2.54 [168]~E(x1681,x1682)+E(f41(x1683,x1681),f41(x1683,x1682))
% 2.58/2.54 [169]~E(x1691,x1692)+E(f29(x1691,x1693),f29(x1692,x1693))
% 2.58/2.54 [170]~E(x1701,x1702)+E(f29(x1703,x1701),f29(x1703,x1702))
% 2.58/2.54 [171]~E(x1711,x1712)+E(f88(x1711,x1713,x1714),f88(x1712,x1713,x1714))
% 2.58/2.54 [172]~E(x1721,x1722)+E(f88(x1723,x1721,x1724),f88(x1723,x1722,x1724))
% 2.58/2.54 [173]~E(x1731,x1732)+E(f88(x1733,x1734,x1731),f88(x1733,x1734,x1732))
% 2.58/2.54 [174]~E(x1741,x1742)+E(f108(x1741,x1743,x1744),f108(x1742,x1743,x1744))
% 2.58/2.55 [175]~E(x1751,x1752)+E(f108(x1753,x1751,x1754),f108(x1753,x1752,x1754))
% 2.58/2.55 [176]~E(x1761,x1762)+E(f108(x1763,x1764,x1761),f108(x1763,x1764,x1762))
% 2.58/2.55 [177]~E(x1771,x1772)+E(f51(x1771,x1773),f51(x1772,x1773))
% 2.58/2.55 [178]~E(x1781,x1782)+E(f51(x1783,x1781),f51(x1783,x1782))
% 2.58/2.55 [179]~E(x1791,x1792)+E(f52(x1791),f52(x1792))
% 2.58/2.55 [180]~E(x1801,x1802)+E(f81(x1801,x1803),f81(x1802,x1803))
% 2.58/2.55 [181]~E(x1811,x1812)+E(f81(x1813,x1811),f81(x1813,x1812))
% 2.58/2.55 [182]~E(x1821,x1822)+E(f75(x1821,x1823),f75(x1822,x1823))
% 2.58/2.55 [183]~E(x1831,x1832)+E(f75(x1833,x1831),f75(x1833,x1832))
% 2.58/2.55 [184]~E(x1841,x1842)+E(f34(x1841,x1843,x1844),f34(x1842,x1843,x1844))
% 2.58/2.55 [185]~E(x1851,x1852)+E(f34(x1853,x1851,x1854),f34(x1853,x1852,x1854))
% 2.58/2.55 [186]~E(x1861,x1862)+E(f34(x1863,x1864,x1861),f34(x1863,x1864,x1862))
% 2.58/2.55 [187]~E(x1871,x1872)+E(f70(x1871,x1873),f70(x1872,x1873))
% 2.58/2.55 [188]~E(x1881,x1882)+E(f70(x1883,x1881),f70(x1883,x1882))
% 2.58/2.55 [189]~E(x1891,x1892)+E(f49(x1891,x1893),f49(x1892,x1893))
% 2.58/2.55 [190]~E(x1901,x1902)+E(f49(x1903,x1901),f49(x1903,x1902))
% 2.58/2.55 [191]~E(x1911,x1912)+E(f89(x1911,x1913,x1914),f89(x1912,x1913,x1914))
% 2.58/2.55 [192]~E(x1921,x1922)+E(f89(x1923,x1921,x1924),f89(x1923,x1922,x1924))
% 2.58/2.55 [193]~E(x1931,x1932)+E(f89(x1933,x1934,x1931),f89(x1933,x1934,x1932))
% 2.58/2.55 [194]~E(x1941,x1942)+E(f86(x1941,x1943),f86(x1942,x1943))
% 2.58/2.55 [195]~E(x1951,x1952)+E(f86(x1953,x1951),f86(x1953,x1952))
% 2.58/2.55 [196]~E(x1961,x1962)+E(f73(x1961,x1963),f73(x1962,x1963))
% 2.58/2.55 [197]~E(x1971,x1972)+E(f73(x1973,x1971),f73(x1973,x1972))
% 2.58/2.55 [198]~E(x1981,x1982)+E(f100(x1981,x1983),f100(x1982,x1983))
% 2.58/2.55 [199]~E(x1991,x1992)+E(f100(x1993,x1991),f100(x1993,x1992))
% 2.58/2.55 [200]~E(x2001,x2002)+E(f82(x2001,x2003),f82(x2002,x2003))
% 2.58/2.55 [201]~E(x2011,x2012)+E(f82(x2013,x2011),f82(x2013,x2012))
% 2.58/2.55 [202]~E(x2021,x2022)+E(f15(x2021,x2023,x2024),f15(x2022,x2023,x2024))
% 2.58/2.55 [203]~E(x2031,x2032)+E(f15(x2033,x2031,x2034),f15(x2033,x2032,x2034))
% 2.58/2.55 [204]~E(x2041,x2042)+E(f15(x2043,x2044,x2041),f15(x2043,x2044,x2042))
% 2.58/2.55 [205]~E(x2051,x2052)+E(f66(x2051,x2053),f66(x2052,x2053))
% 2.58/2.55 [206]~E(x2061,x2062)+E(f66(x2063,x2061),f66(x2063,x2062))
% 2.58/2.55 [207]~E(x2071,x2072)+E(f43(x2071),f43(x2072))
% 2.58/2.55 [208]~E(x2081,x2082)+E(f111(x2081),f111(x2082))
% 2.58/2.55 [209]~E(x2091,x2092)+E(f98(x2091,x2093),f98(x2092,x2093))
% 2.58/2.55 [210]~E(x2101,x2102)+E(f98(x2103,x2101),f98(x2103,x2102))
% 2.58/2.55 [211]~E(x2111,x2112)+E(f58(x2111,x2113),f58(x2112,x2113))
% 2.58/2.55 [212]~E(x2121,x2122)+E(f58(x2123,x2121),f58(x2123,x2122))
% 2.58/2.55 [213]~E(x2131,x2132)+E(f50(x2131,x2133),f50(x2132,x2133))
% 2.58/2.55 [214]~E(x2141,x2142)+E(f50(x2143,x2141),f50(x2143,x2142))
% 2.58/2.55 [215]~E(x2151,x2152)+E(f60(x2151,x2153,x2154),f60(x2152,x2153,x2154))
% 2.58/2.55 [216]~E(x2161,x2162)+E(f60(x2163,x2161,x2164),f60(x2163,x2162,x2164))
% 2.58/2.55 [217]~E(x2171,x2172)+E(f60(x2173,x2174,x2171),f60(x2173,x2174,x2172))
% 2.58/2.55 [218]~E(x2181,x2182)+E(f42(x2181,x2183),f42(x2182,x2183))
% 2.58/2.55 [219]~E(x2191,x2192)+E(f42(x2193,x2191),f42(x2193,x2192))
% 2.58/2.55 [220]~E(x2201,x2202)+E(f47(x2201,x2203),f47(x2202,x2203))
% 2.58/2.55 [221]~E(x2211,x2212)+E(f47(x2213,x2211),f47(x2213,x2212))
% 2.58/2.55 [222]~E(x2221,x2222)+E(f77(x2221,x2223),f77(x2222,x2223))
% 2.58/2.55 [223]~E(x2231,x2232)+E(f77(x2233,x2231),f77(x2233,x2232))
% 2.58/2.55 [224]~E(x2241,x2242)+E(f80(x2241),f80(x2242))
% 2.58/2.55 [225]~E(x2251,x2252)+E(f78(x2251,x2253,x2254),f78(x2252,x2253,x2254))
% 2.58/2.55 [226]~E(x2261,x2262)+E(f78(x2263,x2261,x2264),f78(x2263,x2262,x2264))
% 2.58/2.55 [227]~E(x2271,x2272)+E(f78(x2273,x2274,x2271),f78(x2273,x2274,x2272))
% 2.58/2.55 [228]~E(x2281,x2282)+E(f106(x2281,x2283),f106(x2282,x2283))
% 2.58/2.55 [229]~E(x2291,x2292)+E(f106(x2293,x2291),f106(x2293,x2292))
% 2.58/2.55 [230]~P1(x2301)+P1(x2302)+~E(x2301,x2302)
% 2.58/2.55 [231]~P72(x2311)+P72(x2312)+~E(x2311,x2312)
% 2.58/2.55 [232]~P60(x2321)+P60(x2322)+~E(x2321,x2322)
% 2.58/2.55 [233]~P57(x2331)+P57(x2332)+~E(x2331,x2332)
% 2.58/2.55 [234]~P34(x2341)+P34(x2342)+~E(x2341,x2342)
% 2.58/2.55 [235]~P6(x2351)+P6(x2352)+~E(x2351,x2352)
% 2.58/2.55 [236]~P7(x2361)+P7(x2362)+~E(x2361,x2362)
% 2.58/2.55 [237]~P42(x2371)+P42(x2372)+~E(x2371,x2372)
% 2.58/2.55 [238]~P32(x2381)+P32(x2382)+~E(x2381,x2382)
% 2.58/2.55 [239]~P51(x2391)+P51(x2392)+~E(x2391,x2392)
% 2.58/2.55 [240]~P8(x2401)+P8(x2402)+~E(x2401,x2402)
% 2.58/2.55 [241]~P24(x2411)+P24(x2412)+~E(x2411,x2412)
% 2.58/2.55 [242]~P37(x2421)+P37(x2422)+~E(x2421,x2422)
% 2.58/2.55 [243]~P22(x2431)+P22(x2432)+~E(x2431,x2432)
% 2.58/2.55 [244]~P28(x2441)+P28(x2442)+~E(x2441,x2442)
% 2.58/2.55 [245]~P35(x2451)+P35(x2452)+~E(x2451,x2452)
% 2.58/2.55 [246]~P31(x2461)+P31(x2462)+~E(x2461,x2462)
% 2.58/2.55 [247]~P63(x2471)+P63(x2472)+~E(x2471,x2472)
% 2.58/2.55 [248]P73(x2482,x2483,x2484)+~E(x2481,x2482)+~P73(x2481,x2483,x2484)
% 2.58/2.55 [249]P73(x2493,x2492,x2494)+~E(x2491,x2492)+~P73(x2493,x2491,x2494)
% 2.58/2.55 [250]P73(x2503,x2504,x2502)+~E(x2501,x2502)+~P73(x2503,x2504,x2501)
% 2.58/2.55 [251]~P29(x2511)+P29(x2512)+~E(x2511,x2512)
% 2.58/2.55 [252]~P55(x2521)+P55(x2522)+~E(x2521,x2522)
% 2.58/2.55 [253]P4(x2532,x2533)+~E(x2531,x2532)+~P4(x2531,x2533)
% 2.58/2.55 [254]P4(x2543,x2542)+~E(x2541,x2542)+~P4(x2543,x2541)
% 2.58/2.55 [255]~P9(x2551)+P9(x2552)+~E(x2551,x2552)
% 2.58/2.55 [256]~P36(x2561)+P36(x2562)+~E(x2561,x2562)
% 2.58/2.55 [257]~P38(x2571)+P38(x2572)+~E(x2571,x2572)
% 2.58/2.55 [258]~P30(x2581)+P30(x2582)+~E(x2581,x2582)
% 2.58/2.55 [259]~P17(x2591)+P17(x2592)+~E(x2591,x2592)
% 2.58/2.55 [260]~P12(x2601)+P12(x2602)+~E(x2601,x2602)
% 2.58/2.55 [261]~P10(x2611)+P10(x2612)+~E(x2611,x2612)
% 2.58/2.55 [262]~P27(x2621)+P27(x2622)+~E(x2621,x2622)
% 2.58/2.55 [263]~P26(x2631)+P26(x2632)+~E(x2631,x2632)
% 2.58/2.55 [264]~P20(x2641)+P20(x2642)+~E(x2641,x2642)
% 2.58/2.55 [265]~P23(x2651)+P23(x2652)+~E(x2651,x2652)
% 2.58/2.55 [266]~P62(x2661)+P62(x2662)+~E(x2661,x2662)
% 2.58/2.55 [267]~P41(x2671)+P41(x2672)+~E(x2671,x2672)
% 2.58/2.55 [268]~P47(x2681)+P47(x2682)+~E(x2681,x2682)
% 2.58/2.55 [269]P2(x2692,x2693)+~E(x2691,x2692)+~P2(x2691,x2693)
% 2.58/2.55 [270]P2(x2703,x2702)+~E(x2701,x2702)+~P2(x2703,x2701)
% 2.58/2.55 [271]~P18(x2711)+P18(x2712)+~E(x2711,x2712)
% 2.58/2.55 [272]~P52(x2721)+P52(x2722)+~E(x2721,x2722)
% 2.58/2.55 [273]P3(x2732,x2733)+~E(x2731,x2732)+~P3(x2731,x2733)
% 2.58/2.55 [274]P3(x2743,x2742)+~E(x2741,x2742)+~P3(x2743,x2741)
% 2.58/2.55 [275]~P68(x2751)+P68(x2752)+~E(x2751,x2752)
% 2.58/2.55 [276]~P13(x2761)+P13(x2762)+~E(x2761,x2762)
% 2.58/2.55 [277]~P56(x2771)+P56(x2772)+~E(x2771,x2772)
% 2.58/2.55 [278]~P43(x2781)+P43(x2782)+~E(x2781,x2782)
% 2.58/2.55 [279]~P48(x2791)+P48(x2792)+~E(x2791,x2792)
% 2.58/2.55 [280]~P59(x2801)+P59(x2802)+~E(x2801,x2802)
% 2.58/2.55 [281]~P61(x2811)+P61(x2812)+~E(x2811,x2812)
% 2.58/2.55 [282]~P45(x2821)+P45(x2822)+~E(x2821,x2822)
% 2.58/2.55 [283]~P69(x2831)+P69(x2832)+~E(x2831,x2832)
% 2.58/2.55 [284]~P53(x2841)+P53(x2842)+~E(x2841,x2842)
% 2.58/2.55 [285]~P19(x2851)+P19(x2852)+~E(x2851,x2852)
% 2.58/2.55 [286]~P54(x2861)+P54(x2862)+~E(x2861,x2862)
% 2.58/2.55 [287]~P50(x2871)+P50(x2872)+~E(x2871,x2872)
% 2.58/2.55 [288]~P64(x2881)+P64(x2882)+~E(x2881,x2882)
% 2.58/2.55 [289]~P14(x2891)+P14(x2892)+~E(x2891,x2892)
% 2.58/2.55 [290]~P33(x2901)+P33(x2902)+~E(x2901,x2902)
% 2.58/2.55 [291]~P25(x2911)+P25(x2912)+~E(x2911,x2912)
% 2.58/2.55 [292]~P67(x2921)+P67(x2922)+~E(x2921,x2922)
% 2.58/2.55 [293]~P66(x2931)+P66(x2932)+~E(x2931,x2932)
% 2.58/2.55 [294]P5(x2942,x2943)+~E(x2941,x2942)+~P5(x2941,x2943)
% 2.58/2.55 [295]P5(x2953,x2952)+~E(x2951,x2952)+~P5(x2953,x2951)
% 2.58/2.55 [296]~P21(x2961)+P21(x2962)+~E(x2961,x2962)
% 2.58/2.55 [297]~P44(x2971)+P44(x2972)+~E(x2971,x2972)
% 2.58/2.55 [298]~P11(x2981)+P11(x2982)+~E(x2981,x2982)
% 2.58/2.55 [299]~P71(x2991)+P71(x2992)+~E(x2991,x2992)
% 2.58/2.55 [300]~P58(x3001)+P58(x3002)+~E(x3001,x3002)
% 2.58/2.55 [301]~P16(x3011)+P16(x3012)+~E(x3011,x3012)
% 2.58/2.55 [302]~P15(x3021)+P15(x3022)+~E(x3021,x3022)
% 2.58/2.55 [303]~P39(x3031)+P39(x3032)+~E(x3031,x3032)
% 2.58/2.55 [304]~P46(x3041)+P46(x3042)+~E(x3041,x3042)
% 2.58/2.55 [305]~P65(x3051)+P65(x3052)+~E(x3051,x3052)
% 2.58/2.55 [306]~P49(x3061)+P49(x3062)+~E(x3061,x3062)
% 2.58/2.55 [307]~P40(x3071)+P40(x3072)+~E(x3071,x3072)
% 2.58/2.55 [308]~P70(x3081)+P70(x3082)+~E(x3081,x3082)
% 2.58/2.55
% 2.58/2.55 %-------------------------------------------
% 2.58/2.55 cnf(1973,plain,
% 2.58/2.55 (~P72(f95(f32(a91,f95(f95(f25(a91),x19731),x19732)),x19732))),
% 2.58/2.55 inference(rename_variables,[],[734])).
% 2.58/2.55 cnf(1979,plain,
% 2.58/2.55 (~E(f95(f95(f25(a91),x19791),f5(a91)),x19791)),
% 2.58/2.55 inference(rename_variables,[],[719])).
% 2.58/2.55 cnf(1982,plain,
% 2.58/2.55 (~E(f95(f95(f25(a91),x19821),f5(a91)),x19821)),
% 2.58/2.55 inference(rename_variables,[],[719])).
% 2.58/2.55 cnf(1991,plain,
% 2.58/2.55 (~E(f95(f95(f25(a91),x19911),f5(a91)),x19911)),
% 2.58/2.55 inference(rename_variables,[],[719])).
% 2.58/2.55 cnf(1993,plain,
% 2.58/2.55 (~P72(f95(f31(a91,f95(f95(f25(a91),x19931),f5(a91))),x19931))),
% 2.58/2.55 inference(rename_variables,[],[736])).
% 2.58/2.55 cnf(1996,plain,
% 2.58/2.55 (P72(f95(f31(a91,x19961),x19961))),
% 2.58/2.55 inference(rename_variables,[],[565])).
% 2.58/2.55 cnf(1999,plain,
% 2.58/2.55 (P72(f95(f32(a91,x19991),f95(f95(f25(a91),x19991),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2004,plain,
% 2.58/2.55 (P72(f95(f32(a91,x20041),f95(f95(f25(a91),x20041),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2011,plain,
% 2.58/2.55 (~P72(f95(f32(a91,x20111),x20111))),
% 2.58/2.55 inference(rename_variables,[],[727])).
% 2.58/2.55 cnf(2019,plain,
% 2.58/2.55 (~P72(f95(f32(a91,f95(f95(f25(a91),x20191),x20192)),x20192))),
% 2.58/2.55 inference(rename_variables,[],[734])).
% 2.58/2.55 cnf(2022,plain,
% 2.58/2.55 (P72(f95(f32(a90,x20221),f95(f95(f25(a90),f36(a91,f26(x20221))),f5(a90))))),
% 2.58/2.55 inference(rename_variables,[],[669])).
% 2.58/2.55 cnf(2025,plain,
% 2.58/2.55 (P72(f95(f31(a90,x20251),x20251))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2028,plain,
% 2.58/2.55 (P72(f95(f31(a90,x20281),x20281))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2031,plain,
% 2.58/2.55 (P72(f95(f32(a91,x20311),f95(f95(f25(a91),x20311),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2034,plain,
% 2.58/2.55 (~P72(f95(f32(a91,x20341),x20341))),
% 2.58/2.55 inference(rename_variables,[],[727])).
% 2.58/2.55 cnf(2058,plain,
% 2.58/2.55 (P72(f95(f31(a90,x20581),x20581))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2061,plain,
% 2.58/2.55 (P72(f95(f32(a91,x20611),f95(f95(f25(a91),x20611),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2064,plain,
% 2.58/2.55 (P72(f95(f32(a91,x20641),f95(f95(f25(a91),x20641),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2073,plain,
% 2.58/2.55 (~P72(f95(f32(a91,x20731),x20731))),
% 2.58/2.55 inference(rename_variables,[],[727])).
% 2.58/2.55 cnf(2080,plain,
% 2.58/2.55 (P72(f95(f32(a91,x20801),f95(f95(f25(a91),x20801),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2083,plain,
% 2.58/2.55 (P72(f95(f32(a91,x20831),f95(f95(f25(a91),x20831),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2086,plain,
% 2.58/2.55 (P72(f95(f32(a91,x20861),f95(f95(f25(a91),x20861),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2091,plain,
% 2.58/2.55 (P72(f95(f31(a90,x20911),f36(a91,f27(x20911))))),
% 2.58/2.55 inference(rename_variables,[],[594])).
% 2.58/2.55 cnf(2094,plain,
% 2.58/2.55 (P72(f95(f32(a91,x20941),f95(f95(f25(a91),f95(f95(f25(a91),x20942),x20941)),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[687])).
% 2.58/2.55 cnf(2097,plain,
% 2.58/2.55 (P72(f95(f31(a91,x20971),x20971))),
% 2.58/2.55 inference(rename_variables,[],[565])).
% 2.58/2.55 cnf(2100,plain,
% 2.58/2.55 (P72(f95(f32(a90,x21001),f95(f95(f25(a90),f36(a91,f26(x21001))),f5(a90))))),
% 2.58/2.55 inference(rename_variables,[],[669])).
% 2.58/2.55 cnf(2103,plain,
% 2.58/2.55 (P72(f95(f31(a91,x21031),f95(f95(f24(a91),x21031),x21031)))),
% 2.58/2.55 inference(rename_variables,[],[613])).
% 2.58/2.55 cnf(2106,plain,
% 2.58/2.55 (P72(f95(f31(a92,x21061),x21061))),
% 2.58/2.55 inference(rename_variables,[],[566])).
% 2.58/2.55 cnf(2109,plain,
% 2.58/2.55 (P72(f95(f31(a91,x21091),f95(f95(f24(a91),x21091),x21091)))),
% 2.58/2.55 inference(rename_variables,[],[613])).
% 2.58/2.55 cnf(2112,plain,
% 2.58/2.55 (P72(f95(f32(a91,x21121),f95(f95(f25(a91),f95(f95(f25(a91),x21122),x21121)),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[687])).
% 2.58/2.55 cnf(2115,plain,
% 2.58/2.55 (P72(f95(f31(a91,x21151),f95(f95(f24(a91),x21151),x21151)))),
% 2.58/2.55 inference(rename_variables,[],[613])).
% 2.58/2.55 cnf(2121,plain,
% 2.58/2.55 (~P72(f95(f32(a91,x21211),x21211))),
% 2.58/2.55 inference(rename_variables,[],[727])).
% 2.58/2.55 cnf(2130,plain,
% 2.58/2.55 (P72(f95(f31(a92,x21301),x21301))),
% 2.58/2.55 inference(rename_variables,[],[566])).
% 2.58/2.55 cnf(2143,plain,
% 2.58/2.55 (P72(f95(f31(a90,x21431),f36(a91,f27(x21431))))),
% 2.58/2.55 inference(rename_variables,[],[594])).
% 2.58/2.55 cnf(2146,plain,
% 2.58/2.55 (~P72(f95(f32(a91,f95(f95(f25(a91),x21461),x21462)),x21462))),
% 2.58/2.55 inference(rename_variables,[],[734])).
% 2.58/2.55 cnf(2149,plain,
% 2.58/2.55 (~P72(f95(f32(a91,f95(f95(f25(a91),x21491),x21492)),x21491))),
% 2.58/2.55 inference(rename_variables,[],[735])).
% 2.58/2.55 cnf(2155,plain,
% 2.58/2.55 (~P72(f95(f31(a91,f95(f95(f25(a91),x21551),f5(a91))),x21551))),
% 2.58/2.55 inference(rename_variables,[],[736])).
% 2.58/2.55 cnf(2158,plain,
% 2.58/2.55 (~P72(f95(f31(a91,f95(f95(f25(a91),x21581),f5(a91))),x21581))),
% 2.58/2.55 inference(rename_variables,[],[736])).
% 2.58/2.55 cnf(2161,plain,
% 2.58/2.55 (P72(f95(f32(a91,x21611),f95(f95(f25(a91),x21611),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2167,plain,
% 2.58/2.55 (~P72(f95(f32(a91,f95(f95(f25(a91),x21671),x21672)),x21671))),
% 2.58/2.55 inference(rename_variables,[],[735])).
% 2.58/2.55 cnf(2203,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22031),f95(f95(f25(a91),x22031),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2208,plain,
% 2.58/2.55 (P72(f95(f31(a91,x22081),x22081))),
% 2.58/2.55 inference(rename_variables,[],[565])).
% 2.58/2.55 cnf(2211,plain,
% 2.58/2.55 (~P72(f95(f32(a91,x22111),x22111))),
% 2.58/2.55 inference(rename_variables,[],[727])).
% 2.58/2.55 cnf(2214,plain,
% 2.58/2.55 (P72(f95(f31(a90,x22141),x22141))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2217,plain,
% 2.58/2.55 (P72(f95(f31(a90,x22171),x22171))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2226,plain,
% 2.58/2.55 (E(f95(f8(x22261,x22262,x22263),x22264),x22263)),
% 2.58/2.55 inference(rename_variables,[],[587])).
% 2.58/2.55 cnf(2231,plain,
% 2.58/2.55 (E(f95(f8(x22311,x22312,x22313),x22314),x22313)),
% 2.58/2.55 inference(rename_variables,[],[587])).
% 2.58/2.55 cnf(2233,plain,
% 2.58/2.55 (~E(f95(f95(f25(a91),x22331),f5(a91)),x22331)),
% 2.58/2.55 inference(rename_variables,[],[719])).
% 2.58/2.55 cnf(2235,plain,
% 2.58/2.55 (~P72(f95(f32(a91,x22351),x22351))),
% 2.58/2.55 inference(rename_variables,[],[727])).
% 2.58/2.55 cnf(2236,plain,
% 2.58/2.55 (E(f95(f8(x22361,x22362,x22363),x22364),x22363)),
% 2.58/2.55 inference(rename_variables,[],[587])).
% 2.58/2.55 cnf(2239,plain,
% 2.58/2.55 (~E(f95(f95(f25(a91),x22391),f5(a91)),x22391)),
% 2.58/2.55 inference(rename_variables,[],[719])).
% 2.58/2.55 cnf(2250,plain,
% 2.58/2.55 (~P72(f95(f32(a91,x22501),x22501))),
% 2.58/2.55 inference(rename_variables,[],[727])).
% 2.58/2.55 cnf(2253,plain,
% 2.58/2.55 (P72(f95(f31(a90,x22531),x22531))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2256,plain,
% 2.58/2.55 (~E(f95(f95(f25(a91),x22561),f5(a91)),x22561)),
% 2.58/2.55 inference(rename_variables,[],[719])).
% 2.58/2.55 cnf(2259,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22591),f95(f95(f25(a91),x22591),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2260,plain,
% 2.58/2.55 (~E(f95(f95(f25(a91),x22601),f5(a91)),x22601)),
% 2.58/2.55 inference(rename_variables,[],[719])).
% 2.58/2.55 cnf(2263,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22631),f95(f95(f25(a91),x22631),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2266,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22661),f95(f95(f25(a91),x22661),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2269,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22691),f95(f95(f25(a91),x22691),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2274,plain,
% 2.58/2.55 (P72(f95(f31(a92,x22741),x22741))),
% 2.58/2.55 inference(rename_variables,[],[566])).
% 2.58/2.55 cnf(2277,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22771),f95(f95(f25(a91),x22771),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2278,plain,
% 2.58/2.55 (~P72(f95(f32(a91,x22781),x22781))),
% 2.58/2.55 inference(rename_variables,[],[727])).
% 2.58/2.55 cnf(2288,plain,
% 2.58/2.55 (P72(f95(f31(a90,x22881),x22881))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2291,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22911),f95(f95(f25(a91),x22911),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2295,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22951),f95(f95(f25(a91),x22951),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2298,plain,
% 2.58/2.55 (P72(f95(f32(a91,x22981),f95(f95(f25(a91),x22981),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2299,plain,
% 2.58/2.55 (P72(f95(f31(a90,x22991),x22991))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2302,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23021),f95(f95(f25(a91),x23021),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2303,plain,
% 2.58/2.55 (P72(f95(f31(a90,x23031),x23031))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2306,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23061),f95(f95(f25(a91),x23061),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2309,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23091),f95(f95(f25(a91),x23091),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2313,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23131),f95(f95(f25(a91),x23131),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2316,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23161),f95(f95(f25(a91),x23161),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2319,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23191),f95(f95(f25(a91),x23191),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2322,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23221),f95(f95(f25(a91),x23221),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2327,plain,
% 2.58/2.55 (P72(f95(f31(a90,x23271),x23271))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2328,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23281),f95(f95(f25(a91),x23281),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2331,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23311),f95(f95(f25(a91),x23311),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2334,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23341),f95(f95(f25(a91),x23341),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2348,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23481),f95(f95(f25(a91),x23481),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2351,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23511),f95(f95(f25(a91),x23511),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2354,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23541),f95(f95(f25(a91),x23541),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2357,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23571),f95(f95(f25(a91),x23571),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2360,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23601),f95(f95(f25(a91),x23601),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2374,plain,
% 2.58/2.55 (P72(f95(f31(a90,f37(a94,f95(a124,x23741))),a125))),
% 2.58/2.55 inference(rename_variables,[],[635])).
% 2.58/2.55 cnf(2377,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23771),f95(f95(f25(a91),x23771),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2380,plain,
% 2.58/2.55 (P72(f95(f31(a90,x23801),x23801))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2383,plain,
% 2.58/2.55 (P72(f95(f31(a90,x23831),x23831))),
% 2.58/2.55 inference(rename_variables,[],[564])).
% 2.58/2.55 cnf(2390,plain,
% 2.58/2.55 (P72(f95(f32(a91,x23901),f95(f95(f25(a91),x23901),f5(a91))))),
% 2.58/2.55 inference(rename_variables,[],[617])).
% 2.58/2.55 cnf(2397,plain,
% 2.58/2.55 ($false),
% 2.58/2.55 inference(scs_inference,[],[731,315,322,325,326,330,331,402,426,442,714,522,523,716,516,568,570,569,579,580,612,589,587,2226,2231,2236,564,2025,2028,2058,2214,2217,2253,2288,2299,2303,2327,2380,2383,565,1996,2097,2208,566,2106,2130,2274,727,2011,2034,2073,2121,2211,2235,2250,2278,561,730,662,663,719,1979,1982,1991,2233,2239,2256,2260,551,732,594,2091,2143,635,2374,725,613,2103,2109,2115,734,1973,2019,2146,735,2149,2167,617,1999,2004,2031,2061,2064,2080,2083,2086,2161,2203,2259,2263,2266,2269,2277,2291,2295,2298,2302,2306,2309,2313,2316,2319,2322,2328,2331,2334,2348,2351,2354,2357,2360,2377,2390,670,736,1993,2155,2158,621,737,669,2022,2100,665,687,2094,2112,2,1154,946,827,809,808,807,806,6,1863,1846,1628,1425,1292,1213,1207,1174,1162,1153,1147,1105,1104,1103,1064,993,985,961,938,937,932,885,882,1070,1338,1337,1328,1324,1217,1216,1215,1209,1203,1177,1176,1164,1163,1068,968,1844,1764,1724,1688,1637,1606,1604,1581,1580,1579,1481,1464,1434,1433,1432,1428,1383,1382,1301,1295,1294,1267,1248,1246,1244,1242,1236,1231,1220,1051,1046,1022,1021,988,976,975,1886,1350,1238,1159,1146,1092,1042,1041,1746,1704,1683,1674,1663,1364,1363,1214,1035,1923,291,250,249,248,231,3,944,991,957,956,907,905,1303,1180,1075,995,994,987,986,1054,1583,1477,1457,1456,1455,1446,1402,1401,1352,1351,1346,1344,1320,1319,1318,1317,1315,1314,1313,1312,1012,916,974,1358,1256,1252,1251,1250,1249,1033,908,824,821,1961,1675,1451,1450,1418,1379,1332,1323,1192]),
% 2.58/2.55 ['proof']).
% 2.58/2.55 % SZS output end Proof
% 2.58/2.55 % Total time :0.970000s
%------------------------------------------------------------------------------